Ionization - Knowledge

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with the continuum constitute a lambda system. The mechanism of the lambda type trapping is schematically presented in figure. At the rising part of the pulse (a) the excited state (with two degenerate levels 1 and 2) are not in multiphoton resonance with the ground state. The electron is ionized through multiphoton coupling with the continuum. As the intensity of the pulse is increased the excited state and the continuum are shifted in energy due to the Stark shift. At the peak of the pulse (b) the excited states go into multiphoton resonance with the ground state. As the intensity starts to decrease (c), the two state are coupled through continuum and the population is trapped in a coherent superposition of the two states. Under subsequent action of the same pulse, due to interference in the transition amplitudes of the lambda system, the field cannot ionize the population completely and a fraction of the population will be trapped in a coherent superposition of the quasi degenerate levels. According to this explanation the states with higher angular momentum – with more sublevels – would have a higher probability of trapping the population. In general the strength of the trapping will be determined by the strength of the two photon coupling between the quasi-degenerate levels via the continuum. In 1996, using a very stable laser and by minimizing the masking effects of the focal region expansion with increasing intensity, Talebpour et al. observed structures on the curves of singly charged ions of Xe, Kr and Ar. These structures were attributed to electron trapping in the strong laser field. A more unambiguous demonstration of population trapping has been reported by T. Morishita and

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account. The major difficulty with Keldysh's model was its neglect of the effects of Coulomb interaction on the final state of the electron. As it is observed from figure, the Coulomb field is not very small in magnitude compared to the potential of the laser at larger distances from the nucleus. This is in contrast to the approximation made by neglecting the potential of the laser at regions near the nucleus. Perelomov et al. included the Coulomb interaction at larger internuclear distances. Their model (which we call the PPT model) was derived for short range potential and includes the effect of the long range Coulomb interaction through the first order correction in the quasi-classical action. Larochelle et al. have compared the theoretically predicted ion versus intensity curves of rare gas atoms interacting with a Ti:Sapphire laser with experimental measurement. They have shown that the total ionization rate predicted by the PPT model fit very well the experimental ion yields for all rare gases in the intermediate regime of the Keldysh parameter.

418:. In classical ionization, an electron must have enough energy to make it over the potential barrier, but quantum tunneling allows the electron simply to go through the potential barrier instead of going all the way over it because of the wave nature of the electron. The probability of an electron's tunneling through the barrier drops off exponentially with the width of the potential barrier. Therefore, an electron with a higher energy can make it further up the potential barrier, leaving a much thinner barrier to tunnel through and thus a greater chance to do so. In practice, tunnel ionization is observable when the atom or molecule is interacting with near-infrared strong laser pulses. This process can be understood as a process by which a bounded electron, through the absorption of more than one photon from the laser field, is ionized. This picture is generally known as multiphoton ionization (MPI). 38: 4085:, Corkum, Becker and Faisal and Faisal and Becker. The principal features of the model can be understood easily from Corkum's version. Corkum's model describes the NS ionization as a process whereby an electron is tunnel ionized. The electron then interacts with the laser field where it is accelerated away from the nuclear core. If the electron has been ionized at an appropriate phase of the field, it will pass by the position of the remaining ion half a cycle later, where it can free an additional electron by electron impact. Only half of the time the electron is released with the appropriate phase and the other half it never return to the nuclear core. The maximum kinetic energy that the returning electron can have is 3.17 times the ponderomotive potential ( 4151:

electron a is ionized. The beginning of the ionization process is shown by the intersection with a sloped dashed line. where the MPI occurs. The propagation of the ionized electron in the laser field, during which it absorbs other photons (ATI), is shown by the full thick line. The collision of this electron with the parent atomic ion is shown by a vertical dotted line representing the Coulomb interaction between the electrons. The state marked with c describes the ion excitation to a discrete or continuum state. Figure b describes the exchange process. Kuchiev's model, contrary to Corkum's model, does not predict any threshold intensity for the occurrence of NS ionization.

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of the major mechanisms responsible for the multiple ionization of atoms. The SO model describes the NSI process as a mechanism where one electron is ionized by the laser field and the departure of this electron is so rapid that the remaining electrons do not have enough time to adjust themselves to the new energy states. Therefore, there is a certain probability that, after the ionization of the first electron, a second electron is excited to states with higher energy (shake-up) or even ionized (shake-off). We should mention that, until now, there has been no quantitative calculation based on the SO model, and the model is still qualitative.

