5088:
4821:
3683:
546:
5083:{\displaystyle {\begin{aligned}&{\boldsymbol {\sigma }}_{0}^{1}={\frac {1}{\sqrt {2}}}{\begin{pmatrix}0&1\\1&0\end{pmatrix}}={\frac {1}{\sqrt {2}}}(\uparrow \downarrow +\downarrow \uparrow )\;;\\&{\boldsymbol {\sigma }}_{1}^{1}={\begin{pmatrix}1&0\\0&0\end{pmatrix}}=\;\uparrow \uparrow \;;\;\;{\boldsymbol {\sigma }}_{-1}^{1}={\begin{pmatrix}0&0\\0&1\end{pmatrix}}=\;\downarrow \downarrow \;.\end{aligned}}}
10574:
847:
5367:
3408:
1930:
12377:
449:
9335:
34:
10277:
564:
6221:
1450:
5158:
7424:
12117:
12113:
4418:
1623:
9052:
3678:{\displaystyle {\begin{aligned}&|\chi _{s=1,m=0}\rangle ={\frac {1}{\sqrt {2}}}(|\uparrow \rangle |\downarrow \rangle +|\downarrow \rangle |\uparrow \rangle )\;;\\&|\chi _{s=1,m=1}\rangle =\;|\uparrow \rangle |\uparrow \rangle \;;\;\;|\chi _{s=1,m=-1}\rangle =\;|\downarrow \rangle |\downarrow \rangle \;.\end{aligned}}}
4781:
11051:
5995:
1224:
12379:
The first integral is said to be analogous to classical potential due to
Coulomb interaction, where the squares of wavefunctions are interpreted as electron density. However, no such classical analog exists for the J term. Using Green's theorem, one can show that the J terms are always positive. From
10748:
This is closer to the experimental value, but if a better trial wave function is used, an even more accurate answer could be obtained. An ideal wave function would be one that doesn't ignore the influence of the other electron. In other words, each electron represents a cloud of negative charge which
6740:
3847:
Alternatively, a more generalized representation of the above can be provided without considering the spatial and spin parts separately. This method is useful in situations where such manipulation is not possible, however, it can be applied wherever needed. Since the spin part is tensor product of
1454:
The wavefunction belongs to the tensor product of combined spin states and combined spatial wavefunctions, and since this
Hamiltonian only acts on spatial wavefunctions, we can neglect spin states until after solving the spatial wavefunction. This is possible since, for any general vector, one has
10744:
8082:
3782:
as per symmetrization and total spin number requirement. It is observed that triplet states are symmetric and singlet states are antisymmetric. Since the total wavefunction is antisymmetric, a symmetric spatial wavefunction can only be paired with antisymmetric wavefunction and vice versa. Hence
2078:
is a general combined spatial wavefunction. This energy, however, is not degenerate with multiplicity given by the dimension of the space of combined spin states because of a symmetrization postulate, which requires that physical solutions for identical fermions should be totally antisymmetric,
7221:
8888:
5537:
6445:
3309:
11606:
10569:{\displaystyle \langle H\rangle =8E_{1}+\langle V_{ee}\rangle =8E_{1}+\left({\frac {e^{2}}{4\pi \varepsilon _{0}}}\right)\left({\frac {8}{\pi a^{3}}}\right)^{2}\int {\frac {e^{-4(r_{1}+r_{2})/a}}{|\mathbf {r} _{1}-\mathbf {r} _{2}|}}\,d^{3}\mathbf {r} _{1}\,d^{3}\mathbf {r} _{2}}
11891:
4334:
842:{\displaystyle H(\mathbf {r} _{1},\,\mathbf {r} _{2})=\sum _{i=1,2}\left(-{\frac {\hbar ^{2}}{2\mu }}\nabla _{r_{i}}^{2}-{\frac {Ze^{2}}{4\pi \varepsilon _{0}r_{i}}}\right)-{\frac {\hbar ^{2}}{M}}\nabla _{r_{1}}\cdot \nabla _{r_{2}}+{\frac {e^{2}}{4\pi \varepsilon _{0}r_{12}}}}
3783:
orthohelium (triplet state) has a symmetric spin wavefunction but an antisymmetric spatial wavefunction and parahelium (singlet state) has an antisymmetric spin wavefunction but a symmetric spatial wavefunction. Hence the type of wavefunction of each state is given above. The
5865:
5362:{\displaystyle \sigma _{x}={\frac {1}{\sqrt {2}}}{\begin{pmatrix}1&0\\0&-1\end{pmatrix}},\quad \sigma _{y}={\frac {i}{\sqrt {2}}}{\begin{pmatrix}1&0\\0&1\end{pmatrix}},\quad \sigma _{z}={\frac {1}{\sqrt {2}}}{\begin{pmatrix}0&1\\1&0\end{pmatrix}}.}
4668:
4628:
9574:
5403:
can be solved independently. This is identical to the previously discussed method of finding spatial wavefunction eigenstates independently of the spin states, here spatial wavefunctions of different spin states correspond to the different components of the matrix.
10901:
1925:{\displaystyle H|\Phi \rangle =\sum _{ij}c_{ij}H|\varphi _{i}\rangle |\chi _{j}\rangle =\sum _{ij}c_{ij}(H|\varphi _{i}\rangle )|\chi _{j}\rangle =E\sum _{ij}c_{ij}|\varphi _{i}\rangle |\chi _{j}\rangle =\sum _{ij}c_{ij}E|\varphi _{i}\rangle |\chi _{j}\rangle ,}
12372:{\displaystyle J=\int \int \psi _{100}(\mathbf {r} _{1})\psi _{nlm}(\mathbf {r} _{2}){\frac {ke^{2}}{|\mathbf {r} _{1}-\mathbf {r} _{2}|}}\psi _{nlm}^{\text{*}}(\mathbf {r} _{1})\psi _{100}^{\text{*}}(\mathbf {r} _{2})d^{3}\mathbf {r} _{1}d^{3}\mathbf {r} _{2}}
5628:
4064:
5980:
2356:
Since the
Hamiltonian is independent of spin, it commutes with all spin operators. Since it is also rotationally invariant, the total x, y or z component of angular momentum operator also commutes with the Hamiltonian. From these commutation relations,
5740:
7143:
10273:
10068:
10886:
9918:
9330:{\displaystyle \Delta ^{(1)}=\int \int {\frac {Z^{6}}{\pi ^{2}a_{0}^{6}}}{\frac {ke^{2}}{|\mathbf {r} _{1}-\mathbf {r} _{2}|}}e^{-{\frac {2Z(r_{1}+r_{2})}{a_{0}}}}d^{3}\mathbf {r} _{1}d^{3}\mathbf {r} _{2}={\frac {5}{4}}{\frac {ke^{2}}{a_{0}}}}
3778:
11882:
has a minus symbol. Since due to the symmetrization postulate, the combined spatial wavefunctions differ on symmetric or antisymmetric nature, the J term is responsible for the splitting of energy levels between ortho and para helium states.
6549:
3401:
10581:
8636:
8662:
11418:. The variational approach has been refined to very high accuracy for a comprehensive regime of quantum states by G.W.F. Drake and co-workers as well as J.D. Morgan III, Jonathan Baker and Robert Hill using Hylleraas or Frankowski-
5418:
6280:
7561:
3193:
11391:
11441:
6840:
1546:
7896:
4274:
2756:
6533:
6216:{\displaystyle H=-{\frac {1}{2m}}\mathbf {p} _{1}^{2}-{\frac {1}{2m}}\mathbf {p} _{2}^{2}-{\frac {kZe^{2}}{\mathbf {r} _{1}}}-{\frac {kZe^{2}}{\mathbf {r} _{2}}}+{\frac {ke^{2}}{|\mathbf {r} _{1}-\mathbf {r} _{2}|}}.}
1445:{\displaystyle H=-{\frac {1}{2m}}\mathbf {p} _{1}^{2}-{\frac {1}{2m}}\mathbf {p} _{2}^{2}-{\frac {kZe^{2}}{\mathbf {r} _{1}}}-{\frac {kZe^{2}}{\mathbf {r} _{2}}}+{\frac {ke^{2}}{|\mathbf {r} _{1}-\mathbf {r} _{2}|}}.}
4422:
If the
Hamiltonian had been spin dependent, we would not have been able to treat each these components independently as shown previously since the Hamiltonian need not act in the same manner for all four components.
9739:
1217:
3972:
3909:
2076:
11312:
This shows that the other electron somewhat shields the nucleus reducing the effective charge from 2 to 1.69. This result matches with experimental results closely as well as the calculations of effective Z in
11681:
9047:
8969:
4524:
7419:{\displaystyle \psi _{\pm }^{(0)}(\mathbf {r} _{1}\,,\mathbf {r} _{2})={\frac {1}{\sqrt {2}}}(\psi _{a}(\mathbf {r} _{1})\psi _{b}(\mathbf {r} _{2})\pm \psi _{a}(\mathbf {r} _{2})\psi _{b}(\mathbf {r} _{1}))}
6907:
9399:
4136:
4826:
3413:
10091:
in this case, the screening constant is S = 0.30. For the ground state of helium, for the average shielding approximation, the screening effect of each electron on the other one is equivalent to about
1020:
7766:
5749:
11270:
1997:
12380:
these, the diagram for energy level splitting can be roughly sketched. It also follows that for these states of helium, the energy of parallel spins cannot be more than that of antiparallel spins.
8160:
8121:
5153:
1073:
4529:
2323:
2200:
12108:{\displaystyle I=\int \int |\psi _{100}(\mathbf {r} _{1})|^{2}|\psi _{nlm}(\mathbf {r} _{2})|^{2}{\frac {ke^{2}}{|\mathbf {r} _{1}-\mathbf {r} _{2}|}}d^{3}\mathbf {r} _{1}d^{3}\mathbf {r} _{2}}
8643:
The
Hartree–Fock method is used for a variety of atomic systems. However it is just an approximation, and there are more accurate and efficient methods used today to solve atomic systems. The "
10142:
9923:
4413:{\displaystyle {\boldsymbol {\psi }}={\begin{pmatrix}\psi _{\uparrow \uparrow }&\psi _{\uparrow \downarrow }\\\psi _{\downarrow \uparrow }&\psi _{\downarrow \downarrow }\end{pmatrix}}}
8316:
of each electrons cannot be made on one particle without affecting the other. This follows since the wavefunction is always a superposition of different states where each electron has unique
11755:
10756:
6842:
are independent
Coulomb field Hamiltonian of each electron. Since the unperturbed Hamiltonian is a sum of two independent Hamiltonians (i.e. are separable), the wavefunction must be of form
4458:
7657:
11168:
9759:
4327:
11308:
4175:
3687:
5547:
3313:
4776:{\displaystyle {\boldsymbol {\sigma }}_{0}^{0}={\frac {1}{\sqrt {2}}}{\begin{pmatrix}0&1\\-1&0\end{pmatrix}}={\frac {1}{\sqrt {2}}}(\uparrow \downarrow -\downarrow \uparrow )}
3977:
9371:
895:
5874:
5389:
11800:
8436:
8375:
8314:
8253:
7891:
7830:
5637:
11046:{\displaystyle \langle H\rangle =2Z^{2}E_{1}+2(Z-2)\left({\frac {e^{2}}{4\pi \varepsilon _{0}}}\right)\left\langle {\frac {1}{r}}\right\rangle +\left\langle V_{ee}\right\rangle }
7464:
3173:
7036:
2931:
1581:
9618:
953:
924:
7213:
7178:
6977:
6942:
6271:
2270:
2235:
2147:
2112:
1616:
2508:
Other operators that commute with the
Hamiltonian are the spatial exchange operator and the parity operator. However a good combination of mutually commuting operators are:
2977:
553:
The quantum mechanical description of the helium atom is of special interest, because it is the simplest multi-electron system and can be used to understand the concept of
12492:
8192:
11320:
11080:
10116:
7145:
need not correspond to physical states of identical electrons as per the symmetrization postulate. Thus, to obtain physical solutions symmetrization of the wavefunctions
2351:
11880:
11847:
8428:
7694:
7601:
6745:
2811:
1120:
1146:
2621:
2409:
2382:
4808:
4657:
3816:
3114:
3073:
3047:
3006:
7031:
7004:
2614:
2587:
2560:
2533:
2463:
2436:
2871:
2851:
2831:
1094:
8651:
of helium is known to fifteen digits. In
Hartree–Fock theory, the electrons are assumed to move in a potential created by the nucleus and the other electrons.
8640:
A good theoretical descriptions of helium including the perturbation term can be obtained within the
Hartree–Fock and Thomas–Fermi approximations (see below).
3842:
3116:
states). Since the spin exchange operator can be expressed in terms of dot product of spin vectors, eigenkets of spin exchange operators are also eigenkets of
9634:
6452:
2503:
2483:
418:
12919:
Baker, Jonathan D.; Freund, David E.; Hill, Robert Nyden; Morgan, John D. (1990-02-01). "Radius of convergence and analytic behavior of the 1/Z expansion".
7469:
6735:{\displaystyle H_{0}=-{\frac {1}{2m}}\mathbf {p} _{1}^{2}-{\frac {1}{2m}}\mathbf {p} _{2}^{2}-{\frac {kZe^{2}}{r_{1}}}-{\frac {kZe^{2}}{r_{2}}}=H_{1}+H_{2}}
10739:{\displaystyle \langle H\rangle =8E_{1}+{\frac {5}{4a}}\left({\frac {e^{2}}{4\pi \epsilon _{0}}}\right)=8E_{1}-{\frac {5}{2}}E_{1}=-109+34=-75{\text{ eV}}}
8077:{\textstyle \psi ^{(0)}(\mathbf {r} _{1},\mathbf {r} _{2})=\psi _{n_{1},\ell _{1},m_{1}}(\mathbf {r} _{1})\psi _{n_{2},\ell _{2},m_{2}}(\mathbf {r} _{2})}
4426:
The matrix can also be represented as a linear combination of any given basis of four orthogonal (in the vector-space of 2×2 matrices) constant matrices
11172:
The minimum value of Z needs to be calculated, so taking a derivative with respect to Z and setting the equation to 0 will give the minimum value of Z:
8895:
1458:
462:
11407:
By using more complicated/accurate wave functions, the ground state energy of helium has been calculated closer and closer to the experimental value
4180:
9392:
The energy that we obtained is too low because the repulsion term between the electrons was ignored, whose effect is to raise the energy levels. As
8883:{\displaystyle \psi _{0}(r_{1}\,,r_{2})=\psi _{1,0,0}(r_{1})\psi _{1,0,0}(r_{2})={\frac {Z^{3}}{\pi a_{0}^{3}}}e^{-{\frac {Z(r_{1}+r_{2})}{a_{0}}}}}
13144:
561:
of helium, considered as a three-body system of two electrons and a nucleus and after separating out the centre-of-mass motion, can be written as
5532:{\displaystyle {\boldsymbol {\psi }}_{ij}(\mathbf {r} _{1},\,\mathbf {r} _{2})=-{\boldsymbol {\psi }}_{ji}(\mathbf {r} _{2},\,\mathbf {r} _{1}).}
9620:
is small. The net effect of each electron on the motion of the other one is to screen somewhat the charge of the nucleus, so a simple guess for
6440:{\displaystyle H_{0}=-{\frac {1}{2m}}\mathbf {p} _{1}^{2}-{\frac {1}{2m}}\mathbf {p} _{2}^{2}-{\frac {kZe^{2}}{r_{1}}}-{\frac {kZe^{2}}{r_{2}}}}
11175:
3304:{\displaystyle |\chi _{s=0,m=0}\rangle ={\frac {1}{\sqrt {2}}}(|\uparrow \rangle |\downarrow \rangle -|\downarrow \rangle |\uparrow \rangle )}
12540:
1151:
11601:{\displaystyle H_{0}=-{\frac {1}{2}}\nabla _{r_{1}}^{2}-{\frac {1}{2}}\nabla _{r_{2}}^{2}-{\frac {kZe^{2}}{r_{1}}}-{\frac {kZe^{2}}{r_{2}}}}
12905:
J.D. Baker, R.N. Hill, and J.D. Morgan III (1989), "High
Precision Calculation of Helium Atom Energy Levels", in AIP ConferenceProceedings
3914:
3851:
316:
13086:
G.W.F. Drake (2006). "Springer Handbook of Atomic, molecular, and Optical Physics", Edited by G.W.F. Drake (Springer, New York), 199-219.
8659:
Since ground state corresponds to (1,0,0) state, there can only be one representation of such wavefunction whose spatial wavefunction is:
2002:
7771:
Note that all wavefunction obtained thus far cannot be separated into wavefunctions of each particle (even for electrons with identical
4463:
11611:
8977:
1618:
is the combined spin component. The Hamiltonian operator, since it only acts on the spatial component, gives the eigenvector equation:
11689:
6845:
4077:
2813:
fold degenerate. For electrons, the total spin can have values of 0 or 1. A state with the quantum numbers: principal quantum number
12812:
Yan, Zong-Chao; Drake, G. W. F. (1995-06-12). "High Precision Calculation of Fine Structure Splittings in Helium and He-Like Ions".
2505:
will influence the type of wavefunction required by symmetrization postulate which would in turn influence the energy of the state.
11092:
5860:{\displaystyle {\boldsymbol {\phi }}_{m}=\psi _{-}(\mathbf {r} _{1},\,\mathbf {r} _{2}){\boldsymbol {\sigma }}_{m}^{1},\;m=-1,0,1}
11274:
9756:
is the effective charge. The potential is a Coulomb interaction, so the corresponding individual electron energies are given by
958:
7699:
4623:{\textstyle {\boldsymbol {\psi }}=\sum _{ik}\phi _{i}^{k}(\mathbf {r} _{1},\,\mathbf {r} _{2}){\boldsymbol {\sigma }}_{k}^{i}}
1937:
12691:
12585:
8126:
8087:
13158:
D. Z. Kandula; C. Gohle; T. J. Pinkert; W. Ubachs; K. S. E. Eikema (2010). "Extreme Ultraviolet Frequency Comb Metrology".
5099:
1027:
11760:
9384:. A better approximation for ground state energy is obtained by choosing better trial wavefunction in variational method.
8194:) i.e. the wavefunctions are always in superposition of some kind. In other words, one cannot completely determine states
2275:
2152:
2485:, this would only be true in the absence of symmetrization postulate. Due to the symmetrization postulate, the choice of
9569:{\displaystyle {\bar {H'}}={\frac {ke^{2}}{r_{12}}}-{\frac {kZe^{2}}{r_{1}}}-V(r_{1})-{\frac {kZe^{2}}{r_{2}}}-V(r_{2})}
13106:
457:
13026:"Energies and relativistic corrections for the Rydberg states of helium: Variational results and asymptotic analysis"
12633:
5092:
It is easy to show, that the singlet state is invariant under all rotations (a scalar entity), while the triplet are
4429:
291:
12971:
7606:
13087:
9396:
gets bigger, our approach should yield better results, since the electron-electron repulsion term will get smaller.
5623:{\displaystyle {\boldsymbol {\phi }}=\psi _{+}(\mathbf {r} _{1},\,\mathbf {r} _{2}){\boldsymbol {\sigma }}_{0}^{0}}
4279:
469:
6226:
4141:
4059:{\displaystyle |\uparrow \rangle _{1}|\downarrow \rangle _{2}\neq |\downarrow \rangle _{1}|\uparrow \rangle _{2}}
558:
537:
in 1927. Its success was considered to be one of the earliest signs of validity of Schrödinger's wave mechanics.
6232:
5392:
5990:
Following from the above approximation, effectively reducing three body problem to two body problem, we have:
5975:{\displaystyle \psi _{-}(\mathbf {r} _{1},\,\mathbf {r} _{2})=-\psi _{-}(\mathbf {r} _{2},\,\mathbf {r} _{1})}
10077:
was 1.70, that would make the expression above for the ground state energy agree with the experimental value
7218:
The proper wave function then must be composed of the symmetric (+) and antisymmetric(−) linear combinations:
5735:{\displaystyle \psi _{+}(\mathbf {r} _{1},\,\mathbf {r} _{2})=\psi _{+}(\mathbf {r} _{2},\,\mathbf {r} _{1})}
4177:
describe the spin projection of both electrons in this coordinate system. The usual normalization condition,
549:
Schematic termscheme for Para- and Orthohelium with one electron in ground state 1s and one excited electron.
50:
9342:
7138:{\textstyle \psi (\mathbf {r} _{1},\mathbf {r} _{2})=\psi _{a}(\mathbf {r} _{1})\psi _{b}(\mathbf {r} _{2})}
5093:
854:
12414:. This value was measured experimentally. The theoretic value of Helium atom's second ionization energy is
5372:
258:
10268:{\displaystyle \psi _{0}(\mathbf {r} _{1},\,\mathbf {r} _{2})={\frac {8}{\pi a^{3}}}e^{-2(r_{1}+r_{2})/a}}
10063:{\displaystyle \psi _{0}(r_{1}\,,r_{2})={\sqrt {\frac {Z_{e}^{3}}{\pi a_{0}^{3}}}}e^{-Z_{e}(r_{1}+r_{2})}}
12477:
8319:
8258:
8197:
7835:
7774:
7429:
3119:
10881:{\displaystyle \psi (\mathbf {r} _{1},\mathbf {r} _{2})={\frac {Z^{3}}{\pi a^{3}}}e^{-Z(r_{1}+r_{2})/a}}
2876:
1551:
12607:
929:
900:
12389:
9913:{\displaystyle E_{0}=-{\frac {k(Z-S)^{2}e^{2}}{2a_{0}n^{2}}}=-{\frac {kZ_{e}^{2}e^{2}}{2a_{0}n^{2}}}}
8378:
5408:
5396:
209:
153:
7183:
7148:
6947:
6912:
3773:{\displaystyle \psi (\mathbf {r} _{1},\mathbf {r} _{2})=-\psi (\mathbf {r} _{2}\,,\mathbf {r} _{1})}
2240:
2205:
2117:
2082:
1586:
3396:{\displaystyle \psi (\mathbf {r} _{1},\mathbf {r} _{2})=\psi (\mathbf {r} _{2}\,,\mathbf {r} _{1})}
2936:
203:
10749:
somewhat shields the nucleus so that the other electron actually sees an effective nuclear charge
13229:
12909:, Relativistic, Quantum Electrodynamic, and Weak Interaction Effects in Atoms (AIP, New York),123
12532:
11427:
9589:
8165:
522:
11058:
10094:
7662:
7569:
5400:
2465:. Although the purely spatial form of the Hamiltonian implies that the energy is independent of
2328:
518:
12482:
11852:
11819:
8387:
3848:
spin Hilbert vector spaces, its basis can be represented by tensor product of each of the set,
1099:
514:
389:
2763:
12653:(in German). Vol. Bd. III (Quantenmechanik). Berlin: Akademie-Verlag. Kap. IX, pp. 218.
10127:
8647:" for helium and other few electron systems can be solved quite accurately. For example, the
8631:{\displaystyle E_{n_{1},n_{2}}^{(0)}=E_{n_{1}}+E_{n_{2}}=-{\frac {kZ^{2}e^{2}}{2a_{0}}}\left}
498:
12769:
Drake, G.W.F.; Van, Zong-Chao (1994). "Variational eigenvalues for the S states of helium".
1125:
13177:
13037:
12988:
12928:
12872:
12821:
12778:
12497:
554:
267:
142:
102:
11816:. If the combined spatial wavefunction is symmetric, its energy level has the + symbol in
8974:
We can find the first order correction in energy due to electron repulsion in Hamiltonian
2387:
2360:
78:
8:
13126:
8084:
because then, the spin of the electrons are in a superposition of different spin states:
4787:
4636:
3052:
2985:
68:
13181:
13041:
12992:
12932:
12876:
12825:
12782:
3786:
3084:
3017:
122:
19:
This article is about the physics of atomic helium. For other properties of helium, see
13201:
13167:
13069:
12472:
11423:
7009:
6982:
2856:
2836:
2816:
2592:
2565:
2538:
2511:
2441:
2414:
1079:
1022:. It is important to note that it operates not in normal space, but in a 6-dimensional
502:
12884:
7556:{\displaystyle \psi _{+}^{(0)}=\psi _{a}(\mathbf {r} _{1})\psi _{a}(\mathbf {r} _{2})}
534:
13193:
13138:
13102:
13061:
13053:
12952:
12944:
12888:
12845:
12837:
12794:
12790:
12687:
12654:
12629:
12581:
12502:
12400:
8644:
5391:
in the above (scalar) Hamiltonian are neglected (e.g. an external magnetic field, or
3821:
521:
for the helium atom has not been found. However, various approximations, such as the
494:
13073:
11386:{\displaystyle {\frac {1}{2}}\left({\frac {3}{2}}\right)^{6}E_{1}=-77.5{\text{ eV}}}
13205:
13189:
13185:
13045:
13004:
12996:
12936:
12880:
12829:
12786:
12721:
12713:
12679:
12573:
11419:
11314:
6835:{\displaystyle H_{i}=-{\frac {1}{2m}}\mathbf {p} _{i}^{2}-{\frac {kZe^{2}}{r_{i}}}}
2488:
2468:
1541:{\textstyle |\Phi \rangle =\sum _{ij}c_{ij}|\varphi _{i}\rangle |\chi _{j}\rangle }
429:
336:
13124:
533:
of the atom. Historically, the first such helium spectrum calculation was done by
231:
13234:
12979:
11812:
172:
12833:
12512:
4269:{\textstyle \sum _{ij}\int d\mathbf {r} _{1}d\mathbf {r} _{2}|\psi _{ij}|^{2}=1}
13224:
13000:
12673:
12507:
4067:
2411:
also commutes with the Hamiltonian which implies that energy is independent of
440:
12683:
9586:
is a central potential which is chosen so that the effect of the perturbation
2751:{\displaystyle H|N,L,m_{l},S,m_{s}\rangle =E_{nls}|N,L,m_{l},S,m_{s}\rangle ,}
501:
to a nucleus containing two protons along with two neutrons, depending on the
13218:
13057:
13049:
12948:
12940:
12892:
12841:
12798:
11430:
corrections to get full agreement with experiment to spectroscopic accuracy.
4812:
4661:
3183:
3177:
3077:
3010:
373:
13025:
12658:
13197:
13157:
12849:
12567:
12487:
12446:
8648:
530:
526:
506:
424:
13065:
12956:
12577:
4633:
A convenient basis consists of one anti-symmetric matrix (with total spin
13009:
3175:. Hence parahelium can also be said to be the spin anti-symmetric state (
1219:
disappears, so that in operator language, the Hamiltonian simplifies to:
9734:{\displaystyle V(r)=-{\frac {k(Z-S)e^{2}}{r}}=-{\frac {kZ_{e}e^{2}}{r}}}
6528:{\displaystyle H'={\frac {ke^{2}}{|\mathbf {r} _{1}-\mathbf {r} _{2}|}}}
1212:{\textstyle {\frac {\hbar ^{2}}{M}}\nabla _{r_{1}}\cdot \nabla _{r_{2}}}
12628:(in German). VEB Bibliographisches Institut Leipzig. pp. 192–194.
349:
154:
133:
13101:. Vol. I. McGraw-Hill Book Company, Inc. 1960. pp. 486–487.
3818:
degeneracy solely comes from this spatial wavefunction. Note that for
1096:
is 2 for helium. In the approximation of an infinitely heavy nucleus,
3967:{\displaystyle \{|\uparrow \rangle _{2}\,,|\downarrow \rangle _{2}\}}
3904:{\displaystyle \{|\uparrow \rangle _{1}\,,|\downarrow \rangle _{1}\}}
545:
278:
12970:
Scott, T. C.; Lüchow, A.; Bressanini, D.; Morgan, J. D. III (2007).
12725:
2071:{\textstyle |\psi _{j}\rangle =\sum _{i}c_{ij}|\varphi _{i}\rangle }
439:
Except where otherwise noted, data are given for materials in their
11686:
In general, for (1s)(nl) state, in first order perturbation theory:
8892:
We note that the ground state energy of unperturbed helium atom as:
6229:
for helium with two electrons can be written as a sum of two terms:
510:
192:
13172:
12863:
Drake, G. W. F. (1999). "High Precision Theory of Atomic Helium".
11676:{\textstyle {\frac {ke^{2}}{|\mathbf {r} _{1}-\mathbf {r} _{2}|}}}
9042:{\textstyle {\frac {ke^{2}}{|\mathbf {r} _{1}-\mathbf {r} _{2}|}}}
8964:{\displaystyle E_{0}=-4{\frac {ke^{2}}{a_{0}}}=-108.8{\text{ eV}}}
7466:(both electrons have identical quantum numbers, parahelium only):
5411:, which for fermions (like electrons) requires antisymmetry under
4519:{\displaystyle \phi _{i}^{k}(\mathbf {r} _{1},\,\mathbf {r} _{2})}
101:
10121:
218:
6902:{\textstyle |\psi \rangle =|\psi _{1}\rangle |\psi _{2}\rangle }
5369:
Since all spin interaction terms between the four components of
897:
is the reduced mass of an electron with respect to the nucleus,
11849:, whereas for the antisymmetric combined spatial wavefunction,
10753:
that is less than 2. A wave function of this type is given by:
4131:{\displaystyle \psi _{ij}(\mathbf {r} _{1},\,\mathbf {r} _{2})}
4071:
490:
20:
8654:
10898:. The Hamiltonian using the wave function above is given by:
9339:
The energy for ground state of helium in first order becomes
4066:
but are in fact orthogonal. In the considered approximation (
242:
113:
91:
13125:
Kramida, A.; Ralchenko, Yu.; Reader, J., and NIST ASD Team.
12493:
List of quantum-mechanical systems with analytical solutions
7033:
respectively. However, the spatial wavefunction of the form
4329:
elements. This general spinor can be written as 2×2 matrix:
13130:
12969:
11438:
Consider the same setting where unperturbed Hamiltonian is:
486:
183:
12623:
12394:
10084:= −2.903 a.u. of the ground state energy of helium. Since
4070:), the wave function can be represented as a second order
1015:{\displaystyle r_{12}=|\mathbf {r} _{1}-\mathbf {r} _{2}|}
7761:{\displaystyle \psi _{a}=\psi _{1s},\psi _{b}=\psi _{2s}}
11265:{\displaystyle {\frac {d}{dZ}}\left(\leftE_{1}\right)=0}
9920:
and the corresponding spatial wave function is given by
1992:{\displaystyle H|\psi _{j}\rangle =E|\psi _{j}\rangle ,}
13127:"NIST Atomic Spectra Database Ionization Energies Data"
33:
12425:. The total ground state energy of the helium atom is
11855:
11822:
11614:
11061:
10097:
9345:
8980:
8390:
8322:
8261:
8200:
8168:
8155:{\displaystyle |\downarrow \rangle |\uparrow \rangle }
8116:{\displaystyle |\uparrow \rangle |\downarrow \rangle }
7899:
7838:
7777:
7186:
7151:
7039:
7012:
6985:
6950:
6915:
6848:
5325:
5260:
5192:
5034:
4962:
4867:
4709:
4532:
4351:
4183:
3824:
3789:
3087:
3020:
2766:
2595:
2568:
2541:
2514:
2491:
2471:
2444:
2417:
2390:
2363:
2331:
2243:
2208:
2120:
2085:
2005:
1589:
1554:
1461:
1154:
12918:
12120:
11894:
11763:
11692:
11444:
11323:
11277:
11178:
11095:
10904:
10759:
10584:
10280:
10145:
9926:
9762:
9637:
9592:
9402:
9055:
8898:
8665:
8439:
8255:
of particle 1 and 2, or measurements of all details,
8129:
8090:
7702:
7665:
7609:
7572:
7472:
7432:
7224:
6748:
6552:
6455:
6283:
6235:
5998:
5877:
5752:
5640:
5550:
5421:
5375:
5161:
5148:{\displaystyle (\sigma _{x},\sigma _{y},\sigma _{z})}
5102:
4824:
4790:
4671:
4639:
4466:
4432:
4337:
4282:
4144:
4080:
3980:
3917:
3854:
3690:
3411:
3316:
3196:
3122:
3055:
2988:
2939:
2879:
2859:
2839:
2819:
2624:
2278:
2155:
1940:
1626:
1227:
1128:
1102:
1082:
1068:{\displaystyle (\mathbf {r} _{1},\,\mathbf {r} _{2})}
1030:
961:
932:
903:
857:
567:
6546:
is just the sum of the two hydrogenic Hamiltonians:
2318:{\displaystyle |\psi _{i}\rangle |\chi _{i}\rangle }
2195:{\displaystyle |\psi _{i}\rangle |\chi _{i}\rangle }
12624:Rennert, P.; Schmiedel, H.; Weißmantel, C. (1988).
12972:"The Nodal Surfaces of Helium Atom Eigenfunctions"
12820:(24). American Physical Society (APS): 4791–4794.
12712:Kramida, Alexander; Ralchenko, Yuri (2009-07-21).
12371:
12107:
11874:
11841:
11794:
11749:
11675:
11600:
11385:
11302:
11264:
11162:
11089:the expectation value of the Hamiltonian becomes:
11074:
11045:
10880:
10738:
10568:
10267:
10130:can be applied to the electron-electron potential
10110:
10062:
9912:
9733:
9612:
9568:
9365:
9329:
9041:
8963:
8882:
8630:
8422:
8369:
8308:
8247:
8186:
8154:
8115:
8076:
7885:
7824:
7760:
7688:
7651:
7595:
7555:
7458:
7418:
7207:
7172:
7137:
7025:
6998:
6971:
6936:
6901:
6834:
6734:
6527:
6439:
6265:
6215:
5974:
5859:
5734:
5622:
5531:
5383:
5361:
5147:
5082:
4802:
4775:
4651:
4622:
4518:
4452:
4412:
4321:
4268:
4169:
4130:
4058:
3966:
3903:
3844:, there is no degeneracy in spatial wavefunction.
3836:
3810:
3772:
3677:
3395:
3303:
3167:
3108:
3067:
3041:
3000:
2971:
2925:
2865:
2845:
2825:
2805:
2750:
2608:
2581:
2554:
2527:
2497:
2477:
2457:
2430:
2403:
2376:
2345:
2317:
2264:
2229:
2194:
2141:
2106:
2070:
1991:
1924:
1610:
1575:
1540:
1444:
1211:
1140:
1114:
1088:
1067:
1014:
947:
918:
889:
841:
13036:(5). American Physical Society (APS): 2378–2409.
12927:(3). American Physical Society (APS): 1247–1273.
12565:
11433:
11317:. Hence, we obtain the most accurate result yet:
1934:which implies that one should find solutions for
13216:
12711:
12572:. Cambridge University Press. pp. 455–459.
12383:
6275:where the zero-order unperturbed Hamiltonian is
2237:is the energy eigenket spatial wavefunction and
230:
12648:
11750:{\displaystyle E=E_{100}+E_{nlm}+\Delta ^{(1)}}
5415:(totally antisymmetric wavefunction condition)
5407:The spin here only comes into play through the
4453:{\displaystyle {\boldsymbol {\sigma }}_{k}^{i}}
77:
13024:Drake, G. W. F.; Yan, Zong-Chao (1992-09-01).
12566:Sakurai, J. J.; Napolitano, Jim (2017-09-21).
11404:represents the ionization energy of hydrogen.
10122:Ground state of Helium: The variational method
7652:{\displaystyle \psi _{a}=\psi _{b}=\psi _{1s}}
4784:and three symmetric matrices (with total spin
955:are the electron-nucleus distance vectors and
12541:National Center for Biotechnology Information
5413:simultaneous exchange of spin and coordinates
3181:) or orthohelium to be spin symmetric state (
2353:is merely some superpostion of these states.
13143:: CS1 maint: multiple names: authors list (
12738:
11163:{\displaystyle \langle H\rangle =\leftE_{1}}
11102:
11096:
10911:
10905:
10591:
10585:
10325:
10309:
10287:
10281:
8971:Which is 30% larger than experimental data.
8149:
8138:
8110:
8099:
7202:
7167:
6966:
6931:
6896:
6878:
6857:
5096:representations of an ordinary space vector
4322:{\displaystyle |i\rangle _{1}|j\rangle _{2}}
4310:
4292:
4047:
4029:
4008:
3990:
3961:
3952:
3930:
3918:
3898:
3889:
3867:
3855:
3664:
3653:
3638:
3593:
3582:
3567:
3517:
3506:
3492:
3481:
3452:
3295:
3284:
3270:
3259:
3230:
2742:
2674:
2340:
2312:
2294:
2259:
2224:
2189:
2171:
2136:
2101:
2065:
2021:
1983:
1959:
1916:
1898:
1848:
1830:
1780:
1759:
1706:
1688:
1638:
1605:
1570:
1535:
1517:
1470:
378:−269 °C (−452.20 °F; 4.15 K)
12533:"Helium - PubChem Public Chemical Database"
11303:{\displaystyle Z={\frac {27}{16}}\sim 1.69}
11055:After calculating the expectation value of
8655:Ground state of Helium: Perturbation method
8384:We can infer from these wavefunctions that
4170:{\displaystyle i,j=\,\uparrow ,\downarrow }
5832:
5072:
5068:
5005:
5004:
5000:
4996:
4928:
3667:
3644:
3601:
3600:
3596:
3573:
3523:
2616:. Hence the final solutions are given as:
141:
13171:
13008:
12753:
10543:
10520:
10174:
9950:
9747:is a screening constant and the quantity
8689:
8350:
8336:
8329:
8289:
8275:
8268:
8228:
8214:
8207:
7866:
7852:
7805:
7791:
7261:
5956:
5906:
5796:
5716:
5669:
5587:
5510:
5455:
4587:
4500:
4157:
4112:
3939:
3876:
3751:
3374:
1049:
589:
266:
13120:
13118:
13023:
12811:
12768:
12649:Landau, L. D.; Lifschitz, E. M. (1971).
11608:and perturbation is electron repulsion:
5985:
4276:, follows from the orthogonality of all
2079:imposing a restriction on the choice of
544:
12671:
12395:Experimental value of ionization energy
10894:as a variational parameter to minimize
10578:After integrating this, the result is:
9366:{\textstyle E\approx -74.8{\text{ eV}}}
5814:
5755:
5605:
5552:
5479:
5424:
5377:
5008:
4939:
4832:
4674:
4605:
4534:
4435:
4339:
2149:. Hence the solutions are of the form:
1583:is a combined spatial wavefunction and
208:
13217:
12605:
11422:basis functions. One needs to include
9373:compared to its experimental value of
7659:) for orthohelium, where consequently
6537:is the electron-electron interaction.
890:{\displaystyle \mu ={\frac {mM}{m+M}}}
13115:
12862:
12758:(Second ed.). Pearson Education.
10126:To obtain a more accurate energy the
5384:{\displaystyle {\boldsymbol {\psi }}}
303:Key: SWQJXJOGLNCZEY-UHFFFAOYSA-N
121:
12707:
12705:
12703:
12601:
12599:
12597:
12561:
12559:
11795:{\displaystyle \Delta ^{(1)}=I\pm J}
8370:{\textstyle (n\,,l\,,m_{l}\,,m_{s})}
8309:{\textstyle (n\,,l\,,m_{l}\,,m_{s})}
8248:{\textstyle (n\,,l\,,m_{l}\,,m_{s})}
7886:{\textstyle (n_{2}\,,l_{2}\,,m_{2})}
7825:{\textstyle (n_{1}\,,l_{1}\,,m_{1})}
428:
9387:
7459:{\displaystyle \psi _{a}=\psi _{b}}
3168:{\displaystyle S=(S_{1}+S_{2})^{2}}
221:
191:
13:
13099:Quantum Theory of Atomic Structure
13091:
12743:(2nd ed.). Pearson Education.
11857:
11824:
11765:
11732:
11507:
11472:
9057:
7768:) is the metastable ground state.
4460:with scalar function coefficients
2926:{\displaystyle J=|L-S|,\dots ,L+S}
2337:
1635:
1576:{\textstyle |\varphi _{i}\rangle }
1467:
1193:
1173:
1109:
778:
758:
661:
14:
13246:
12885:10.1238/physica.topical.083a00083
12756:Introduction to Quantum Mechanics
12739:Bransden, B. H.; Joachain, C. J.
12700:
12651:Lehrbuch der Theoretischen Physik
12594:
12556:
12553:Unsöld, Ann. Phys., 82 (1927) 355
7566:This explains the absence of the
2272:is a spin wavefunction such that
12359:
12337:
12312:
12279:
12235:
12220:
12182:
12148:
12095:
12073:
12043:
12028:
11978:
11927:
11655:
11640:
10783:
10768:
10556:
10533:
10502:
10487:
10177:
10161:
9275:
9253:
9162:
9147:
9021:
9006:
8061:
8000:
7936:
7921:
7540:
7512:
7400:
7372:
7341:
7313:
7267:
7251:
7122:
7094:
7063:
7048:
6782:
6621:
6586:
6507:
6492:
6352:
6317:
6192:
6177:
6137:
6100:
6060:
6025:
5959:
5943:
5909:
5893:
5799:
5783:
5719:
5703:
5672:
5656:
5590:
5574:
5513:
5497:
5458:
5442:
4590:
4574:
4503:
4487:
4220:
4205:
4115:
4099:
3757:
3741:
3714:
3699:
3405:and triplet states are given as:
3380:
3364:
3340:
3325:
1421:
1406:
1366:
1329:
1289:
1254:
1052:
1036:
997:
982:
948:{\displaystyle \mathbf {r} _{2}}
935:
919:{\displaystyle \mathbf {r} _{1}}
906:
592:
576:
447:
32:
13151:
13080:
13017:
12963:
12912:
12899:
12856:
12805:
12762:
12747:
12675:Principles of Quantum Mechanics
8433:The corresponding energies are:
7208:{\textstyle |\psi _{2}\rangle }
7173:{\textstyle |\psi _{1}\rangle }
6972:{\textstyle |\psi _{2}\rangle }
6937:{\textstyle |\psi _{1}\rangle }
5294:
5229:
2265:{\textstyle |\chi _{i}\rangle }
2230:{\textstyle |\psi _{i}\rangle }
2142:{\textstyle |\psi _{i}\rangle }
2107:{\textstyle |\chi _{i}\rangle }
1611:{\textstyle |\chi _{i}\rangle }
1148:and the mass polarization term
540:
443:(at 25 °C , 100 kPa).
13190:10.1103/PhysRevLett.105.063001
12741:Physics of Atoms and Molecules
12732:
12665:
12642:
12617:
12547:
12525:
12322:
12307:
12289:
12274:
12246:
12214:
12192:
12177:
12158:
12143:
12054:
12022:
11993:
11988:
11973:
11953:
11942:
11937:
11922:
11908:
11867:
11861:
11834:
11828:
11775:
11769:
11742:
11736:
11666:
11634:
11434:Perturbation theory for Helium
10958:
10946:
10865:
10839:
10793:
10763:
10513:
10481:
10466:
10440:
10252:
10226:
10187:
10156:
10055:
10029:
9964:
9937:
9798:
9785:
9674:
9662:
9647:
9641:
9604:
9563:
9550:
9506:
9493:
9414:
9223:
9197:
9173:
9141:
9067:
9061:
9032:
9000:
8862:
8836:
8782:
8769:
8744:
8731:
8703:
8676:
8476:
8470:
8364:
8323:
8303:
8262:
8242:
8201:
8146:
8142:
8135:
8131:
8107:
8103:
8096:
8092:
8071:
8056:
8010:
7995:
7946:
7916:
7911:
7905:
7880:
7839:
7819:
7778:
7550:
7535:
7522:
7507:
7489:
7483:
7413:
7410:
7395:
7382:
7367:
7351:
7336:
7323:
7308:
7295:
7277:
7246:
7241:
7235:
7188:
7153:
7132:
7117:
7104:
7089:
7073:
7043:
6952:
6917:
6882:
6864:
6850:
6518:
6486:
6203:
6171:
5969:
5938:
5919:
5888:
5809:
5778:
5729:
5698:
5682:
5651:
5600:
5569:
5523:
5492:
5468:
5437:
5142:
5103:
5069:
4997:
4925:
4922:
4916:
4913:
4770:
4767:
4761:
4758:
4600:
4569:
4513:
4482:
4397:
4385:
4371:
4359:
4302:
4284:
4250:
4231:
4164:
4158:
4125:
4094:
4043:
4039:
4025:
4021:
4004:
4000:
3986:
3982:
3948:
3944:
3926:
3922:
3885:
3881:
3863:
3859:
3805:
3790:
3767:
3736:
3724:
3694:
3661:
3657:
3650:
3646:
3603:
3590:
3586:
3579:
3575:
3535:
3520:
3514:
3510:
3503:
3499:
3489:
3485:
3478:
3474:
3470:
3420:
3390:
3359:
3350:
3320:
3298:
3292:
3288:
3281:
3277:
3267:
3263:
3256:
3252:
3248:
3198:
3190:The singlet state is given as:
3156:
3129:
2901:
2887:
2800:
2785:
2782:
2767:
2697:
2629:
2333:
2298:
2280:
2245:
2210:
2175:
2157:
2122:
2087:
2051:
2007:
1969:
1945:
1902:
1884:
1834:
1816:
1766:
1762:
1745:
1738:
1692:
1674:
1631:
1591:
1556:
1521:
1503:
1463:
1432:
1400:
1062:
1031:
1008:
976:
602:
571:
525:, can be used to estimate the
342:
1:
12777:(4–5). Elsevier BV: 486–490.
12519:
12384:First excited state of Helium
5155:, with the three components:
2972:{\displaystyle n^{2S+1}L_{J}}
12871:(1). IOP Publishing: 83–92.
12791:10.1016/0009-2614(94)01085-4
12754:Griffiths, David I. (2005).
12513:"Helium atom" on Wikiversity
8377:. This is in agreement with
8187:{\textstyle \sigma _{0}^{0}}
7426:or for the special cases of
6449:while the perturbation term:
7:
12834:10.1103/physrevlett.74.4791
12465:
11075:{\textstyle {\frac {1}{r}}}
10111:{\textstyle {\frac {1}{3}}}
9613:{\displaystyle {\bar {H'}}}
3081:, so called as there exist
3014:, so called as there exist
2873:and total angular momentum
2346:{\textstyle |\Phi \rangle }
10:
13251:
13001:10.1103/PhysRevA.75.060101
12626:Kleine Enzyklopädie Physik
12387:
11875:{\textstyle \Delta ^{(1)}}
11842:{\textstyle \Delta ^{(1)}}
8423:{\textstyle E=E_{a}+E_{b}}
7689:{\displaystyle 2^{3}S_{1}}
7596:{\displaystyle 1^{3}S_{1}}
6266:{\displaystyle H=H_{0}+H'}
5544:is then the singlet state
18:
12714:"Atomic Spectra Database"
12684:10.1007/978-1-4757-0576-8
12390:Fermi heap and Fermi hole
8379:Pauli exclusion principle
5409:Pauli exclusion principle
5397:angular momentum coupling
3075:are called orthohelium (
3008:, are called parahelium (
2853:, angular quantum number
2806:{\textstyle (2l+1)(2s+1)}
1115:{\displaystyle M=\infty }
437:
411:
382:
329:
312:
287:
61:
49:
44:
31:
13050:10.1103/physreva.46.2378
12941:10.1103/physreva.41.1247
12771:Chemical Physics Letters
12569:Modern Quantum Mechanics
11886:They are calculated as:
10139:using the wave function
10118:of the electric charge.
2982:States corresponding to
493:. Helium is composed of
489:of the chemical element
407:126.151-126.155 J K mol
12814:Physical Review Letters
12478:Araki–Sucher correction
5094:spherical vector tensor
505:, held together by the
12483:Hydrogen molecular ion
12373:
12109:
11876:
11843:
11796:
11751:
11677:
11602:
11428:quantum electrodynamic
11387:
11304:
11266:
11164:
11076:
11047:
10882:
10740:
10570:
10269:
10112:
10064:
9914:
9735:
9614:
9570:
9367:
9331:
9043:
8965:
8884:
8632:
8424:
8371:
8310:
8249:
8188:
8156:
8117:
8078:
7893:where wavefunction is
7887:
7826:
7762:
7690:
7653:
7597:
7557:
7460:
7420:
7209:
7174:
7139:
7027:
7000:
6973:
6938:
6903:
6836:
6736:
6529:
6441:
6267:
6217:
5976:
5861:
5736:
5624:
5533:
5385:
5363:
5149:
5084:
4804:
4777:
4653:
4624:
4520:
4454:
4414:
4323:
4270:
4171:
4132:
4060:
3968:
3911:with each of the set,
3905:
3838:
3812:
3774:
3679:
3397:
3305:
3169:
3110:
3069:
3043:
3002:
2973:
2927:
2867:
2847:
2827:
2807:
2752:
2610:
2583:
2556:
2529:
2499:
2479:
2459:
2432:
2405:
2378:
2347:
2319:
2266:
2231:
2196:
2143:
2108:
2072:
1993:
1926:
1612:
1577:
1542:
1446:
1213:
1142:
1141:{\displaystyle \mu =m}
1116:
1090:
1076:. The nuclear charge,
1069:
1016:
949:
920:
891:
843:
550:
12578:10.1017/9781108499996
12374:
12110:
11877:
11844:
11797:
11752:
11678:
11603:
11388:
11305:
11267:
11165:
11077:
11048:
10883:
10741:
10571:
10270:
10128:variational principle
10113:
10065:
9915:
9736:
9615:
9571:
9368:
9332:
9044:
8966:
8885:
8633:
8425:
8372:
8311:
8250:
8189:
8157:
8118:
8079:
7888:
7827:
7763:
7691:
7654:
7598:
7558:
7461:
7421:
7210:
7175:
7140:
7028:
7001:
6974:
6939:
6904:
6837:
6737:
6530:
6442:
6268:
6218:
5986:Approximation methods
5977:
5862:
5746:is the triplet state
5737:
5625:
5534:
5401:Schrödinger equations
5386:
5364:
5150:
5085:
4810:, corresponding to a
4805:
4778:
4659:, corresponding to a
4654:
4625:
4521:
4455:
4415:
4324:
4271:
4172:
4133:
4061:
3969:
3906:
3839:
3813:
3775:
3680:
3398:
3306:
3170:
3111:
3070:
3044:
3003:
2974:
2928:
2868:
2848:
2828:
2808:
2753:
2611:
2584:
2557:
2530:
2500:
2480:
2460:
2433:
2406:
2404:{\textstyle L_{\pm }}
2379:
2377:{\textstyle S_{\pm }}
2348:
2325:is antisymmetric and
2320:
2267:
2232:
2197:
2144:
2109:
2073:
1994:
1927:
1613:
1578:
1543:
1447:
1214:
1143:
1117:
1091:
1070:
1017:
950:
921:
892:
844:
548:
499:electromagnetic force
51:Systematic IUPAC name
13129:. Gaithersburg, MD:
12672:Shankar, R. (1994).
12606:Littlejohn, Robert.
12498:Quantum field theory
12118:
11892:
11853:
11820:
11802:where I is known as
11761:
11690:
11612:
11442:
11321:
11275:
11176:
11093:
11059:
10902:
10757:
10582:
10278:
10143:
10095:
9924:
9760:
9635:
9590:
9400:
9343:
9053:
8978:
8896:
8663:
8437:
8388:
8320:
8259:
8198:
8166:
8127:
8088:
7897:
7836:
7775:
7700:
7663:
7607:
7570:
7470:
7430:
7222:
7184:
7149:
7037:
7010:
6983:
6948:
6913:
6846:
6746:
6550:
6453:
6281:
6233:
5996:
5875:
5750:
5638:
5548:
5419:
5393:relativistic effects
5373:
5159:
5100:
4822:
4788:
4669:
4637:
4530:
4464:
4430:
4335:
4280:
4181:
4142:
4138:, where the indices
4078:
3978:
3915:
3852:
3822:
3787:
3688:
3409:
3314:
3194:
3120:
3085:
3053:
3018:
2986:
2937:
2877:
2857:
2837:
2817:
2764:
2760:where the energy is
2622:
2593:
2566:
2539:
2512:
2489:
2469:
2442:
2415:
2388:
2361:
2329:
2276:
2241:
2206:
2153:
2118:
2083:
2003:
1938:
1624:
1587:
1552:
1459:
1225:
1152:
1126:
1100:
1080:
1028:
1024:configuration space
959:
930:
901:
855:
565:
555:quantum entanglement
519:Schrödinger equation
515:closed-form solution
13182:2010PhRvL.105f3001K
13042:1992PhRvA..46.2378D
12993:2007PhRvA..75f0101S
12933:1990PhRvA..41.1247B
12877:1999PhST...83...83D
12826:1995PhRvL..74.4791Y
12783:1994CPL...229..486D
12537:The PubChem Project
12306:
12273:
11527:
11492:
10006:
9987:
9871:
9118:
8818:
8620:
8595:
8480:
8183:
7493:
7245:
6796:
6635:
6600:
6366:
6331:
6074:
6039:
5828:
5619:
5025:
4953:
4846:
4803:{\displaystyle S=1}
4688:
4652:{\displaystyle S=0}
4619:
4568:
4481:
4449:
4068:Pauli approximation
3811:{\textstyle (2l+1)}
3109:{\textstyle 2s+1=3}
3068:{\displaystyle S=1}
3042:{\textstyle 2s+1=1}
3001:{\displaystyle S=0}
2114:based on solutions
1303:
1268:
681:
523:Hartree–Fock method
360: g·mol
28:
12473:Isotopes of helium
12369:
12292:
12253:
12105:
11872:
11839:
11806:and J is known as
11792:
11747:
11673:
11598:
11506:
11471:
11383:
11300:
11262:
11160:
11072:
11043:
10878:
10736:
10566:
10265:
10108:
10060:
9992:
9973:
9910:
9857:
9731:
9610:
9566:
9363:
9327:
9104:
9039:
8961:
8880:
8804:
8628:
8606:
8581:
8440:
8420:
8367:
8306:
8245:
8184:
8169:
8152:
8113:
8074:
7883:
7822:
7758:
7686:
7649:
7593:
7553:
7473:
7456:
7416:
7225:
7205:
7170:
7135:
7026:{\textstyle H_{2}}
7023:
6999:{\textstyle H_{1}}
6996:
6969:
6934:
6899:
6832:
6780:
6732:
6619:
6584:
6525:
6437:
6350:
6315:
6263:
6213:
6058:
6023:
5972:
5857:
5812:
5732:
5620:
5603:
5529:
5381:
5359:
5350:
5285:
5220:
5145:
5080:
5078:
5070:↓ ↓
5059:
5006:
4998:↑ ↑
4987:
4937:
4923:↓ ↑
4917:↑ ↓
4892:
4830:
4800:
4773:
4768:↓ ↑
4762:↑ ↓
4737:
4672:
4649:
4620:
4603:
4554:
4553:
4516:
4467:
4450:
4433:
4410:
4404:
4398:↓ ↓
4386:↓ ↑
4372:↑ ↓
4360:↑ ↑
4319:
4266:
4196:
4167:
4128:
4074:with 4 components
4056:
3964:
3901:
3834:
3808:
3770:
3675:
3673:
3393:
3301:
3165:
3106:
3065:
3039:
2998:
2969:
2923:
2863:
2843:
2823:
2803:
2748:
2609:{\textstyle S_{z}}
2606:
2582:{\textstyle S^{2}}
2579:
2555:{\textstyle L_{z}}
2552:
2528:{\textstyle L^{2}}
2525:
2495:
2475:
2458:{\textstyle m_{s}}
2455:
2431:{\textstyle m_{l}}
2428:
2401:
2374:
2343:
2315:
2262:
2227:
2192:
2139:
2104:
2068:
2036:
1989:
1922:
1866:
1801:
1724:
1656:
1608:
1573:
1538:
1488:
1442:
1287:
1252:
1209:
1138:
1112:
1086:
1065:
1012:
945:
916:
887:
839:
660:
629:
551:
470:Infobox references
26:
13030:Physical Review A
12921:Physical Review A
12693:978-1-4757-0578-2
12587:978-1-108-49999-6
12503:Quantum mechanics
12401:ionization energy
12304:
12271:
12251:
12059:
11808:exchange integral
11671:
11596:
11561:
11504:
11469:
11381:
11347:
11332:
11292:
11231:
11192:
11140:
11070:
11013:
10995:
10826:
10734:
10695:
10662:
10626:
10518:
10412:
10381:
10213:
10106:
10009:
10008:
9908:
9843:
9729:
9691:
9607:
9542:
9485:
9450:
9417:
9361:
9325:
9296:
9237:
9178:
9120:
9037:
8959:
8945:
8876:
8820:
8645:many-body problem
8621:
8596:
8569:
7293:
7292:
6979:are eigenkets of
6830:
6778:
6704:
6669:
6617:
6582:
6523:
6435:
6400:
6348:
6313:
6208:
6147:
6110:
6056:
6021:
5871:spatial function
5634:spatial function
5318:
5317:
5253:
5252:
5185:
5184:
4911:
4910:
4860:
4859:
4756:
4755:
4702:
4701:
4541:
4184:
3974:. Note that here
3468:
3467:
3246:
3245:
2866:{\displaystyle L}
2846:{\displaystyle S}
2826:{\displaystyle n}
2027:
1854:
1789:
1712:
1644:
1476:
1437:
1376:
1339:
1285:
1250:
1170:
1089:{\displaystyle Z}
885:
837:
755:
730:
658:
608:
478:Chemical compound
476:
475:
103:Interactive image
13242:
13210:
13209:
13175:
13155:
13149:
13148:
13142:
13134:
13122:
13113:
13112:
13095:
13089:
13084:
13078:
13077:
13021:
13015:
13014:
13012:
12976:
12967:
12961:
12960:
12916:
12910:
12903:
12897:
12896:
12860:
12854:
12853:
12809:
12803:
12802:
12766:
12760:
12759:
12751:
12745:
12744:
12736:
12730:
12729:
12709:
12698:
12697:
12669:
12663:
12662:
12646:
12640:
12639:
12621:
12615:
12614:
12612:
12603:
12592:
12591:
12563:
12554:
12551:
12545:
12544:
12529:
12461:
12459:
12456:
12450:
12444:
12441:
12435:
12433:
12430:
12424:
12422:
12419:
12413:
12411:
12408:
12378:
12376:
12375:
12370:
12368:
12367:
12362:
12356:
12355:
12346:
12345:
12340:
12334:
12333:
12321:
12320:
12315:
12305:
12302:
12300:
12288:
12287:
12282:
12272:
12269:
12267:
12252:
12250:
12249:
12244:
12243:
12238:
12229:
12228:
12223:
12217:
12211:
12210:
12209:
12196:
12191:
12190:
12185:
12176:
12175:
12157:
12156:
12151:
12142:
12141:
12114:
12112:
12111:
12106:
12104:
12103:
12098:
12092:
12091:
12082:
12081:
12076:
12070:
12069:
12060:
12058:
12057:
12052:
12051:
12046:
12037:
12036:
12031:
12025:
12019:
12018:
12017:
12004:
12002:
12001:
11996:
11987:
11986:
11981:
11972:
11971:
11956:
11951:
11950:
11945:
11936:
11935:
11930:
11921:
11920:
11911:
11881:
11879:
11878:
11873:
11871:
11870:
11848:
11846:
11845:
11840:
11838:
11837:
11801:
11799:
11798:
11793:
11779:
11778:
11756:
11754:
11753:
11748:
11746:
11745:
11727:
11726:
11708:
11707:
11682:
11680:
11679:
11674:
11672:
11670:
11669:
11664:
11663:
11658:
11649:
11648:
11643:
11637:
11631:
11630:
11629:
11616:
11607:
11605:
11604:
11599:
11597:
11595:
11594:
11585:
11584:
11583:
11567:
11562:
11560:
11559:
11550:
11549:
11548:
11532:
11526:
11521:
11520:
11519:
11505:
11497:
11491:
11486:
11485:
11484:
11470:
11462:
11454:
11453:
11417:
11415:
11412:
11403:
11392:
11390:
11389:
11384:
11382:
11379:
11368:
11367:
11358:
11357:
11352:
11348:
11340:
11333:
11325:
11315:screening effect
11309:
11307:
11306:
11301:
11293:
11285:
11271:
11269:
11268:
11263:
11255:
11251:
11250:
11249:
11240:
11236:
11232:
11224:
11219:
11218:
11193:
11191:
11180:
11169:
11167:
11166:
11161:
11159:
11158:
11149:
11145:
11141:
11133:
11128:
11127:
11081:
11079:
11078:
11073:
11071:
11063:
11052:
11050:
11049:
11044:
11042:
11038:
11037:
11018:
11014:
11006:
11000:
10996:
10994:
10993:
10992:
10976:
10975:
10966:
10939:
10938:
10929:
10928:
10887:
10885:
10884:
10879:
10877:
10876:
10872:
10864:
10863:
10851:
10850:
10827:
10825:
10824:
10823:
10810:
10809:
10800:
10792:
10791:
10786:
10777:
10776:
10771:
10745:
10743:
10742:
10737:
10735:
10732:
10706:
10705:
10696:
10688:
10683:
10682:
10667:
10663:
10661:
10660:
10659:
10643:
10642:
10633:
10627:
10625:
10614:
10609:
10608:
10575:
10573:
10572:
10567:
10565:
10564:
10559:
10553:
10552:
10542:
10541:
10536:
10530:
10529:
10519:
10517:
10516:
10511:
10510:
10505:
10496:
10495:
10490:
10484:
10478:
10477:
10473:
10465:
10464:
10452:
10451:
10428:
10423:
10422:
10417:
10413:
10411:
10410:
10409:
10393:
10386:
10382:
10380:
10379:
10378:
10362:
10361:
10352:
10343:
10342:
10324:
10323:
10305:
10304:
10274:
10272:
10271:
10266:
10264:
10263:
10259:
10251:
10250:
10238:
10237:
10214:
10212:
10211:
10210:
10194:
10186:
10185:
10180:
10170:
10169:
10164:
10155:
10154:
10138:
10117:
10115:
10114:
10109:
10107:
10099:
10090:
10069:
10067:
10066:
10061:
10059:
10058:
10054:
10053:
10041:
10040:
10028:
10027:
10010:
10007:
10005:
10000:
9986:
9981:
9972:
9971:
9963:
9962:
9949:
9948:
9936:
9935:
9919:
9917:
9916:
9911:
9909:
9907:
9906:
9905:
9896:
9895:
9882:
9881:
9880:
9870:
9865:
9852:
9844:
9842:
9841:
9840:
9831:
9830:
9817:
9816:
9815:
9806:
9805:
9780:
9772:
9771:
9755:
9746:
9740:
9738:
9737:
9732:
9730:
9725:
9724:
9723:
9714:
9713:
9700:
9692:
9687:
9686:
9685:
9657:
9630:
9619:
9617:
9616:
9611:
9609:
9608:
9603:
9595:
9585:
9575:
9573:
9572:
9567:
9562:
9561:
9543:
9541:
9540:
9531:
9530:
9529:
9513:
9505:
9504:
9486:
9484:
9483:
9474:
9473:
9472:
9456:
9451:
9449:
9448:
9439:
9438:
9437:
9424:
9419:
9418:
9413:
9405:
9395:
9388:Screening effect
9383:
9381:
9378:
9372:
9370:
9369:
9364:
9362:
9359:
9336:
9334:
9333:
9328:
9326:
9324:
9323:
9314:
9313:
9312:
9299:
9297:
9289:
9284:
9283:
9278:
9272:
9271:
9262:
9261:
9256:
9250:
9249:
9240:
9239:
9238:
9236:
9235:
9226:
9222:
9221:
9209:
9208:
9189:
9179:
9177:
9176:
9171:
9170:
9165:
9156:
9155:
9150:
9144:
9138:
9137:
9136:
9123:
9121:
9119:
9117:
9112:
9103:
9102:
9092:
9091:
9082:
9071:
9070:
9048:
9046:
9045:
9040:
9038:
9036:
9035:
9030:
9029:
9024:
9015:
9014:
9009:
9003:
8997:
8996:
8995:
8982:
8970:
8968:
8967:
8962:
8960:
8957:
8946:
8944:
8943:
8934:
8933:
8932:
8919:
8908:
8907:
8889:
8887:
8886:
8881:
8879:
8878:
8877:
8875:
8874:
8865:
8861:
8860:
8848:
8847:
8831:
8821:
8819:
8817:
8812:
8799:
8798:
8789:
8781:
8780:
8768:
8767:
8743:
8742:
8730:
8729:
8702:
8701:
8688:
8687:
8675:
8674:
8637:
8635:
8634:
8629:
8627:
8623:
8622:
8619:
8614:
8602:
8597:
8594:
8589:
8577:
8570:
8568:
8567:
8566:
8553:
8552:
8551:
8542:
8541:
8528:
8520:
8519:
8518:
8517:
8500:
8499:
8498:
8497:
8479:
8468:
8467:
8466:
8454:
8453:
8429:
8427:
8426:
8421:
8419:
8418:
8406:
8405:
8376:
8374:
8373:
8368:
8363:
8362:
8349:
8348:
8315:
8313:
8312:
8307:
8302:
8301:
8288:
8287:
8254:
8252:
8251:
8246:
8241:
8240:
8227:
8226:
8193:
8191:
8190:
8185:
8182:
8177:
8161:
8159:
8158:
8153:
8145:
8134:
8122:
8120:
8119:
8114:
8106:
8095:
8083:
8081:
8080:
8075:
8070:
8069:
8064:
8055:
8054:
8053:
8052:
8040:
8039:
8027:
8026:
8009:
8008:
8003:
7994:
7993:
7992:
7991:
7979:
7978:
7966:
7965:
7945:
7944:
7939:
7930:
7929:
7924:
7915:
7914:
7892:
7890:
7889:
7884:
7879:
7878:
7865:
7864:
7851:
7850:
7831:
7829:
7828:
7823:
7818:
7817:
7804:
7803:
7790:
7789:
7767:
7765:
7764:
7759:
7757:
7756:
7741:
7740:
7728:
7727:
7712:
7711:
7695:
7693:
7692:
7687:
7685:
7684:
7675:
7674:
7658:
7656:
7655:
7650:
7648:
7647:
7632:
7631:
7619:
7618:
7602:
7600:
7599:
7594:
7592:
7591:
7582:
7581:
7562:
7560:
7559:
7554:
7549:
7548:
7543:
7534:
7533:
7521:
7520:
7515:
7506:
7505:
7492:
7481:
7465:
7463:
7462:
7457:
7455:
7454:
7442:
7441:
7425:
7423:
7422:
7417:
7409:
7408:
7403:
7394:
7393:
7381:
7380:
7375:
7366:
7365:
7350:
7349:
7344:
7335:
7334:
7322:
7321:
7316:
7307:
7306:
7294:
7288:
7284:
7276:
7275:
7270:
7260:
7259:
7254:
7244:
7233:
7215:is carried out.
7214:
7212:
7211:
7206:
7201:
7200:
7191:
7179:
7177:
7176:
7171:
7166:
7165:
7156:
7144:
7142:
7141:
7136:
7131:
7130:
7125:
7116:
7115:
7103:
7102:
7097:
7088:
7087:
7072:
7071:
7066:
7057:
7056:
7051:
7032:
7030:
7029:
7024:
7022:
7021:
7005:
7003:
7002:
6997:
6995:
6994:
6978:
6976:
6975:
6970:
6965:
6964:
6955:
6943:
6941:
6940:
6935:
6930:
6929:
6920:
6908:
6906:
6905:
6900:
6895:
6894:
6885:
6877:
6876:
6867:
6853:
6841:
6839:
6838:
6833:
6831:
6829:
6828:
6819:
6818:
6817:
6801:
6795:
6790:
6785:
6779:
6777:
6766:
6758:
6757:
6741:
6739:
6738:
6733:
6731:
6730:
6718:
6717:
6705:
6703:
6702:
6693:
6692:
6691:
6675:
6670:
6668:
6667:
6658:
6657:
6656:
6640:
6634:
6629:
6624:
6618:
6616:
6605:
6599:
6594:
6589:
6583:
6581:
6570:
6562:
6561:
6545:
6534:
6532:
6531:
6526:
6524:
6522:
6521:
6516:
6515:
6510:
6501:
6500:
6495:
6489:
6483:
6482:
6481:
6468:
6463:
6446:
6444:
6443:
6438:
6436:
6434:
6433:
6424:
6423:
6422:
6406:
6401:
6399:
6398:
6389:
6388:
6387:
6371:
6365:
6360:
6355:
6349:
6347:
6336:
6330:
6325:
6320:
6314:
6312:
6301:
6293:
6292:
6272:
6270:
6269:
6264:
6262:
6251:
6250:
6222:
6220:
6219:
6214:
6209:
6207:
6206:
6201:
6200:
6195:
6186:
6185:
6180:
6174:
6168:
6167:
6166:
6153:
6148:
6146:
6145:
6140:
6134:
6133:
6132:
6116:
6111:
6109:
6108:
6103:
6097:
6096:
6095:
6079:
6073:
6068:
6063:
6057:
6055:
6044:
6038:
6033:
6028:
6022:
6020:
6009:
5981:
5979:
5978:
5973:
5968:
5967:
5962:
5952:
5951:
5946:
5937:
5936:
5918:
5917:
5912:
5902:
5901:
5896:
5887:
5886:
5866:
5864:
5863:
5858:
5827:
5822:
5817:
5808:
5807:
5802:
5792:
5791:
5786:
5777:
5776:
5764:
5763:
5758:
5741:
5739:
5738:
5733:
5728:
5727:
5722:
5712:
5711:
5706:
5697:
5696:
5681:
5680:
5675:
5665:
5664:
5659:
5650:
5649:
5629:
5627:
5626:
5621:
5618:
5613:
5608:
5599:
5598:
5593:
5583:
5582:
5577:
5568:
5567:
5555:
5538:
5536:
5535:
5530:
5522:
5521:
5516:
5506:
5505:
5500:
5491:
5490:
5482:
5467:
5466:
5461:
5451:
5450:
5445:
5436:
5435:
5427:
5390:
5388:
5387:
5382:
5380:
5368:
5366:
5365:
5360:
5355:
5354:
5319:
5313:
5309:
5304:
5303:
5290:
5289:
5254:
5248:
5244:
5239:
5238:
5225:
5224:
5186:
5180:
5176:
5171:
5170:
5154:
5152:
5151:
5146:
5141:
5140:
5128:
5127:
5115:
5114:
5089:
5087:
5086:
5081:
5079:
5064:
5063:
5024:
5019:
5011:
4992:
4991:
4952:
4947:
4942:
4935:
4912:
4906:
4902:
4897:
4896:
4861:
4855:
4851:
4845:
4840:
4835:
4828:
4809:
4807:
4806:
4801:
4782:
4780:
4779:
4774:
4757:
4751:
4747:
4742:
4741:
4703:
4697:
4693:
4687:
4682:
4677:
4658:
4656:
4655:
4650:
4629:
4627:
4626:
4621:
4618:
4613:
4608:
4599:
4598:
4593:
4583:
4582:
4577:
4567:
4562:
4552:
4537:
4525:
4523:
4522:
4517:
4512:
4511:
4506:
4496:
4495:
4490:
4480:
4475:
4459:
4457:
4456:
4451:
4448:
4443:
4438:
4419:
4417:
4416:
4411:
4409:
4408:
4401:
4400:
4389:
4388:
4375:
4374:
4363:
4362:
4342:
4328:
4326:
4325:
4320:
4318:
4317:
4305:
4300:
4299:
4287:
4275:
4273:
4272:
4267:
4259:
4258:
4253:
4247:
4246:
4234:
4229:
4228:
4223:
4214:
4213:
4208:
4195:
4176:
4174:
4173:
4168:
4137:
4135:
4134:
4129:
4124:
4123:
4118:
4108:
4107:
4102:
4093:
4092:
4065:
4063:
4062:
4057:
4055:
4054:
4042:
4037:
4036:
4024:
4016:
4015:
4003:
3998:
3997:
3985:
3973:
3971:
3970:
3965:
3960:
3959:
3947:
3938:
3937:
3925:
3910:
3908:
3907:
3902:
3897:
3896:
3884:
3875:
3874:
3862:
3843:
3841:
3840:
3837:{\textstyle l=0}
3835:
3817:
3815:
3814:
3809:
3779:
3777:
3776:
3771:
3766:
3765:
3760:
3750:
3749:
3744:
3723:
3722:
3717:
3708:
3707:
3702:
3684:
3682:
3681:
3676:
3674:
3660:
3649:
3637:
3636:
3606:
3589:
3578:
3566:
3565:
3538:
3530:
3513:
3502:
3488:
3477:
3469:
3463:
3459:
3451:
3450:
3423:
3415:
3402:
3400:
3399:
3394:
3389:
3388:
3383:
3373:
3372:
3367:
3349:
3348:
3343:
3334:
3333:
3328:
3310:
3308:
3307:
3302:
3291:
3280:
3266:
3255:
3247:
3241:
3237:
3229:
3228:
3201:
3174:
3172:
3171:
3166:
3164:
3163:
3154:
3153:
3141:
3140:
3115:
3113:
3112:
3107:
3074:
3072:
3071:
3066:
3048:
3046:
3045:
3040:
3007:
3005:
3004:
2999:
2978:
2976:
2975:
2970:
2968:
2967:
2958:
2957:
2932:
2930:
2929:
2924:
2904:
2890:
2872:
2870:
2869:
2864:
2852:
2850:
2849:
2844:
2832:
2830:
2829:
2824:
2812:
2810:
2809:
2804:
2757:
2755:
2754:
2749:
2741:
2740:
2722:
2721:
2700:
2695:
2694:
2673:
2672:
2654:
2653:
2632:
2615:
2613:
2612:
2607:
2605:
2604:
2588:
2586:
2585:
2580:
2578:
2577:
2561:
2559:
2558:
2553:
2551:
2550:
2534:
2532:
2531:
2526:
2524:
2523:
2504:
2502:
2501:
2496:
2484:
2482:
2481:
2476:
2464:
2462:
2461:
2456:
2454:
2453:
2437:
2435:
2434:
2429:
2427:
2426:
2410:
2408:
2407:
2402:
2400:
2399:
2383:
2381:
2380:
2375:
2373:
2372:
2352:
2350:
2349:
2344:
2336:
2324:
2322:
2321:
2316:
2311:
2310:
2301:
2293:
2292:
2283:
2271:
2269:
2268:
2263:
2258:
2257:
2248:
2236:
2234:
2233:
2228:
2223:
2222:
2213:
2201:
2199:
2198:
2193:
2188:
2187:
2178:
2170:
2169:
2160:
2148:
2146:
2145:
2140:
2135:
2134:
2125:
2113:
2111:
2110:
2105:
2100:
2099:
2090:
2077:
2075:
2074:
2069:
2064:
2063:
2054:
2049:
2048:
2035:
2020:
2019:
2010:
1998:
1996:
1995:
1990:
1982:
1981:
1972:
1958:
1957:
1948:
1931:
1929:
1928:
1923:
1915:
1914:
1905:
1897:
1896:
1887:
1879:
1878:
1865:
1847:
1846:
1837:
1829:
1828:
1819:
1814:
1813:
1800:
1779:
1778:
1769:
1758:
1757:
1748:
1737:
1736:
1723:
1705:
1704:
1695:
1687:
1686:
1677:
1669:
1668:
1655:
1634:
1617:
1615:
1614:
1609:
1604:
1603:
1594:
1582:
1580:
1579:
1574:
1569:
1568:
1559:
1547:
1545:
1544:
1539:
1534:
1533:
1524:
1516:
1515:
1506:
1501:
1500:
1487:
1466:
1451:
1449:
1448:
1443:
1438:
1436:
1435:
1430:
1429:
1424:
1415:
1414:
1409:
1403:
1397:
1396:
1395:
1382:
1377:
1375:
1374:
1369:
1363:
1362:
1361:
1345:
1340:
1338:
1337:
1332:
1326:
1325:
1324:
1308:
1302:
1297:
1292:
1286:
1284:
1273:
1267:
1262:
1257:
1251:
1249:
1238:
1218:
1216:
1215:
1210:
1208:
1207:
1206:
1205:
1188:
1187:
1186:
1185:
1171:
1166:
1165:
1156:
1147:
1145:
1144:
1139:
1121:
1119:
1118:
1113:
1095:
1093:
1092:
1087:
1074:
1072:
1071:
1066:
1061:
1060:
1055:
1045:
1044:
1039:
1021:
1019:
1018:
1013:
1011:
1006:
1005:
1000:
991:
990:
985:
979:
971:
970:
954:
952:
951:
946:
944:
943:
938:
925:
923:
922:
917:
915:
914:
909:
896:
894:
893:
888:
886:
884:
873:
865:
848:
846:
845:
840:
838:
836:
835:
834:
825:
824:
808:
807:
798:
793:
792:
791:
790:
773:
772:
771:
770:
756:
751:
750:
741:
736:
732:
731:
729:
728:
727:
718:
717:
701:
700:
699:
686:
680:
675:
674:
673:
659:
657:
649:
648:
639:
628:
601:
600:
595:
585:
584:
579:
460:
454:
451:
450:
432:
403:
383:Thermochemistry
359:
358:
344:
337:Chemical formula
270:
234:
223:
212:
195:
173:Gmelin Reference
156:
145:
125:
105:
81:
36:
29:
25:
13250:
13249:
13245:
13244:
13243:
13241:
13240:
13239:
13215:
13214:
13213:
13160:Phys. Rev. Lett
13156:
13152:
13136:
13135:
13123:
13116:
13109:
13097:
13096:
13092:
13085:
13081:
13022:
13018:
12974:
12968:
12964:
12917:
12913:
12904:
12900:
12865:Physica Scripta
12861:
12857:
12810:
12806:
12767:
12763:
12752:
12748:
12737:
12733:
12726:10.18434/t4w30f
12710:
12701:
12694:
12678:. p. 274.
12670:
12666:
12647:
12643:
12636:
12622:
12618:
12610:
12604:
12595:
12588:
12564:
12557:
12552:
12548:
12531:
12530:
12526:
12522:
12517:
12468:
12457:
12454:
12452:
12451:, which equals
12442:
12439:
12437:
12431:
12428:
12426:
12420:
12417:
12415:
12409:
12406:
12404:
12399:Helium's first
12397:
12392:
12386:
12363:
12358:
12357:
12351:
12347:
12341:
12336:
12335:
12329:
12325:
12316:
12311:
12310:
12301:
12296:
12283:
12278:
12277:
12268:
12257:
12245:
12239:
12234:
12233:
12224:
12219:
12218:
12213:
12212:
12205:
12201:
12197:
12195:
12186:
12181:
12180:
12165:
12161:
12152:
12147:
12146:
12137:
12133:
12119:
12116:
12115:
12099:
12094:
12093:
12087:
12083:
12077:
12072:
12071:
12065:
12061:
12053:
12047:
12042:
12041:
12032:
12027:
12026:
12021:
12020:
12013:
12009:
12005:
12003:
11997:
11992:
11991:
11982:
11977:
11976:
11961:
11957:
11952:
11946:
11941:
11940:
11931:
11926:
11925:
11916:
11912:
11907:
11893:
11890:
11889:
11860:
11856:
11854:
11851:
11850:
11827:
11823:
11821:
11818:
11817:
11813:exchange energy
11804:direct integral
11768:
11764:
11762:
11759:
11758:
11735:
11731:
11716:
11712:
11703:
11699:
11691:
11688:
11687:
11665:
11659:
11654:
11653:
11644:
11639:
11638:
11633:
11632:
11625:
11621:
11617:
11615:
11613:
11610:
11609:
11590:
11586:
11579:
11575:
11568:
11566:
11555:
11551:
11544:
11540:
11533:
11531:
11522:
11515:
11511:
11510:
11496:
11487:
11480:
11476:
11475:
11461:
11449:
11445:
11443:
11440:
11439:
11436:
11413:
11410:
11408:
11402:
11396:
11378:
11363:
11359:
11353:
11339:
11335:
11334:
11324:
11322:
11319:
11318:
11284:
11276:
11273:
11272:
11245:
11241:
11223:
11214:
11210:
11203:
11199:
11198:
11194:
11184:
11179:
11177:
11174:
11173:
11154:
11150:
11132:
11123:
11119:
11112:
11108:
11094:
11091:
11090:
11088:
11062:
11060:
11057:
11056:
11030:
11026:
11022:
11005:
11001:
10988:
10984:
10977:
10971:
10967:
10965:
10961:
10934:
10930:
10924:
10920:
10903:
10900:
10899:
10868:
10859:
10855:
10846:
10842:
10832:
10828:
10819:
10815:
10811:
10805:
10801:
10799:
10787:
10782:
10781:
10772:
10767:
10766:
10758:
10755:
10754:
10731:
10701:
10697:
10687:
10678:
10674:
10655:
10651:
10644:
10638:
10634:
10632:
10628:
10618:
10613:
10604:
10600:
10583:
10580:
10579:
10560:
10555:
10554:
10548:
10544:
10537:
10532:
10531:
10525:
10521:
10512:
10506:
10501:
10500:
10491:
10486:
10485:
10480:
10479:
10469:
10460:
10456:
10447:
10443:
10433:
10429:
10427:
10418:
10405:
10401:
10397:
10392:
10388:
10387:
10374:
10370:
10363:
10357:
10353:
10351:
10347:
10338:
10334:
10316:
10312:
10300:
10296:
10279:
10276:
10275:
10255:
10246:
10242:
10233:
10229:
10219:
10215:
10206:
10202:
10198:
10193:
10181:
10176:
10175:
10165:
10160:
10159:
10150:
10146:
10144:
10141:
10140:
10137:
10131:
10124:
10098:
10096:
10093:
10092:
10085:
10083:
10076:
10049:
10045:
10036:
10032:
10023:
10019:
10015:
10011:
10001:
9996:
9988:
9982:
9977:
9970:
9958:
9954:
9944:
9940:
9931:
9927:
9925:
9922:
9921:
9901:
9897:
9891:
9887:
9883:
9876:
9872:
9866:
9861:
9853:
9851:
9836:
9832:
9826:
9822:
9818:
9811:
9807:
9801:
9797:
9781:
9779:
9767:
9763:
9761:
9758:
9757:
9754:
9748:
9742:
9719:
9715:
9709:
9705:
9701:
9699:
9681:
9677:
9658:
9656:
9636:
9633:
9632:
9621:
9596:
9594:
9593:
9591:
9588:
9587:
9576:
9557:
9553:
9536:
9532:
9525:
9521:
9514:
9512:
9500:
9496:
9479:
9475:
9468:
9464:
9457:
9455:
9444:
9440:
9433:
9429:
9425:
9423:
9406:
9404:
9403:
9401:
9398:
9397:
9393:
9390:
9379:
9376:
9374:
9358:
9344:
9341:
9340:
9319:
9315:
9308:
9304:
9300:
9298:
9288:
9279:
9274:
9273:
9267:
9263:
9257:
9252:
9251:
9245:
9241:
9231:
9227:
9217:
9213:
9204:
9200:
9190:
9188:
9184:
9180:
9172:
9166:
9161:
9160:
9151:
9146:
9145:
9140:
9139:
9132:
9128:
9124:
9122:
9113:
9108:
9098:
9094:
9093:
9087:
9083:
9081:
9060:
9056:
9054:
9051:
9050:
9031:
9025:
9020:
9019:
9010:
9005:
9004:
8999:
8998:
8991:
8987:
8983:
8981:
8979:
8976:
8975:
8956:
8939:
8935:
8928:
8924:
8920:
8918:
8903:
8899:
8897:
8894:
8893:
8870:
8866:
8856:
8852:
8843:
8839:
8832:
8830:
8826:
8822:
8813:
8808:
8800:
8794:
8790:
8788:
8776:
8772:
8751:
8747:
8738:
8734:
8713:
8709:
8697:
8693:
8683:
8679:
8670:
8666:
8664:
8661:
8660:
8657:
8615:
8610:
8601:
8590:
8585:
8576:
8575:
8571:
8562:
8558:
8554:
8547:
8543:
8537:
8533:
8529:
8527:
8513:
8509:
8508:
8504:
8493:
8489:
8488:
8484:
8469:
8462:
8458:
8449:
8445:
8444:
8438:
8435:
8434:
8414:
8410:
8401:
8397:
8389:
8386:
8385:
8358:
8354:
8344:
8340:
8321:
8318:
8317:
8297:
8293:
8283:
8279:
8260:
8257:
8256:
8236:
8232:
8222:
8218:
8199:
8196:
8195:
8178:
8173:
8167:
8164:
8163:
8141:
8130:
8128:
8125:
8124:
8102:
8091:
8089:
8086:
8085:
8065:
8060:
8059:
8048:
8044:
8035:
8031:
8022:
8018:
8017:
8013:
8004:
7999:
7998:
7987:
7983:
7974:
7970:
7961:
7957:
7956:
7952:
7940:
7935:
7934:
7925:
7920:
7919:
7904:
7900:
7898:
7895:
7894:
7874:
7870:
7860:
7856:
7846:
7842:
7837:
7834:
7833:
7813:
7809:
7799:
7795:
7785:
7781:
7776:
7773:
7772:
7749:
7745:
7736:
7732:
7720:
7716:
7707:
7703:
7701:
7698:
7697:
7680:
7676:
7670:
7666:
7664:
7661:
7660:
7640:
7636:
7627:
7623:
7614:
7610:
7608:
7605:
7604:
7587:
7583:
7577:
7573:
7571:
7568:
7567:
7544:
7539:
7538:
7529:
7525:
7516:
7511:
7510:
7501:
7497:
7482:
7477:
7471:
7468:
7467:
7450:
7446:
7437:
7433:
7431:
7428:
7427:
7404:
7399:
7398:
7389:
7385:
7376:
7371:
7370:
7361:
7357:
7345:
7340:
7339:
7330:
7326:
7317:
7312:
7311:
7302:
7298:
7283:
7271:
7266:
7265:
7255:
7250:
7249:
7234:
7229:
7223:
7220:
7219:
7196:
7192:
7187:
7185:
7182:
7181:
7161:
7157:
7152:
7150:
7147:
7146:
7126:
7121:
7120:
7111:
7107:
7098:
7093:
7092:
7083:
7079:
7067:
7062:
7061:
7052:
7047:
7046:
7038:
7035:
7034:
7017:
7013:
7011:
7008:
7007:
6990:
6986:
6984:
6981:
6980:
6960:
6956:
6951:
6949:
6946:
6945:
6925:
6921:
6916:
6914:
6911:
6910:
6890:
6886:
6881:
6872:
6868:
6863:
6849:
6847:
6844:
6843:
6824:
6820:
6813:
6809:
6802:
6800:
6791:
6786:
6781:
6770:
6765:
6753:
6749:
6747:
6744:
6743:
6726:
6722:
6713:
6709:
6698:
6694:
6687:
6683:
6676:
6674:
6663:
6659:
6652:
6648:
6641:
6639:
6630:
6625:
6620:
6609:
6604:
6595:
6590:
6585:
6574:
6569:
6557:
6553:
6551:
6548:
6547:
6544:
6538:
6517:
6511:
6506:
6505:
6496:
6491:
6490:
6485:
6484:
6477:
6473:
6469:
6467:
6456:
6454:
6451:
6450:
6429:
6425:
6418:
6414:
6407:
6405:
6394:
6390:
6383:
6379:
6372:
6370:
6361:
6356:
6351:
6340:
6335:
6326:
6321:
6316:
6305:
6300:
6288:
6284:
6282:
6279:
6278:
6255:
6246:
6242:
6234:
6231:
6230:
6202:
6196:
6191:
6190:
6181:
6176:
6175:
6170:
6169:
6162:
6158:
6154:
6152:
6141:
6136:
6135:
6128:
6124:
6117:
6115:
6104:
6099:
6098:
6091:
6087:
6080:
6078:
6069:
6064:
6059:
6048:
6043:
6034:
6029:
6024:
6013:
6008:
5997:
5994:
5993:
5988:
5963:
5958:
5957:
5947:
5942:
5941:
5932:
5928:
5913:
5908:
5907:
5897:
5892:
5891:
5882:
5878:
5876:
5873:
5872:
5823:
5818:
5813:
5803:
5798:
5797:
5787:
5782:
5781:
5772:
5768:
5759:
5754:
5753:
5751:
5748:
5747:
5723:
5718:
5717:
5707:
5702:
5701:
5692:
5688:
5676:
5671:
5670:
5660:
5655:
5654:
5645:
5641:
5639:
5636:
5635:
5614:
5609:
5604:
5594:
5589:
5588:
5578:
5573:
5572:
5563:
5559:
5551:
5549:
5546:
5545:
5517:
5512:
5511:
5501:
5496:
5495:
5483:
5478:
5477:
5462:
5457:
5456:
5446:
5441:
5440:
5428:
5423:
5422:
5420:
5417:
5416:
5376:
5374:
5371:
5370:
5349:
5348:
5343:
5337:
5336:
5331:
5321:
5320:
5308:
5299:
5295:
5284:
5283:
5278:
5272:
5271:
5266:
5256:
5255:
5243:
5234:
5230:
5219:
5218:
5210:
5204:
5203:
5198:
5188:
5187:
5175:
5166:
5162:
5160:
5157:
5156:
5136:
5132:
5123:
5119:
5110:
5106:
5101:
5098:
5097:
5077:
5076:
5058:
5057:
5052:
5046:
5045:
5040:
5030:
5029:
5020:
5012:
5007:
4986:
4985:
4980:
4974:
4973:
4968:
4958:
4957:
4948:
4943:
4938:
4933:
4932:
4901:
4891:
4890:
4885:
4879:
4878:
4873:
4863:
4862:
4850:
4841:
4836:
4831:
4825:
4823:
4820:
4819:
4789:
4786:
4785:
4783:
4746:
4736:
4735:
4730:
4721:
4720:
4715:
4705:
4704:
4692:
4683:
4678:
4673:
4670:
4667:
4666:
4638:
4635:
4634:
4614:
4609:
4604:
4594:
4589:
4588:
4578:
4573:
4572:
4563:
4558:
4545:
4533:
4531:
4528:
4527:
4507:
4502:
4501:
4491:
4486:
4485:
4476:
4471:
4465:
4462:
4461:
4444:
4439:
4434:
4431:
4428:
4427:
4403:
4402:
4396:
4392:
4390:
4384:
4380:
4377:
4376:
4370:
4366:
4364:
4358:
4354:
4347:
4346:
4338:
4336:
4333:
4332:
4313:
4309:
4301:
4295:
4291:
4283:
4281:
4278:
4277:
4254:
4249:
4248:
4239:
4235:
4230:
4224:
4219:
4218:
4209:
4204:
4203:
4188:
4182:
4179:
4178:
4143:
4140:
4139:
4119:
4114:
4113:
4103:
4098:
4097:
4085:
4081:
4079:
4076:
4075:
4050:
4046:
4038:
4032:
4028:
4020:
4011:
4007:
3999:
3993:
3989:
3981:
3979:
3976:
3975:
3955:
3951:
3943:
3933:
3929:
3921:
3916:
3913:
3912:
3892:
3888:
3880:
3870:
3866:
3858:
3853:
3850:
3849:
3823:
3820:
3819:
3788:
3785:
3784:
3761:
3756:
3755:
3745:
3740:
3739:
3718:
3713:
3712:
3703:
3698:
3697:
3689:
3686:
3685:
3672:
3671:
3656:
3645:
3611:
3607:
3602:
3585:
3574:
3543:
3539:
3534:
3528:
3527:
3509:
3498:
3484:
3473:
3458:
3428:
3424:
3419:
3412:
3410:
3407:
3406:
3384:
3379:
3378:
3368:
3363:
3362:
3344:
3339:
3338:
3329:
3324:
3323:
3315:
3312:
3311:
3287:
3276:
3262:
3251:
3236:
3206:
3202:
3197:
3195:
3192:
3191:
3159:
3155:
3149:
3145:
3136:
3132:
3121:
3118:
3117:
3086:
3083:
3082:
3054:
3051:
3050:
3019:
3016:
3015:
2987:
2984:
2983:
2963:
2959:
2944:
2940:
2938:
2935:
2934:
2900:
2886:
2878:
2875:
2874:
2858:
2855:
2854:
2838:
2835:
2834:
2818:
2815:
2814:
2765:
2762:
2761:
2736:
2732:
2717:
2713:
2696:
2684:
2680:
2668:
2664:
2649:
2645:
2628:
2623:
2620:
2619:
2600:
2596:
2594:
2591:
2590:
2573:
2569:
2567:
2564:
2563:
2546:
2542:
2540:
2537:
2536:
2519:
2515:
2513:
2510:
2509:
2490:
2487:
2486:
2470:
2467:
2466:
2449:
2445:
2443:
2440:
2439:
2422:
2418:
2416:
2413:
2412:
2395:
2391:
2389:
2386:
2385:
2368:
2364:
2362:
2359:
2358:
2332:
2330:
2327:
2326:
2306:
2302:
2297:
2288:
2284:
2279:
2277:
2274:
2273:
2253:
2249:
2244:
2242:
2239:
2238:
2218:
2214:
2209:
2207:
2204:
2203:
2183:
2179:
2174:
2165:
2161:
2156:
2154:
2151:
2150:
2130:
2126:
2121:
2119:
2116:
2115:
2095:
2091:
2086:
2084:
2081:
2080:
2059:
2055:
2050:
2041:
2037:
2031:
2015:
2011:
2006:
2004:
2001:
2000:
1977:
1973:
1968:
1953:
1949:
1944:
1939:
1936:
1935:
1910:
1906:
1901:
1892:
1888:
1883:
1871:
1867:
1858:
1842:
1838:
1833:
1824:
1820:
1815:
1806:
1802:
1793:
1774:
1770:
1765:
1753:
1749:
1744:
1729:
1725:
1716:
1700:
1696:
1691:
1682:
1678:
1673:
1661:
1657:
1648:
1630:
1625:
1622:
1621:
1599:
1595:
1590:
1588:
1585:
1584:
1564:
1560:
1555:
1553:
1550:
1549:
1529:
1525:
1520:
1511:
1507:
1502:
1493:
1489:
1480:
1462:
1460:
1457:
1456:
1431:
1425:
1420:
1419:
1410:
1405:
1404:
1399:
1398:
1391:
1387:
1383:
1381:
1370:
1365:
1364:
1357:
1353:
1346:
1344:
1333:
1328:
1327:
1320:
1316:
1309:
1307:
1298:
1293:
1288:
1277:
1272:
1263:
1258:
1253:
1242:
1237:
1226:
1223:
1222:
1201:
1197:
1196:
1192:
1181:
1177:
1176:
1172:
1161:
1157:
1155:
1153:
1150:
1149:
1127:
1124:
1123:
1101:
1098:
1097:
1081:
1078:
1077:
1056:
1051:
1050:
1040:
1035:
1034:
1029:
1026:
1025:
1007:
1001:
996:
995:
986:
981:
980:
975:
966:
962:
960:
957:
956:
939:
934:
933:
931:
928:
927:
910:
905:
904:
902:
899:
898:
874:
866:
864:
856:
853:
852:
830:
826:
820:
816:
809:
803:
799:
797:
786:
782:
781:
777:
766:
762:
761:
757:
746:
742:
740:
723:
719:
713:
709:
702:
695:
691:
687:
685:
676:
669:
665:
664:
650:
644:
640:
638:
634:
630:
612:
596:
591:
590:
580:
575:
574:
566:
563:
562:
543:
535:Albrecht Unsöld
479:
472:
467:
466:
465: ?)
456:
452:
448:
444:
421:
404:
401:
394:
391:
368:Colourless gas
356:
354:
339:
325:
320:
319:
308:
305:
304:
301:
295:
294:
273:
253:
237:
224:
198:
175:
166:
148:
128:
108:
95:
84:
71:
57:
56:
40:
37:
24:
17:
12:
11:
5:
13248:
13238:
13237:
13232:
13230:Quantum models
13227:
13212:
13211:
13150:
13114:
13108:978-0070580404
13107:
13090:
13079:
13016:
12962:
12911:
12898:
12855:
12804:
12761:
12746:
12731:
12699:
12692:
12664:
12641:
12634:
12616:
12593:
12586:
12555:
12546:
12523:
12521:
12518:
12516:
12515:
12510:
12508:Quantum states
12505:
12500:
12495:
12490:
12485:
12480:
12475:
12469:
12467:
12464:
12396:
12393:
12388:Main article:
12385:
12382:
12366:
12361:
12354:
12350:
12344:
12339:
12332:
12328:
12324:
12319:
12314:
12309:
12299:
12295:
12291:
12286:
12281:
12276:
12266:
12263:
12260:
12256:
12248:
12242:
12237:
12232:
12227:
12222:
12216:
12208:
12204:
12200:
12194:
12189:
12184:
12179:
12174:
12171:
12168:
12164:
12160:
12155:
12150:
12145:
12140:
12136:
12132:
12129:
12126:
12123:
12102:
12097:
12090:
12086:
12080:
12075:
12068:
12064:
12056:
12050:
12045:
12040:
12035:
12030:
12024:
12016:
12012:
12008:
12000:
11995:
11990:
11985:
11980:
11975:
11970:
11967:
11964:
11960:
11955:
11949:
11944:
11939:
11934:
11929:
11924:
11919:
11915:
11910:
11906:
11903:
11900:
11897:
11869:
11866:
11863:
11859:
11836:
11833:
11830:
11826:
11791:
11788:
11785:
11782:
11777:
11774:
11771:
11767:
11744:
11741:
11738:
11734:
11730:
11725:
11722:
11719:
11715:
11711:
11706:
11702:
11698:
11695:
11668:
11662:
11657:
11652:
11647:
11642:
11636:
11628:
11624:
11620:
11593:
11589:
11582:
11578:
11574:
11571:
11565:
11558:
11554:
11547:
11543:
11539:
11536:
11530:
11525:
11518:
11514:
11509:
11503:
11500:
11495:
11490:
11483:
11479:
11474:
11468:
11465:
11460:
11457:
11452:
11448:
11435:
11432:
11400:
11377:
11374:
11371:
11366:
11362:
11356:
11351:
11346:
11343:
11338:
11331:
11328:
11299:
11296:
11291:
11288:
11283:
11280:
11261:
11258:
11254:
11248:
11244:
11239:
11235:
11230:
11227:
11222:
11217:
11213:
11209:
11206:
11202:
11197:
11190:
11187:
11183:
11157:
11153:
11148:
11144:
11139:
11136:
11131:
11126:
11122:
11118:
11115:
11111:
11107:
11104:
11101:
11098:
11086:
11069:
11066:
11041:
11036:
11033:
11029:
11025:
11021:
11017:
11012:
11009:
11004:
10999:
10991:
10987:
10983:
10980:
10974:
10970:
10964:
10960:
10957:
10954:
10951:
10948:
10945:
10942:
10937:
10933:
10927:
10923:
10919:
10916:
10913:
10910:
10907:
10875:
10871:
10867:
10862:
10858:
10854:
10849:
10845:
10841:
10838:
10835:
10831:
10822:
10818:
10814:
10808:
10804:
10798:
10795:
10790:
10785:
10780:
10775:
10770:
10765:
10762:
10730:
10727:
10724:
10721:
10718:
10715:
10712:
10709:
10704:
10700:
10694:
10691:
10686:
10681:
10677:
10673:
10670:
10666:
10658:
10654:
10650:
10647:
10641:
10637:
10631:
10624:
10621:
10617:
10612:
10607:
10603:
10599:
10596:
10593:
10590:
10587:
10563:
10558:
10551:
10547:
10540:
10535:
10528:
10524:
10515:
10509:
10504:
10499:
10494:
10489:
10483:
10476:
10472:
10468:
10463:
10459:
10455:
10450:
10446:
10442:
10439:
10436:
10432:
10426:
10421:
10416:
10408:
10404:
10400:
10396:
10391:
10385:
10377:
10373:
10369:
10366:
10360:
10356:
10350:
10346:
10341:
10337:
10333:
10330:
10327:
10322:
10319:
10315:
10311:
10308:
10303:
10299:
10295:
10292:
10289:
10286:
10283:
10262:
10258:
10254:
10249:
10245:
10241:
10236:
10232:
10228:
10225:
10222:
10218:
10209:
10205:
10201:
10197:
10192:
10189:
10184:
10179:
10173:
10168:
10163:
10158:
10153:
10149:
10135:
10123:
10120:
10105:
10102:
10081:
10074:
10057:
10052:
10048:
10044:
10039:
10035:
10031:
10026:
10022:
10018:
10014:
10004:
9999:
9995:
9991:
9985:
9980:
9976:
9969:
9966:
9961:
9957:
9953:
9947:
9943:
9939:
9934:
9930:
9904:
9900:
9894:
9890:
9886:
9879:
9875:
9869:
9864:
9860:
9856:
9850:
9847:
9839:
9835:
9829:
9825:
9821:
9814:
9810:
9804:
9800:
9796:
9793:
9790:
9787:
9784:
9778:
9775:
9770:
9766:
9752:
9728:
9722:
9718:
9712:
9708:
9704:
9698:
9695:
9690:
9684:
9680:
9676:
9673:
9670:
9667:
9664:
9661:
9655:
9652:
9649:
9646:
9643:
9640:
9606:
9602:
9599:
9565:
9560:
9556:
9552:
9549:
9546:
9539:
9535:
9528:
9524:
9520:
9517:
9511:
9508:
9503:
9499:
9495:
9492:
9489:
9482:
9478:
9471:
9467:
9463:
9460:
9454:
9447:
9443:
9436:
9432:
9428:
9422:
9416:
9412:
9409:
9389:
9386:
9357:
9354:
9351:
9348:
9322:
9318:
9311:
9307:
9303:
9295:
9292:
9287:
9282:
9277:
9270:
9266:
9260:
9255:
9248:
9244:
9234:
9230:
9225:
9220:
9216:
9212:
9207:
9203:
9199:
9196:
9193:
9187:
9183:
9175:
9169:
9164:
9159:
9154:
9149:
9143:
9135:
9131:
9127:
9116:
9111:
9107:
9101:
9097:
9090:
9086:
9080:
9077:
9074:
9069:
9066:
9063:
9059:
9034:
9028:
9023:
9018:
9013:
9008:
9002:
8994:
8990:
8986:
8955:
8952:
8949:
8942:
8938:
8931:
8927:
8923:
8917:
8914:
8911:
8906:
8902:
8873:
8869:
8864:
8859:
8855:
8851:
8846:
8842:
8838:
8835:
8829:
8825:
8816:
8811:
8807:
8803:
8797:
8793:
8787:
8784:
8779:
8775:
8771:
8766:
8763:
8760:
8757:
8754:
8750:
8746:
8741:
8737:
8733:
8728:
8725:
8722:
8719:
8716:
8712:
8708:
8705:
8700:
8696:
8692:
8686:
8682:
8678:
8673:
8669:
8656:
8653:
8626:
8618:
8613:
8609:
8605:
8600:
8593:
8588:
8584:
8580:
8574:
8565:
8561:
8557:
8550:
8546:
8540:
8536:
8532:
8526:
8523:
8516:
8512:
8507:
8503:
8496:
8492:
8487:
8483:
8478:
8475:
8472:
8465:
8461:
8457:
8452:
8448:
8443:
8417:
8413:
8409:
8404:
8400:
8396:
8393:
8366:
8361:
8357:
8353:
8347:
8343:
8339:
8335:
8332:
8328:
8325:
8305:
8300:
8296:
8292:
8286:
8282:
8278:
8274:
8271:
8267:
8264:
8244:
8239:
8235:
8231:
8225:
8221:
8217:
8213:
8210:
8206:
8203:
8181:
8176:
8172:
8151:
8148:
8144:
8140:
8137:
8133:
8112:
8109:
8105:
8101:
8098:
8094:
8073:
8068:
8063:
8058:
8051:
8047:
8043:
8038:
8034:
8030:
8025:
8021:
8016:
8012:
8007:
8002:
7997:
7990:
7986:
7982:
7977:
7973:
7969:
7964:
7960:
7955:
7951:
7948:
7943:
7938:
7933:
7928:
7923:
7918:
7913:
7910:
7907:
7903:
7882:
7877:
7873:
7869:
7863:
7859:
7855:
7849:
7845:
7841:
7821:
7816:
7812:
7808:
7802:
7798:
7794:
7788:
7784:
7780:
7755:
7752:
7748:
7744:
7739:
7735:
7731:
7726:
7723:
7719:
7715:
7710:
7706:
7683:
7679:
7673:
7669:
7646:
7643:
7639:
7635:
7630:
7626:
7622:
7617:
7613:
7590:
7586:
7580:
7576:
7552:
7547:
7542:
7537:
7532:
7528:
7524:
7519:
7514:
7509:
7504:
7500:
7496:
7491:
7488:
7485:
7480:
7476:
7453:
7449:
7445:
7440:
7436:
7415:
7412:
7407:
7402:
7397:
7392:
7388:
7384:
7379:
7374:
7369:
7364:
7360:
7356:
7353:
7348:
7343:
7338:
7333:
7329:
7325:
7320:
7315:
7310:
7305:
7301:
7297:
7291:
7287:
7282:
7279:
7274:
7269:
7264:
7258:
7253:
7248:
7243:
7240:
7237:
7232:
7228:
7204:
7199:
7195:
7190:
7169:
7164:
7160:
7155:
7134:
7129:
7124:
7119:
7114:
7110:
7106:
7101:
7096:
7091:
7086:
7082:
7078:
7075:
7070:
7065:
7060:
7055:
7050:
7045:
7042:
7020:
7016:
6993:
6989:
6968:
6963:
6959:
6954:
6933:
6928:
6924:
6919:
6898:
6893:
6889:
6884:
6880:
6875:
6871:
6866:
6862:
6859:
6856:
6852:
6827:
6823:
6816:
6812:
6808:
6805:
6799:
6794:
6789:
6784:
6776:
6773:
6769:
6764:
6761:
6756:
6752:
6729:
6725:
6721:
6716:
6712:
6708:
6701:
6697:
6690:
6686:
6682:
6679:
6673:
6666:
6662:
6655:
6651:
6647:
6644:
6638:
6633:
6628:
6623:
6615:
6612:
6608:
6603:
6598:
6593:
6588:
6580:
6577:
6573:
6568:
6565:
6560:
6556:
6542:
6520:
6514:
6509:
6504:
6499:
6494:
6488:
6480:
6476:
6472:
6466:
6462:
6459:
6432:
6428:
6421:
6417:
6413:
6410:
6404:
6397:
6393:
6386:
6382:
6378:
6375:
6369:
6364:
6359:
6354:
6346:
6343:
6339:
6334:
6329:
6324:
6319:
6311:
6308:
6304:
6299:
6296:
6291:
6287:
6261:
6258:
6254:
6249:
6245:
6241:
6238:
6212:
6205:
6199:
6194:
6189:
6184:
6179:
6173:
6165:
6161:
6157:
6151:
6144:
6139:
6131:
6127:
6123:
6120:
6114:
6107:
6102:
6094:
6090:
6086:
6083:
6077:
6072:
6067:
6062:
6054:
6051:
6047:
6042:
6037:
6032:
6027:
6019:
6016:
6012:
6007:
6004:
6001:
5987:
5984:
5971:
5966:
5961:
5955:
5950:
5945:
5940:
5935:
5931:
5927:
5924:
5921:
5916:
5911:
5905:
5900:
5895:
5890:
5885:
5881:
5869:antisymmetric
5856:
5853:
5850:
5847:
5844:
5841:
5838:
5835:
5831:
5826:
5821:
5816:
5811:
5806:
5801:
5795:
5790:
5785:
5780:
5775:
5771:
5767:
5762:
5757:
5731:
5726:
5721:
5715:
5710:
5705:
5700:
5695:
5691:
5687:
5684:
5679:
5674:
5668:
5663:
5658:
5653:
5648:
5644:
5617:
5612:
5607:
5602:
5597:
5592:
5586:
5581:
5576:
5571:
5566:
5562:
5558:
5554:
5528:
5525:
5520:
5515:
5509:
5504:
5499:
5494:
5489:
5486:
5481:
5476:
5473:
5470:
5465:
5460:
5454:
5449:
5444:
5439:
5434:
5431:
5426:
5379:
5358:
5353:
5347:
5344:
5342:
5339:
5338:
5335:
5332:
5330:
5327:
5326:
5324:
5316:
5312:
5307:
5302:
5298:
5293:
5288:
5282:
5279:
5277:
5274:
5273:
5270:
5267:
5265:
5262:
5261:
5259:
5251:
5247:
5242:
5237:
5233:
5228:
5223:
5217:
5214:
5211:
5209:
5206:
5205:
5202:
5199:
5197:
5194:
5193:
5191:
5183:
5179:
5174:
5169:
5165:
5144:
5139:
5135:
5131:
5126:
5122:
5118:
5113:
5109:
5105:
5075:
5071:
5067:
5062:
5056:
5053:
5051:
5048:
5047:
5044:
5041:
5039:
5036:
5035:
5033:
5028:
5023:
5018:
5015:
5010:
5003:
4999:
4995:
4990:
4984:
4981:
4979:
4976:
4975:
4972:
4969:
4967:
4964:
4963:
4961:
4956:
4951:
4946:
4941:
4936:
4934:
4931:
4927:
4924:
4921:
4918:
4915:
4909:
4905:
4900:
4895:
4889:
4886:
4884:
4881:
4880:
4877:
4874:
4872:
4869:
4868:
4866:
4858:
4854:
4849:
4844:
4839:
4834:
4829:
4827:
4799:
4796:
4793:
4772:
4769:
4766:
4763:
4760:
4754:
4750:
4745:
4740:
4734:
4731:
4729:
4726:
4723:
4722:
4719:
4716:
4714:
4711:
4710:
4708:
4700:
4696:
4691:
4686:
4681:
4676:
4648:
4645:
4642:
4617:
4612:
4607:
4602:
4597:
4592:
4586:
4581:
4576:
4571:
4566:
4561:
4557:
4551:
4548:
4544:
4540:
4536:
4515:
4510:
4505:
4499:
4494:
4489:
4484:
4479:
4474:
4470:
4447:
4442:
4437:
4407:
4399:
4395:
4391:
4387:
4383:
4379:
4378:
4373:
4369:
4365:
4361:
4357:
4353:
4352:
4350:
4345:
4341:
4316:
4312:
4308:
4304:
4298:
4294:
4290:
4286:
4265:
4262:
4257:
4252:
4245:
4242:
4238:
4233:
4227:
4222:
4217:
4212:
4207:
4202:
4199:
4194:
4191:
4187:
4166:
4163:
4160:
4156:
4153:
4150:
4147:
4127:
4122:
4117:
4111:
4106:
4101:
4096:
4091:
4088:
4084:
4053:
4049:
4045:
4041:
4035:
4031:
4027:
4023:
4019:
4014:
4010:
4006:
4002:
3996:
3992:
3988:
3984:
3963:
3958:
3954:
3950:
3946:
3942:
3936:
3932:
3928:
3924:
3920:
3900:
3895:
3891:
3887:
3883:
3879:
3873:
3869:
3865:
3861:
3857:
3833:
3830:
3827:
3807:
3804:
3801:
3798:
3795:
3792:
3769:
3764:
3759:
3754:
3748:
3743:
3738:
3735:
3732:
3729:
3726:
3721:
3716:
3711:
3706:
3701:
3696:
3693:
3670:
3666:
3663:
3659:
3655:
3652:
3648:
3643:
3640:
3635:
3632:
3629:
3626:
3623:
3620:
3617:
3614:
3610:
3605:
3599:
3595:
3592:
3588:
3584:
3581:
3577:
3572:
3569:
3564:
3561:
3558:
3555:
3552:
3549:
3546:
3542:
3537:
3533:
3531:
3529:
3526:
3522:
3519:
3516:
3512:
3508:
3505:
3501:
3497:
3494:
3491:
3487:
3483:
3480:
3476:
3472:
3466:
3462:
3457:
3454:
3449:
3446:
3443:
3440:
3437:
3434:
3431:
3427:
3422:
3418:
3416:
3414:
3392:
3387:
3382:
3377:
3371:
3366:
3361:
3358:
3355:
3352:
3347:
3342:
3337:
3332:
3327:
3322:
3319:
3300:
3297:
3294:
3290:
3286:
3283:
3279:
3275:
3272:
3269:
3265:
3261:
3258:
3254:
3250:
3244:
3240:
3235:
3232:
3227:
3224:
3221:
3218:
3215:
3212:
3209:
3205:
3200:
3162:
3158:
3152:
3148:
3144:
3139:
3135:
3131:
3128:
3125:
3105:
3102:
3099:
3096:
3093:
3090:
3064:
3061:
3058:
3038:
3035:
3032:
3029:
3026:
3023:
2997:
2994:
2991:
2966:
2962:
2956:
2953:
2950:
2947:
2943:
2933:is denoted by
2922:
2919:
2916:
2913:
2910:
2907:
2903:
2899:
2896:
2893:
2889:
2885:
2882:
2862:
2842:
2822:
2802:
2799:
2796:
2793:
2790:
2787:
2784:
2781:
2778:
2775:
2772:
2769:
2747:
2744:
2739:
2735:
2731:
2728:
2725:
2720:
2716:
2712:
2709:
2706:
2703:
2699:
2693:
2690:
2687:
2683:
2679:
2676:
2671:
2667:
2663:
2660:
2657:
2652:
2648:
2644:
2641:
2638:
2635:
2631:
2627:
2603:
2599:
2576:
2572:
2549:
2545:
2522:
2518:
2498:{\textstyle s}
2494:
2478:{\textstyle s}
2474:
2452:
2448:
2425:
2421:
2398:
2394:
2371:
2367:
2342:
2339:
2335:
2314:
2309:
2305:
2300:
2296:
2291:
2287:
2282:
2261:
2256:
2252:
2247:
2226:
2221:
2217:
2212:
2191:
2186:
2182:
2177:
2173:
2168:
2164:
2159:
2138:
2133:
2129:
2124:
2103:
2098:
2094:
2089:
2067:
2062:
2058:
2053:
2047:
2044:
2040:
2034:
2030:
2026:
2023:
2018:
2014:
2009:
1988:
1985:
1980:
1976:
1971:
1967:
1964:
1961:
1956:
1952:
1947:
1943:
1921:
1918:
1913:
1909:
1904:
1900:
1895:
1891:
1886:
1882:
1877:
1874:
1870:
1864:
1861:
1857:
1853:
1850:
1845:
1841:
1836:
1832:
1827:
1823:
1818:
1812:
1809:
1805:
1799:
1796:
1792:
1788:
1785:
1782:
1777:
1773:
1768:
1764:
1761:
1756:
1752:
1747:
1743:
1740:
1735:
1732:
1728:
1722:
1719:
1715:
1711:
1708:
1703:
1699:
1694:
1690:
1685:
1681:
1676:
1672:
1667:
1664:
1660:
1654:
1651:
1647:
1643:
1640:
1637:
1633:
1629:
1607:
1602:
1598:
1593:
1572:
1567:
1563:
1558:
1537:
1532:
1528:
1523:
1519:
1514:
1510:
1505:
1499:
1496:
1492:
1486:
1483:
1479:
1475:
1472:
1469:
1465:
1441:
1434:
1428:
1423:
1418:
1413:
1408:
1402:
1394:
1390:
1386:
1380:
1373:
1368:
1360:
1356:
1352:
1349:
1343:
1336:
1331:
1323:
1319:
1315:
1312:
1306:
1301:
1296:
1291:
1283:
1280:
1276:
1271:
1266:
1261:
1256:
1248:
1245:
1241:
1236:
1233:
1230:
1204:
1200:
1195:
1191:
1184:
1180:
1175:
1169:
1164:
1160:
1137:
1134:
1131:
1111:
1108:
1105:
1085:
1064:
1059:
1054:
1048:
1043:
1038:
1033:
1010:
1004:
999:
994:
989:
984:
978:
974:
969:
965:
942:
937:
913:
908:
883:
880:
877:
872:
869:
863:
860:
833:
829:
823:
819:
815:
812:
806:
802:
796:
789:
785:
780:
776:
769:
765:
760:
754:
749:
745:
739:
735:
726:
722:
716:
712:
708:
705:
698:
694:
690:
684:
679:
672:
668:
663:
656:
653:
647:
643:
637:
633:
627:
624:
621:
618:
615:
611:
607:
604:
599:
594:
588:
583:
578:
573:
570:
542:
539:
477:
474:
473:
468:
446:
445:
441:standard state
438:
435:
434:
422:
417:
414:
413:
409:
408:
405:
399:
388:
385:
384:
380:
379:
376:
370:
369:
366:
362:
361:
352:
346:
345:
340:
335:
332:
331:
327:
326:
324:
323:
315:
314:
313:
310:
309:
307:
306:
302:
299:
298:
290:
289:
288:
285:
284:
281:
275:
274:
272:
271:
263:
261:
255:
254:
252:
251:
247:
245:
239:
238:
236:
235:
227:
225:
217:
214:
213:
206:
200:
199:
197:
196:
188:
186:
180:
179:
176:
171:
168:
167:
165:
164:
160:
158:
150:
149:
147:
146:
138:
136:
130:
129:
127:
126:
118:
116:
110:
109:
107:
106:
98:
96:
89:
86:
85:
83:
82:
74:
72:
67:
64:
63:
59:
58:
54:
53:
47:
46:
42:
41:
38:
16:Atom of helium
15:
9:
6:
4:
3:
2:
13247:
13236:
13233:
13231:
13228:
13226:
13223:
13222:
13220:
13207:
13203:
13199:
13195:
13191:
13187:
13183:
13179:
13174:
13169:
13166:(6): 063001.
13165:
13161:
13154:
13146:
13140:
13132:
13128:
13121:
13119:
13110:
13104:
13100:
13094:
13088:
13083:
13075:
13071:
13067:
13063:
13059:
13055:
13051:
13047:
13043:
13039:
13035:
13031:
13027:
13020:
13011:
13010:11383/1679348
13006:
13002:
12998:
12994:
12990:
12987:(6): 060101.
12986:
12982:
12981:
12973:
12966:
12958:
12954:
12950:
12946:
12942:
12938:
12934:
12930:
12926:
12922:
12915:
12908:
12902:
12894:
12890:
12886:
12882:
12878:
12874:
12870:
12866:
12859:
12851:
12847:
12843:
12839:
12835:
12831:
12827:
12823:
12819:
12815:
12808:
12800:
12796:
12792:
12788:
12784:
12780:
12776:
12772:
12765:
12757:
12750:
12742:
12735:
12727:
12723:
12719:
12715:
12708:
12706:
12704:
12695:
12689:
12685:
12681:
12677:
12676:
12668:
12660:
12656:
12652:
12645:
12637:
12635:3-323-00011-0
12631:
12627:
12620:
12609:
12602:
12600:
12598:
12589:
12583:
12579:
12575:
12571:
12570:
12562:
12560:
12550:
12542:
12538:
12534:
12528:
12524:
12514:
12511:
12509:
12506:
12504:
12501:
12499:
12496:
12494:
12491:
12489:
12486:
12484:
12481:
12479:
12476:
12474:
12471:
12470:
12463:
12448:
12402:
12391:
12381:
12364:
12352:
12348:
12342:
12330:
12326:
12317:
12297:
12293:
12284:
12264:
12261:
12258:
12254:
12240:
12230:
12225:
12206:
12202:
12198:
12187:
12172:
12169:
12166:
12162:
12153:
12138:
12134:
12130:
12127:
12124:
12121:
12100:
12088:
12084:
12078:
12066:
12062:
12048:
12038:
12033:
12014:
12010:
12006:
11998:
11983:
11968:
11965:
11962:
11958:
11947:
11932:
11917:
11913:
11904:
11901:
11898:
11895:
11887:
11884:
11864:
11831:
11815:
11814:
11809:
11805:
11789:
11786:
11783:
11780:
11772:
11739:
11728:
11723:
11720:
11717:
11713:
11709:
11704:
11700:
11696:
11693:
11684:
11660:
11650:
11645:
11626:
11622:
11618:
11591:
11587:
11580:
11576:
11572:
11569:
11563:
11556:
11552:
11545:
11541:
11537:
11534:
11528:
11523:
11516:
11512:
11501:
11498:
11493:
11488:
11481:
11477:
11466:
11463:
11458:
11455:
11450:
11446:
11431:
11429:
11425:
11421:
11405:
11399:
11395:Where again,
11393:
11375:
11372:
11369:
11364:
11360:
11354:
11349:
11344:
11341:
11336:
11329:
11326:
11316:
11310:
11297:
11294:
11289:
11286:
11281:
11278:
11259:
11256:
11252:
11246:
11242:
11237:
11233:
11228:
11225:
11220:
11215:
11211:
11207:
11204:
11200:
11195:
11188:
11185:
11181:
11170:
11155:
11151:
11146:
11142:
11137:
11134:
11129:
11124:
11120:
11116:
11113:
11109:
11105:
11099:
11085:
11067:
11064:
11053:
11039:
11034:
11031:
11027:
11023:
11019:
11015:
11010:
11007:
11002:
10997:
10989:
10985:
10981:
10978:
10972:
10968:
10962:
10955:
10952:
10949:
10943:
10940:
10935:
10931:
10925:
10921:
10917:
10914:
10908:
10897:
10893:
10888:
10873:
10869:
10860:
10856:
10852:
10847:
10843:
10836:
10833:
10829:
10820:
10816:
10812:
10806:
10802:
10796:
10788:
10778:
10773:
10760:
10752:
10746:
10728:
10725:
10722:
10719:
10716:
10713:
10710:
10707:
10702:
10698:
10692:
10689:
10684:
10679:
10675:
10671:
10668:
10664:
10656:
10652:
10648:
10645:
10639:
10635:
10629:
10622:
10619:
10615:
10610:
10605:
10601:
10597:
10594:
10588:
10576:
10561:
10549:
10545:
10538:
10526:
10522:
10507:
10497:
10492:
10474:
10470:
10461:
10457:
10453:
10448:
10444:
10437:
10434:
10430:
10424:
10419:
10414:
10406:
10402:
10398:
10394:
10389:
10383:
10375:
10371:
10367:
10364:
10358:
10354:
10348:
10344:
10339:
10335:
10331:
10328:
10320:
10317:
10313:
10306:
10301:
10297:
10293:
10290:
10284:
10260:
10256:
10247:
10243:
10239:
10234:
10230:
10223:
10220:
10216:
10207:
10203:
10199:
10195:
10190:
10182:
10171:
10166:
10151:
10147:
10134:
10129:
10119:
10103:
10100:
10088:
10080:
10073:
10050:
10046:
10042:
10037:
10033:
10024:
10020:
10016:
10012:
10002:
9997:
9993:
9989:
9983:
9978:
9974:
9967:
9959:
9955:
9951:
9945:
9941:
9932:
9928:
9902:
9898:
9892:
9888:
9884:
9877:
9873:
9867:
9862:
9858:
9854:
9848:
9845:
9837:
9833:
9827:
9823:
9819:
9812:
9808:
9802:
9794:
9791:
9788:
9782:
9776:
9773:
9768:
9764:
9751:
9745:
9726:
9720:
9716:
9710:
9706:
9702:
9696:
9693:
9688:
9682:
9678:
9671:
9668:
9665:
9659:
9653:
9650:
9644:
9638:
9628:
9624:
9600:
9597:
9583:
9579:
9558:
9554:
9547:
9544:
9537:
9533:
9526:
9522:
9518:
9515:
9509:
9501:
9497:
9490:
9487:
9480:
9476:
9469:
9465:
9461:
9458:
9452:
9445:
9441:
9434:
9430:
9426:
9420:
9410:
9407:
9385:
9355:
9352:
9349:
9346:
9337:
9320:
9316:
9309:
9305:
9301:
9293:
9290:
9285:
9280:
9268:
9264:
9258:
9246:
9242:
9232:
9228:
9218:
9214:
9210:
9205:
9201:
9194:
9191:
9185:
9181:
9167:
9157:
9152:
9133:
9129:
9125:
9114:
9109:
9105:
9099:
9095:
9088:
9084:
9078:
9075:
9072:
9064:
9026:
9016:
9011:
8992:
8988:
8984:
8972:
8953:
8950:
8947:
8940:
8936:
8929:
8925:
8921:
8915:
8912:
8909:
8904:
8900:
8890:
8871:
8867:
8857:
8853:
8849:
8844:
8840:
8833:
8827:
8823:
8814:
8809:
8805:
8801:
8795:
8791:
8785:
8777:
8773:
8764:
8761:
8758:
8755:
8752:
8748:
8739:
8735:
8726:
8723:
8720:
8717:
8714:
8710:
8706:
8698:
8694:
8690:
8684:
8680:
8671:
8667:
8652:
8650:
8646:
8641:
8638:
8624:
8616:
8611:
8607:
8603:
8598:
8591:
8586:
8582:
8578:
8572:
8563:
8559:
8555:
8548:
8544:
8538:
8534:
8530:
8524:
8521:
8514:
8510:
8505:
8501:
8494:
8490:
8485:
8481:
8473:
8463:
8459:
8455:
8450:
8446:
8441:
8431:
8415:
8411:
8407:
8402:
8398:
8394:
8391:
8382:
8380:
8359:
8355:
8351:
8345:
8341:
8337:
8333:
8330:
8326:
8298:
8294:
8290:
8284:
8280:
8276:
8272:
8269:
8265:
8237:
8233:
8229:
8223:
8219:
8215:
8211:
8208:
8204:
8179:
8174:
8170:
8066:
8049:
8045:
8041:
8036:
8032:
8028:
8023:
8019:
8014:
8005:
7988:
7984:
7980:
7975:
7971:
7967:
7962:
7958:
7953:
7949:
7941:
7931:
7926:
7908:
7901:
7875:
7871:
7867:
7861:
7857:
7853:
7847:
7843:
7814:
7810:
7806:
7800:
7796:
7792:
7786:
7782:
7769:
7753:
7750:
7746:
7742:
7737:
7733:
7729:
7724:
7721:
7717:
7713:
7708:
7704:
7681:
7677:
7671:
7667:
7644:
7641:
7637:
7633:
7628:
7624:
7620:
7615:
7611:
7588:
7584:
7578:
7574:
7564:
7545:
7530:
7526:
7517:
7502:
7498:
7494:
7486:
7478:
7474:
7451:
7447:
7443:
7438:
7434:
7405:
7390:
7386:
7377:
7362:
7358:
7354:
7346:
7331:
7327:
7318:
7303:
7299:
7289:
7285:
7280:
7272:
7262:
7256:
7238:
7230:
7226:
7216:
7197:
7193:
7162:
7158:
7127:
7112:
7108:
7099:
7084:
7080:
7076:
7068:
7058:
7053:
7040:
7018:
7014:
6991:
6987:
6961:
6957:
6926:
6922:
6891:
6887:
6873:
6869:
6860:
6854:
6825:
6821:
6814:
6810:
6806:
6803:
6797:
6792:
6787:
6774:
6771:
6767:
6762:
6759:
6754:
6750:
6727:
6723:
6719:
6714:
6710:
6706:
6699:
6695:
6688:
6684:
6680:
6677:
6671:
6664:
6660:
6653:
6649:
6645:
6642:
6636:
6631:
6626:
6613:
6610:
6606:
6601:
6596:
6591:
6578:
6575:
6571:
6566:
6563:
6558:
6554:
6541:
6535:
6512:
6502:
6497:
6478:
6474:
6470:
6464:
6460:
6457:
6447:
6430:
6426:
6419:
6415:
6411:
6408:
6402:
6395:
6391:
6384:
6380:
6376:
6373:
6367:
6362:
6357:
6344:
6341:
6337:
6332:
6327:
6322:
6309:
6306:
6302:
6297:
6294:
6289:
6285:
6276:
6273:
6259:
6256:
6252:
6247:
6243:
6239:
6236:
6228:
6223:
6210:
6197:
6187:
6182:
6163:
6159:
6155:
6149:
6142:
6129:
6125:
6121:
6118:
6112:
6105:
6092:
6088:
6084:
6081:
6075:
6070:
6065:
6052:
6049:
6045:
6040:
6035:
6030:
6017:
6014:
6010:
6005:
6002:
5999:
5991:
5983:
5964:
5953:
5948:
5933:
5929:
5925:
5922:
5914:
5903:
5898:
5883:
5879:
5870:
5854:
5851:
5848:
5845:
5842:
5839:
5836:
5833:
5829:
5824:
5819:
5804:
5793:
5788:
5773:
5769:
5765:
5760:
5745:
5724:
5713:
5708:
5693:
5689:
5685:
5677:
5666:
5661:
5646:
5642:
5633:
5615:
5610:
5595:
5584:
5579:
5564:
5560:
5556:
5543:
5539:
5526:
5518:
5507:
5502:
5487:
5484:
5474:
5471:
5463:
5452:
5447:
5432:
5429:
5414:
5410:
5405:
5402:
5398:
5394:
5356:
5351:
5345:
5340:
5333:
5328:
5322:
5314:
5310:
5305:
5300:
5296:
5291:
5286:
5280:
5275:
5268:
5263:
5257:
5249:
5245:
5240:
5235:
5231:
5226:
5221:
5215:
5212:
5207:
5200:
5195:
5189:
5181:
5177:
5172:
5167:
5163:
5137:
5133:
5129:
5124:
5120:
5116:
5111:
5107:
5095:
5090:
5073:
5065:
5060:
5054:
5049:
5042:
5037:
5031:
5026:
5021:
5016:
5013:
5001:
4993:
4988:
4982:
4977:
4970:
4965:
4959:
4954:
4949:
4944:
4929:
4919:
4907:
4903:
4898:
4893:
4887:
4882:
4875:
4870:
4864:
4856:
4852:
4847:
4842:
4837:
4817:
4815:
4814:
4813:triplet state
4797:
4794:
4791:
4764:
4752:
4748:
4743:
4738:
4732:
4727:
4724:
4717:
4712:
4706:
4698:
4694:
4689:
4684:
4679:
4664:
4663:
4662:singlet state
4646:
4643:
4640:
4631:
4615:
4610:
4595:
4584:
4579:
4564:
4559:
4555:
4549:
4546:
4542:
4538:
4508:
4497:
4492:
4477:
4472:
4468:
4445:
4440:
4424:
4420:
4405:
4393:
4381:
4367:
4355:
4348:
4343:
4330:
4314:
4306:
4296:
4288:
4263:
4260:
4255:
4243:
4240:
4236:
4225:
4215:
4210:
4200:
4197:
4192:
4189:
4185:
4161:
4154:
4151:
4148:
4145:
4120:
4109:
4104:
4089:
4086:
4082:
4073:
4069:
4051:
4033:
4017:
4012:
3994:
3956:
3940:
3934:
3893:
3877:
3871:
3845:
3831:
3828:
3825:
3802:
3799:
3796:
3793:
3780:
3762:
3752:
3746:
3733:
3730:
3727:
3719:
3709:
3704:
3691:
3668:
3641:
3633:
3630:
3627:
3624:
3621:
3618:
3615:
3612:
3608:
3597:
3570:
3562:
3559:
3556:
3553:
3550:
3547:
3544:
3540:
3532:
3524:
3495:
3464:
3460:
3455:
3447:
3444:
3441:
3438:
3435:
3432:
3429:
3425:
3417:
3403:
3385:
3375:
3369:
3356:
3353:
3345:
3335:
3330:
3317:
3273:
3242:
3238:
3233:
3225:
3222:
3219:
3216:
3213:
3210:
3207:
3203:
3188:
3186:
3185:
3184:triplet state
3180:
3179:
3178:singlet state
3160:
3150:
3146:
3142:
3137:
3133:
3126:
3123:
3103:
3100:
3097:
3094:
3091:
3088:
3080:
3079:
3078:triplet state
3062:
3059:
3056:
3036:
3033:
3030:
3027:
3024:
3021:
3013:
3012:
3011:singlet state
2995:
2992:
2989:
2980:
2964:
2960:
2954:
2951:
2948:
2945:
2941:
2920:
2917:
2914:
2911:
2908:
2905:
2897:
2894:
2891:
2883:
2880:
2860:
2840:
2833:, total spin
2820:
2797:
2794:
2791:
2788:
2779:
2776:
2773:
2770:
2758:
2745:
2737:
2733:
2729:
2726:
2723:
2718:
2714:
2710:
2707:
2704:
2701:
2691:
2688:
2685:
2681:
2677:
2669:
2665:
2661:
2658:
2655:
2650:
2646:
2642:
2639:
2636:
2633:
2625:
2617:
2601:
2597:
2574:
2570:
2547:
2543:
2520:
2516:
2506:
2492:
2472:
2450:
2446:
2423:
2419:
2396:
2392:
2369:
2365:
2354:
2307:
2303:
2289:
2285:
2254:
2250:
2219:
2215:
2184:
2180:
2166:
2162:
2131:
2127:
2096:
2092:
2060:
2056:
2045:
2042:
2038:
2032:
2028:
2024:
2016:
2012:
1986:
1978:
1974:
1965:
1962:
1954:
1950:
1941:
1932:
1919:
1911:
1907:
1893:
1889:
1880:
1875:
1872:
1868:
1862:
1859:
1855:
1851:
1843:
1839:
1825:
1821:
1810:
1807:
1803:
1797:
1794:
1790:
1786:
1783:
1775:
1771:
1754:
1750:
1741:
1733:
1730:
1726:
1720:
1717:
1713:
1709:
1701:
1697:
1683:
1679:
1670:
1665:
1662:
1658:
1652:
1649:
1645:
1641:
1627:
1619:
1600:
1596:
1565:
1561:
1530:
1526:
1512:
1508:
1497:
1494:
1490:
1484:
1481:
1477:
1473:
1452:
1439:
1426:
1416:
1411:
1392:
1388:
1384:
1378:
1371:
1358:
1354:
1350:
1347:
1341:
1334:
1321:
1317:
1313:
1310:
1304:
1299:
1294:
1281:
1278:
1274:
1269:
1264:
1259:
1246:
1243:
1239:
1234:
1231:
1228:
1220:
1202:
1198:
1189:
1182:
1178:
1167:
1162:
1158:
1135:
1132:
1129:
1106:
1103:
1083:
1075:
1057:
1046:
1041:
1002:
992:
987:
972:
967:
963:
940:
911:
881:
878:
875:
870:
867:
861:
858:
849:
831:
827:
821:
817:
813:
810:
804:
800:
794:
787:
783:
774:
767:
763:
752:
747:
743:
737:
733:
724:
720:
714:
710:
706:
703:
696:
692:
688:
682:
677:
670:
666:
654:
651:
645:
641:
635:
631:
625:
622:
619:
616:
613:
609:
605:
597:
586:
581:
568:
560:
556:
547:
538:
536:
532:
528:
524:
520:
516:
512:
509:. Unlike for
508:
504:
500:
497:bound by the
496:
495:two electrons
492:
488:
484:
471:
464:
459:
442:
436:
431:
426:
423:
420:
416:
415:
412:Pharmacology
410:
406:
398:
393:
387:
386:
381:
377:
375:
374:Boiling point
372:
371:
367:
364:
363:
353:
351:
348:
347:
341:
338:
334:
333:
328:
322:
321:
318:
311:
297:
296:
293:
286:
282:
280:
277:
276:
269:
265:
264:
262:
260:
257:
256:
249:
248:
246:
244:
241:
240:
233:
229:
228:
226:
220:
216:
215:
211:
207:
205:
202:
201:
194:
190:
189:
187:
185:
182:
181:
177:
174:
170:
169:
162:
161:
159:
157:
152:
151:
144:
140:
139:
137:
135:
132:
131:
124:
120:
119:
117:
115:
112:
111:
104:
100:
99:
97:
93:
88:
87:
80:
76:
75:
73:
70:
66:
65:
60:
52:
48:
43:
35:
30:
22:
13163:
13159:
13153:
13098:
13093:
13082:
13033:
13029:
13019:
12984:
12980:Phys. Rev. A
12978:
12965:
12924:
12920:
12914:
12906:
12901:
12868:
12864:
12858:
12817:
12813:
12807:
12774:
12770:
12764:
12755:
12749:
12740:
12734:
12717:
12674:
12667:
12650:
12644:
12625:
12619:
12568:
12549:
12536:
12527:
12488:Lithium atom
12460:(26) Ry
12447:Atomic units
12434:(25) eV
12412:(25) eV
12398:
11888:
11885:
11811:
11807:
11803:
11685:
11437:
11424:relativistic
11416:(25) eV
11406:
11397:
11394:
11311:
11171:
11083:
11054:
10895:
10891:
10889:
10750:
10747:
10577:
10132:
10125:
10086:
10078:
10071:
9749:
9743:
9626:
9622:
9581:
9577:
9391:
9382:(25) eV
9338:
8973:
8891:
8658:
8649:ground state
8642:
8639:
8432:
8383:
7770:
7603:state (with
7565:
7217:
6539:
6536:
6448:
6277:
6274:
6224:
5992:
5989:
5868:
5743:
5631:
5541:
5540:
5412:
5406:
5399:), the four
5091:
4818:
4811:
4660:
4632:
4425:
4421:
4331:
3846:
3781:
3404:
3189:
3182:
3176:
3076:
3009:
2981:
2759:
2618:
2507:
2355:
1933:
1620:
1453:
1221:
1023:
850:
552:
541:Introduction
531:wavefunction
527:ground state
507:strong force
482:
480:
396:
243:RTECS number
62:Identifiers
27:Helium atom
12423:(2) eV
6227:Hamiltonian
5744:orthohelium
3049:state) and
559:Hamiltonian
529:energy and
483:helium atom
365:Appearance
330:Properties
300:InChI=1S/He
123:CHEBI:33681
13219:Categories
12520:References
12445:(13)
5632:symmetric
5542:Parahelium
350:Molar mass
268:206GF3GB41
134:ChemSpider
90:3D model (
69:CAS Number
13173:1004.5110
13058:1050-2947
12949:1050-2947
12893:0031-8949
12842:0031-9007
12799:0009-2614
12294:ψ
12255:ψ
12231:−
12163:ψ
12135:ψ
12131:∫
12128:∫
12039:−
11959:ψ
11914:ψ
11905:∫
11902:∫
11858:Δ
11825:Δ
11787:±
11766:Δ
11733:Δ
11651:−
11564:−
11529:−
11508:∇
11494:−
11473:∇
11459:−
11373:−
11295:∼
11205:−
11114:−
11103:⟩
11097:⟨
10986:ε
10982:π
10953:−
10912:⟩
10906:⟨
10890:Treating
10834:−
10813:π
10761:ψ
10726:−
10711:−
10685:−
10653:ϵ
10649:π
10592:⟩
10586:⟨
10498:−
10435:−
10425:∫
10399:π
10372:ε
10368:π
10326:⟩
10310:⟨
10288:⟩
10282:⟨
10221:−
10200:π
10148:ψ
10017:−
9990:π
9929:ψ
9849:−
9792:−
9777:−
9697:−
9669:−
9654:−
9605:¯
9545:−
9510:−
9488:−
9453:−
9415:¯
9353:−
9350:≈
9186:−
9158:−
9096:π
9079:∫
9076:∫
9058:Δ
9017:−
8951:−
8913:−
8828:−
8802:π
8749:ψ
8711:ψ
8668:ψ
8525:−
8171:σ
8150:⟩
8147:↑
8139:⟩
8136:↓
8111:⟩
8108:↓
8100:⟩
8097:↑
8033:ℓ
8015:ψ
7972:ℓ
7954:ψ
7902:ψ
7747:ψ
7734:ψ
7718:ψ
7705:ψ
7638:ψ
7625:ψ
7612:ψ
7527:ψ
7499:ψ
7475:ψ
7448:ψ
7435:ψ
7387:ψ
7359:ψ
7355:±
7328:ψ
7300:ψ
7231:±
7227:ψ
7203:⟩
7194:ψ
7168:⟩
7159:ψ
7109:ψ
7081:ψ
7041:ψ
6967:⟩
6958:ψ
6932:⟩
6923:ψ
6897:⟩
6888:ψ
6879:⟩
6870:ψ
6858:⟩
6855:ψ
6798:−
6763:−
6672:−
6637:−
6602:−
6567:−
6503:−
6403:−
6368:−
6333:−
6298:−
6188:−
6113:−
6076:−
6041:−
6006:−
5934:−
5930:ψ
5926:−
5884:−
5880:ψ
5840:−
5815:σ
5774:−
5770:ψ
5756:ϕ
5690:ψ
5643:ψ
5606:σ
5561:ψ
5553:ϕ
5480:ψ
5475:−
5425:ψ
5378:ψ
5297:σ
5232:σ
5213:−
5164:σ
5134:σ
5121:σ
5108:σ
5014:−
5009:σ
4940:σ
4833:σ
4765:−
4725:−
4675:σ
4606:σ
4556:ϕ
4543:∑
4535:ψ
4469:ϕ
4436:σ
4394:ψ
4382:ψ
4368:ψ
4356:ψ
4340:ψ
4311:⟩
4293:⟩
4237:ψ
4198:∫
4186:∑
4165:↓
4159:↑
4083:ψ
4048:⟩
4044:↑
4030:⟩
4026:↓
4018:≠
4009:⟩
4005:↓
3991:⟩
3987:↑
3953:⟩
3949:↓
3931:⟩
3927:↑
3890:⟩
3886:↓
3868:⟩
3864:↑
3734:ψ
3731:−
3692:ψ
3665:⟩
3662:↓
3654:⟩
3651:↓
3639:⟩
3631:−
3609:χ
3594:⟩
3591:↑
3583:⟩
3580:↑
3568:⟩
3541:χ
3518:⟩
3515:↑
3507:⟩
3504:↓
3493:⟩
3490:↓
3482:⟩
3479:↑
3453:⟩
3426:χ
3357:ψ
3318:ψ
3296:⟩
3293:↑
3285:⟩
3282:↓
3274:−
3271:⟩
3268:↓
3260:⟩
3257:↑
3231:⟩
3204:χ
2909:…
2895:−
2743:⟩
2675:⟩
2397:±
2370:±
2341:⟩
2338:Φ
2313:⟩
2304:χ
2295:⟩
2286:ψ
2260:⟩
2251:χ
2225:⟩
2216:ψ
2190:⟩
2181:χ
2172:⟩
2163:ψ
2137:⟩
2128:ψ
2102:⟩
2093:χ
2066:⟩
2057:φ
2029:∑
2022:⟩
2013:ψ
1984:⟩
1975:ψ
1960:⟩
1951:ψ
1917:⟩
1908:χ
1899:⟩
1890:φ
1856:∑
1849:⟩
1840:χ
1831:⟩
1822:φ
1791:∑
1781:⟩
1772:χ
1760:⟩
1751:φ
1714:∑
1707:⟩
1698:χ
1689:⟩
1680:φ
1646:∑
1639:⟩
1636:Φ
1606:⟩
1597:χ
1571:⟩
1562:φ
1536:⟩
1527:χ
1518:⟩
1509:φ
1478:∑
1471:⟩
1468:Φ
1417:−
1342:−
1305:−
1270:−
1235:−
1194:∇
1190:⋅
1174:∇
1159:ℏ
1130:μ
1110:∞
993:−
859:μ
818:ε
814:π
779:∇
775:⋅
759:∇
744:ℏ
738:−
711:ε
707:π
683:−
662:∇
655:μ
642:ℏ
636:−
610:∑
390:Std molar
279:UN number
250:MH6520000
163:231-168-5
155:EC Number
79:7440-59-7
13198:20867977
13139:cite web
13074:36134307
12850:10058600
12659:25750516
12608:"Helium"
12466:See also
11380: eV
11040:⟩
11024:⟨
11016:⟩
11003:⟨
10733: eV
9601:′
9411:′
9360: eV
8958: eV
6461:′
6260:′
5867:with an
1122:we have
511:hydrogen
433:)
419:ATC code
39:Helium-4
13206:2499460
13178:Bibcode
13066:9908396
13038:Bibcode
12989:Bibcode
12957:9903218
12929:Bibcode
12873:Bibcode
12822:Bibcode
12779:Bibcode
12539:. USA:
12427:−79.005
12416:−54.417
12405:−24.587
11420:Pekeris
11409:−79.005
9375:−79.005
5630:with a
5395:, like
517:to the
503:isotope
463:what is
461: (
427: (
425:V03AN03
392:entropy
219:PubChem
13235:Helium
13204:
13196:
13105:
13072:
13064:
13056:
12955:
12947:
12891:
12848:
12840:
12797:
12690:
12657:
12632:
12584:
12453:−5.806
12438:−2.903
9741:where
7696:(with
6909:where
4072:spinor
2589:, and
2202:where
1999:where
1548:where
851:where
557:. The
491:helium
485:is an
458:verify
455:
317:SMILES
210:Helium
193:D04420
178:16294
55:Helium
45:Names
21:Helium
13225:Atoms
13202:S2CID
13168:arXiv
13070:S2CID
12975:(PDF)
12611:(PDF)
12436:, or
11757:with:
8954:108.8
8162:from
6742:where
6225:This
1455:that
355:4.002
292:InChI
283:1046
232:23987
143:22423
114:ChEBI
92:JSmol
13194:PMID
13145:link
13131:NIST
13103:ISBN
13062:PMID
13054:ISSN
12953:PMID
12945:ISSN
12889:ISSN
12846:PMID
12838:ISSN
12795:ISSN
12718:NIST
12688:ISBN
12655:OCLC
12630:ISBN
12582:ISBN
12449:a.u.
11426:and
11376:77.5
11298:1.69
11082:and
9356:74.8
8123:and
7832:and
7180:and
7006:and
6944:and
5742:and
2438:and
2384:and
926:and
513:, a
487:atom
259:UNII
204:MeSH
184:KEGG
13186:doi
13164:105
13046:doi
13005:hdl
12997:doi
12937:doi
12907:189
12881:doi
12869:T83
12830:doi
12787:doi
12775:229
12722:doi
12680:doi
12574:doi
12455:771
12440:385
12432:539
12429:154
12418:763
12410:936
12407:387
12403:is
12298:100
12139:100
11918:100
11810:or
11705:100
11414:539
11411:154
10714:109
10089:= 2
10070:If
9631:is
9380:539
9377:154
4526:as
3187:).
430:WHO
400:298
357:602
222:CID
13221::
13200:.
13192:.
13184:.
13176:.
13162:.
13141:}}
13137:{{
13117:^
13068:.
13060:.
13052:.
13044:.
13034:46
13032:.
13028:.
13003:.
12995:.
12985:75
12983:.
12977:.
12951:.
12943:.
12935:.
12925:41
12923:.
12887:.
12879:.
12867:.
12844:.
12836:.
12828:.
12818:74
12816:.
12793:.
12785:.
12773:.
12720:.
12716:.
12702:^
12686:.
12596:^
12580:.
12558:^
12535:.
12462:.
12458:66
12443:83
12421:11
11683:.
11290:16
11287:27
11226:27
11135:27
11087:ee
10729:75
10720:34
10136:ee
9446:12
8430:.
8381:.
7563:.
5982:.
4816:)
4630:.
2979:.
2562:,
2535:,
968:12
832:12
481:A
343:He
13208:.
13188::
13180::
13170::
13147:)
13133:.
13111:.
13076:.
13048::
13040::
13013:.
13007::
12999::
12991::
12959:.
12939::
12931::
12895:.
12883::
12875::
12852:.
12832::
12824::
12801:.
12789::
12781::
12728:.
12724::
12696:.
12682::
12661:.
12638:.
12613:.
12590:.
12576::
12543:.
12365:2
12360:r
12353:3
12349:d
12343:1
12338:r
12331:3
12327:d
12323:)
12318:2
12313:r
12308:(
12303:*
12290:)
12285:1
12280:r
12275:(
12270:*
12265:m
12262:l
12259:n
12247:|
12241:2
12236:r
12226:1
12221:r
12215:|
12207:2
12203:e
12199:k
12193:)
12188:2
12183:r
12178:(
12173:m
12170:l
12167:n
12159:)
12154:1
12149:r
12144:(
12125:=
12122:J
12101:2
12096:r
12089:3
12085:d
12079:1
12074:r
12067:3
12063:d
12055:|
12049:2
12044:r
12034:1
12029:r
12023:|
12015:2
12011:e
12007:k
11999:2
11994:|
11989:)
11984:2
11979:r
11974:(
11969:m
11966:l
11963:n
11954:|
11948:2
11943:|
11938:)
11933:1
11928:r
11923:(
11909:|
11899:=
11896:I
11868:)
11865:1
11862:(
11835:)
11832:1
11829:(
11790:J
11784:I
11781:=
11776:)
11773:1
11770:(
11743:)
11740:1
11737:(
11729:+
11724:m
11721:l
11718:n
11714:E
11710:+
11701:E
11697:=
11694:E
11667:|
11661:2
11656:r
11646:1
11641:r
11635:|
11627:2
11623:e
11619:k
11592:2
11588:r
11581:2
11577:e
11573:Z
11570:k
11557:1
11553:r
11546:2
11542:e
11538:Z
11535:k
11524:2
11517:2
11513:r
11502:2
11499:1
11489:2
11482:1
11478:r
11467:2
11464:1
11456:=
11451:0
11447:H
11401:1
11398:E
11370:=
11365:1
11361:E
11355:6
11350:)
11345:2
11342:3
11337:(
11330:2
11327:1
11282:=
11279:Z
11260:0
11257:=
11253:)
11247:1
11243:E
11238:]
11234:Z
11229:4
11221:+
11216:2
11212:Z
11208:2
11201:[
11196:(
11189:Z
11186:d
11182:d
11156:1
11152:E
11147:]
11143:Z
11138:4
11130:+
11125:2
11121:Z
11117:2
11110:[
11106:=
11100:H
11084:V
11068:r
11065:1
11035:e
11032:e
11028:V
11020:+
11011:r
11008:1
10998:)
10990:0
10979:4
10973:2
10969:e
10963:(
10959:)
10956:2
10950:Z
10947:(
10944:2
10941:+
10936:1
10932:E
10926:2
10922:Z
10918:2
10915:=
10909:H
10896:H
10892:Z
10874:a
10870:/
10866:)
10861:2
10857:r
10853:+
10848:1
10844:r
10840:(
10837:Z
10830:e
10821:3
10817:a
10807:3
10803:Z
10797:=
10794:)
10789:2
10784:r
10779:,
10774:1
10769:r
10764:(
10751:Z
10723:=
10717:+
10708:=
10703:1
10699:E
10693:2
10690:5
10680:1
10676:E
10672:8
10669:=
10665:)
10657:0
10646:4
10640:2
10636:e
10630:(
10623:a
10620:4
10616:5
10611:+
10606:1
10602:E
10598:8
10595:=
10589:H
10562:2
10557:r
10550:3
10546:d
10539:1
10534:r
10527:3
10523:d
10514:|
10508:2
10503:r
10493:1
10488:r
10482:|
10475:a
10471:/
10467:)
10462:2
10458:r
10454:+
10449:1
10445:r
10441:(
10438:4
10431:e
10420:2
10415:)
10407:3
10403:a
10395:8
10390:(
10384:)
10376:0
10365:4
10359:2
10355:e
10349:(
10345:+
10340:1
10336:E
10332:8
10329:=
10321:e
10318:e
10314:V
10307:+
10302:1
10298:E
10294:8
10291:=
10285:H
10261:a
10257:/
10253:)
10248:2
10244:r
10240:+
10235:1
10231:r
10227:(
10224:2
10217:e
10208:3
10204:a
10196:8
10191:=
10188:)
10183:2
10178:r
10172:,
10167:1
10162:r
10157:(
10152:0
10133:V
10104:3
10101:1
10087:Z
10082:0
10079:E
10075:e
10072:Z
10056:)
10051:2
10047:r
10043:+
10038:1
10034:r
10030:(
10025:e
10021:Z
10013:e
10003:3
9998:0
9994:a
9984:3
9979:e
9975:Z
9968:=
9965:)
9960:2
9956:r
9952:,
9946:1
9942:r
9938:(
9933:0
9903:2
9899:n
9893:0
9889:a
9885:2
9878:2
9874:e
9868:2
9863:e
9859:Z
9855:k
9846:=
9838:2
9834:n
9828:0
9824:a
9820:2
9813:2
9809:e
9803:2
9799:)
9795:S
9789:Z
9786:(
9783:k
9774:=
9769:0
9765:E
9753:e
9750:Z
9744:S
9727:r
9721:2
9717:e
9711:e
9707:Z
9703:k
9694:=
9689:r
9683:2
9679:e
9675:)
9672:S
9666:Z
9663:(
9660:k
9651:=
9648:)
9645:r
9642:(
9639:V
9629:)
9627:r
9625:(
9623:V
9598:H
9584:)
9582:r
9580:(
9578:V
9564:)
9559:2
9555:r
9551:(
9548:V
9538:2
9534:r
9527:2
9523:e
9519:Z
9516:k
9507:)
9502:1
9498:r
9494:(
9491:V
9481:1
9477:r
9470:2
9466:e
9462:Z
9459:k
9442:r
9435:2
9431:e
9427:k
9421:=
9408:H
9394:Z
9347:E
9321:0
9317:a
9310:2
9306:e
9302:k
9294:4
9291:5
9286:=
9281:2
9276:r
9269:3
9265:d
9259:1
9254:r
9247:3
9243:d
9233:0
9229:a
9224:)
9219:2
9215:r
9211:+
9206:1
9202:r
9198:(
9195:Z
9192:2
9182:e
9174:|
9168:2
9163:r
9153:1
9148:r
9142:|
9134:2
9130:e
9126:k
9115:6
9110:0
9106:a
9100:2
9089:6
9085:Z
9073:=
9068:)
9065:1
9062:(
9049::
9033:|
9027:2
9022:r
9012:1
9007:r
9001:|
8993:2
8989:e
8985:k
8948:=
8941:0
8937:a
8930:2
8926:e
8922:k
8916:4
8910:=
8905:0
8901:E
8872:0
8868:a
8863:)
8858:2
8854:r
8850:+
8845:1
8841:r
8837:(
8834:Z
8824:e
8815:3
8810:0
8806:a
8796:3
8792:Z
8786:=
8783:)
8778:2
8774:r
8770:(
8765:0
8762:,
8759:0
8756:,
8753:1
8745:)
8740:1
8736:r
8732:(
8727:0
8724:,
8721:0
8718:,
8715:1
8707:=
8704:)
8699:2
8695:r
8691:,
8685:1
8681:r
8677:(
8672:0
8625:]
8617:2
8612:2
8608:n
8604:1
8599:+
8592:2
8587:1
8583:n
8579:1
8573:[
8564:0
8560:a
8556:2
8549:2
8545:e
8539:2
8535:Z
8531:k
8522:=
8515:2
8511:n
8506:E
8502:+
8495:1
8491:n
8486:E
8482:=
8477:)
8474:0
8471:(
8464:2
8460:n
8456:,
8451:1
8447:n
8442:E
8416:b
8412:E
8408:+
8403:a
8399:E
8395:=
8392:E
8365:)
8360:s
8356:m
8352:,
8346:l
8342:m
8338:,
8334:l
8331:,
8327:n
8324:(
8304:)
8299:s
8295:m
8291:,
8285:l
8281:m
8277:,
8273:l
8270:,
8266:n
8263:(
8243:)
8238:s
8234:m
8230:,
8224:l
8220:m
8216:,
8212:l
8209:,
8205:n
8202:(
8180:0
8175:0
8143:|
8132:|
8104:|
8093:|
8072:)
8067:2
8062:r
8057:(
8050:2
8046:m
8042:,
8037:2
8029:,
8024:2
8020:n
8011:)
8006:1
8001:r
7996:(
7989:1
7985:m
7981:,
7976:1
7968:,
7963:1
7959:n
7950:=
7947:)
7942:2
7937:r
7932:,
7927:1
7922:r
7917:(
7912:)
7909:0
7906:(
7881:)
7876:2
7872:m
7868:,
7862:2
7858:l
7854:,
7848:2
7844:n
7840:(
7820:)
7815:1
7811:m
7807:,
7801:1
7797:l
7793:,
7787:1
7783:n
7779:(
7754:s
7751:2
7743:=
7738:b
7730:,
7725:s
7722:1
7714:=
7709:a
7682:1
7678:S
7672:3
7668:2
7645:s
7642:1
7634:=
7629:b
7621:=
7616:a
7589:1
7585:S
7579:3
7575:1
7551:)
7546:2
7541:r
7536:(
7531:a
7523:)
7518:1
7513:r
7508:(
7503:a
7495:=
7490:)
7487:0
7484:(
7479:+
7452:b
7444:=
7439:a
7414:)
7411:)
7406:1
7401:r
7396:(
7391:b
7383:)
7378:2
7373:r
7368:(
7363:a
7352:)
7347:2
7342:r
7337:(
7332:b
7324:)
7319:1
7314:r
7309:(
7304:a
7296:(
7290:2
7286:1
7281:=
7278:)
7273:2
7268:r
7263:,
7257:1
7252:r
7247:(
7242:)
7239:0
7236:(
7198:2
7189:|
7163:1
7154:|
7133:)
7128:2
7123:r
7118:(
7113:b
7105:)
7100:1
7095:r
7090:(
7085:a
7077:=
7074:)
7069:2
7064:r
7059:,
7054:1
7049:r
7044:(
7019:2
7015:H
6992:1
6988:H
6962:2
6953:|
6927:1
6918:|
6892:2
6883:|
6874:1
6865:|
6861:=
6851:|
6826:i
6822:r
6815:2
6811:e
6807:Z
6804:k
6793:2
6788:i
6783:p
6775:m
6772:2
6768:1
6760:=
6755:i
6751:H
6728:2
6724:H
6720:+
6715:1
6711:H
6707:=
6700:2
6696:r
6689:2
6685:e
6681:Z
6678:k
6665:1
6661:r
6654:2
6650:e
6646:Z
6643:k
6632:2
6627:2
6622:p
6614:m
6611:2
6607:1
6597:2
6592:1
6587:p
6579:m
6576:2
6572:1
6564:=
6559:0
6555:H
6543:0
6540:H
6519:|
6513:2
6508:r
6498:1
6493:r
6487:|
6479:2
6475:e
6471:k
6465:=
6458:H
6431:2
6427:r
6420:2
6416:e
6412:Z
6409:k
6396:1
6392:r
6385:2
6381:e
6377:Z
6374:k
6363:2
6358:2
6353:p
6345:m
6342:2
6338:1
6328:2
6323:1
6318:p
6310:m
6307:2
6303:1
6295:=
6290:0
6286:H
6257:H
6253:+
6248:0
6244:H
6240:=
6237:H
6211:.
6204:|
6198:2
6193:r
6183:1
6178:r
6172:|
6164:2
6160:e
6156:k
6150:+
6143:2
6138:r
6130:2
6126:e
6122:Z
6119:k
6106:1
6101:r
6093:2
6089:e
6085:Z
6082:k
6071:2
6066:2
6061:p
6053:m
6050:2
6046:1
6036:2
6031:1
6026:p
6018:m
6015:2
6011:1
6003:=
6000:H
5970:)
5965:1
5960:r
5954:,
5949:2
5944:r
5939:(
5923:=
5920:)
5915:2
5910:r
5904:,
5899:1
5894:r
5889:(
5855:1
5852:,
5849:0
5846:,
5843:1
5837:=
5834:m
5830:,
5825:1
5820:m
5810:)
5805:2
5800:r
5794:,
5789:1
5784:r
5779:(
5766:=
5761:m
5730:)
5725:1
5720:r
5714:,
5709:2
5704:r
5699:(
5694:+
5686:=
5683:)
5678:2
5673:r
5667:,
5662:1
5657:r
5652:(
5647:+
5616:0
5611:0
5601:)
5596:2
5591:r
5585:,
5580:1
5575:r
5570:(
5565:+
5557:=
5527:.
5524:)
5519:1
5514:r
5508:,
5503:2
5498:r
5493:(
5488:i
5485:j
5472:=
5469:)
5464:2
5459:r
5453:,
5448:1
5443:r
5438:(
5433:j
5430:i
5357:.
5352:)
5346:0
5341:1
5334:1
5329:0
5323:(
5315:2
5311:1
5306:=
5301:z
5292:,
5287:)
5281:1
5276:0
5269:0
5264:1
5258:(
5250:2
5246:i
5241:=
5236:y
5227:,
5222:)
5216:1
5208:0
5201:0
5196:1
5190:(
5182:2
5178:1
5173:=
5168:x
5143:)
5138:z
5130:,
5125:y
5117:,
5112:x
5104:(
5074:.
5066:=
5061:)
5055:1
5050:0
5043:0
5038:0
5032:(
5027:=
5022:1
5017:1
5002:;
4994:=
4989:)
4983:0
4978:0
4971:0
4966:1
4960:(
4955:=
4950:1
4945:1
4930:;
4926:)
4920:+
4914:(
4908:2
4904:1
4899:=
4894:)
4888:0
4883:1
4876:1
4871:0
4865:(
4857:2
4853:1
4848:=
4843:1
4838:0
4798:1
4795:=
4792:S
4771:)
4759:(
4753:2
4749:1
4744:=
4739:)
4733:0
4728:1
4718:1
4713:0
4707:(
4699:2
4695:1
4690:=
4685:0
4680:0
4665:)
4647:0
4644:=
4641:S
4616:i
4611:k
4601:)
4596:2
4591:r
4585:,
4580:1
4575:r
4570:(
4565:k
4560:i
4550:k
4547:i
4539:=
4514:)
4509:2
4504:r
4498:,
4493:1
4488:r
4483:(
4478:k
4473:i
4446:i
4441:k
4406:)
4349:(
4344:=
4315:2
4307:j
4303:|
4297:1
4289:i
4285:|
4264:1
4261:=
4256:2
4251:|
4244:j
4241:i
4232:|
4226:2
4221:r
4216:d
4211:1
4206:r
4201:d
4193:j
4190:i
4162:,
4155:=
4152:j
4149:,
4146:i
4126:)
4121:2
4116:r
4110:,
4105:1
4100:r
4095:(
4090:j
4087:i
4052:2
4040:|
4034:1
4022:|
4013:2
4001:|
3995:1
3983:|
3962:}
3957:2
3945:|
3941:,
3935:2
3923:|
3919:{
3899:}
3894:1
3882:|
3878:,
3872:1
3860:|
3856:{
3832:0
3829:=
3826:l
3806:)
3803:1
3800:+
3797:l
3794:2
3791:(
3768:)
3763:1
3758:r
3753:,
3747:2
3742:r
3737:(
3728:=
3725:)
3720:2
3715:r
3710:,
3705:1
3700:r
3695:(
3669:.
3658:|
3647:|
3642:=
3634:1
3628:=
3625:m
3622:,
3619:1
3616:=
3613:s
3604:|
3598:;
3587:|
3576:|
3571:=
3563:1
3560:=
3557:m
3554:,
3551:1
3548:=
3545:s
3536:|
3525:;
3521:)
3511:|
3500:|
3496:+
3486:|
3475:|
3471:(
3465:2
3461:1
3456:=
3448:0
3445:=
3442:m
3439:,
3436:1
3433:=
3430:s
3421:|
3391:)
3386:1
3381:r
3376:,
3370:2
3365:r
3360:(
3354:=
3351:)
3346:2
3341:r
3336:,
3331:1
3326:r
3321:(
3299:)
3289:|
3278:|
3264:|
3253:|
3249:(
3243:2
3239:1
3234:=
3226:0
3223:=
3220:m
3217:,
3214:0
3211:=
3208:s
3199:|
3161:2
3157:)
3151:2
3147:S
3143:+
3138:1
3134:S
3130:(
3127:=
3124:S
3104:3
3101:=
3098:1
3095:+
3092:s
3089:2
3063:1
3060:=
3057:S
3037:1
3034:=
3031:1
3028:+
3025:s
3022:2
2996:0
2993:=
2990:S
2965:J
2961:L
2955:1
2952:+
2949:S
2946:2
2942:n
2921:S
2918:+
2915:L
2912:,
2906:,
2902:|
2898:S
2892:L
2888:|
2884:=
2881:J
2861:L
2841:S
2821:n
2801:)
2798:1
2795:+
2792:s
2789:2
2786:(
2783:)
2780:1
2777:+
2774:l
2771:2
2768:(
2746:,
2738:s
2734:m
2730:,
2727:S
2724:,
2719:l
2715:m
2711:,
2708:L
2705:,
2702:N
2698:|
2692:s
2689:l
2686:n
2682:E
2678:=
2670:s
2666:m
2662:,
2659:S
2656:,
2651:l
2647:m
2643:,
2640:L
2637:,
2634:N
2630:|
2626:H
2602:z
2598:S
2575:2
2571:S
2548:z
2544:L
2521:2
2517:L
2493:s
2473:s
2451:s
2447:m
2424:l
2420:m
2393:L
2366:S
2334:|
2308:i
2299:|
2290:i
2281:|
2255:i
2246:|
2220:i
2211:|
2185:i
2176:|
2167:i
2158:|
2132:i
2123:|
2097:i
2088:|
2061:i
2052:|
2046:j
2043:i
2039:c
2033:i
2025:=
2017:j
2008:|
1987:,
1979:j
1970:|
1966:E
1963:=
1955:j
1946:|
1942:H
1920:,
1912:j
1903:|
1894:i
1885:|
1881:E
1876:j
1873:i
1869:c
1863:j
1860:i
1852:=
1844:j
1835:|
1826:i
1817:|
1811:j
1808:i
1804:c
1798:j
1795:i
1787:E
1784:=
1776:j
1767:|
1763:)
1755:i
1746:|
1742:H
1739:(
1734:j
1731:i
1727:c
1721:j
1718:i
1710:=
1702:j
1693:|
1684:i
1675:|
1671:H
1666:j
1663:i
1659:c
1653:j
1650:i
1642:=
1632:|
1628:H
1601:i
1592:|
1566:i
1557:|
1531:j
1522:|
1513:i
1504:|
1498:j
1495:i
1491:c
1485:j
1482:i
1474:=
1464:|
1440:.
1433:|
1427:2
1422:r
1412:1
1407:r
1401:|
1393:2
1389:e
1385:k
1379:+
1372:2
1367:r
1359:2
1355:e
1351:Z
1348:k
1335:1
1330:r
1322:2
1318:e
1314:Z
1311:k
1300:2
1295:2
1290:p
1282:m
1279:2
1275:1
1265:2
1260:1
1255:p
1247:m
1244:2
1240:1
1232:=
1229:H
1203:2
1199:r
1183:1
1179:r
1168:M
1163:2
1136:m
1133:=
1107:=
1104:M
1084:Z
1063:)
1058:2
1053:r
1047:,
1042:1
1037:r
1032:(
1009:|
1003:2
998:r
988:1
983:r
977:|
973:=
964:r
941:2
936:r
912:1
907:r
882:M
879:+
876:m
871:M
868:m
862:=
828:r
822:0
811:4
805:2
801:e
795:+
788:2
784:r
768:1
764:r
753:M
748:2
734:)
725:i
721:r
715:0
704:4
697:2
693:e
689:Z
678:2
671:i
667:r
652:2
646:2
632:(
626:2
623:,
620:1
617:=
614:i
606:=
603:)
598:2
593:r
587:,
582:1
577:r
572:(
569:H
453:N
402:)
397:S
395:(
94:)
23:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