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In fact, their model is more exact and does not suffer from the large number of approximations made by Kuchiev. Their calculation results perfectly fit with the experimental results of Walker et al. Becker and Faisal have been able to fit the experimental results on the multiple NSI of rare gas atoms using their model. As a result, the electron re-scattering can be taken as the main mechanism for the occurrence of the NSI process.

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From the experimental point of view, the NS double ionization refers to processes which somehow enhance the rate of production of doubly charged ions by a huge factor at intensities below the saturation intensity of the singly charged ion. Many, on the other hand, prefer to define the NSI as a process by which two electrons are ionized nearly simultaneously. This definition implies that apart from the sequential channel

478: 1146: 2804: 2489: 1879: 1890: 837:{\displaystyle W_{PPT}=\left|C_{n^{*}l^{*}}\right|^{2}{\sqrt {\frac {6}{\pi }}}f_{lm}E_{i}\left({\frac {2}{F}}\left(2E_{i}\right)^{\frac {3}{2}}\right)^{2n^{*}-|m|-{\frac {3}{2}}}\left(1+\gamma ^{2}\right)^{\left|{\frac {m}{2}}\right|+{\frac {3}{4}}}A_{m}(\omega ,\gamma )e^{-{\frac {2}{F}}\left(2E_{i}\right)^{\frac {3}{2}}g\left(\gamma \right)}} 1584:{\displaystyle {\begin{aligned}f_{lm}&={\frac {(2l+1)(l+|m|)!}{2^{m}|m|!(l-|m|)!}}\\g(\gamma )&={\frac {3}{2\gamma }}\left(1+{\frac {1}{2\gamma ^{2}}}\sinh ^{-1}(\gamma )-{\frac {\sqrt {1+\gamma ^{2}}}{2\gamma }}\right)\\|C_{n^{*}l^{*}}|^{2}&={\frac {2^{2n^{*}}}{n^{*}\Gamma (n^{*}+l^{*}+1)\Gamma (n^{*}-l^{*})}}\end{aligned}}} 2553: 2220: 1642: 4530:

one moves to the ‘oscillating’ or ‘Kramers–Henneberger’ frame, in which the classical electron is at rest. By a phase factor transformation for convenience one obtains the ‘space-translated’ Hamiltonian, which is unitarily equivalent to the lab-frame Hamiltonian, which contains the original potential

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The short pulse induced molecular fragmentation may be used as an ion source for high performance mass spectroscopy. The selectivity provided by a short pulse based source is superior to that expected when using the conventional electron ionization based sources, in particular when the identification

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Two models have been proposed to explain the non-sequential ionization; the shake-off model and electron re-scattering model. The shake-off (SO) model, first proposed by Fittinghoff et al., is adopted from the field of ionization of atoms by X rays and electron projectiles where the SO process is one

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In 1992, de Boer and Muller showed that Xe atoms subjected to short laser pulses could survive in the highly excited states 4f, 5f, and 6f. These states were believed to have been excited by the dynamic Stark shift of the levels into multiphoton resonance with the field during the rising part of the

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The phenomenon of non-sequential ionization (NSI) of atoms exposed to intense laser fields has been a subject of many theoretical and experimental studies since 1983. The pioneering work began with the observation of a "knee" structure on the Xe ion signal versus intensity curve by L’Huillier et al.

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In calculating the rate of MPI of atoms only transitions to the continuum states are considered. Such an approximation is acceptable as long as there is no multiphoton resonance between the ground state and some excited states. However, in real situation of interaction with pulsed lasers, during the

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The KH frame is thus employed in theoretical studies of strong-field ionization and atomic stabilization (a predicted phenomenon in which the ionization probability of an atom in a high-intensity, high-frequency field actually decreases for intensities above a certain threshold) in conjunction with

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Kuchiev did not include the Coulomb effects on the dynamics of the ionized electron. This resulted in the underestimation of the double ionization rate by a huge factor. Obviously, in the approach of Becker and Faisal (which is equivalent to Kuchiev's model in spirit), this drawback does not exist.

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Keldysh modeled the MPI process as a transition of the electron from the ground state of the atom to the Volkov states. In this model the perturbation of the ground state by the laser field is neglected and the details of atomic structure in determining the ionization probability are not taken into

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Schematic presentation of lambda type population trapping. G is the ground state of the atom. 1 and 2 are two degenerate excited states. After the population is transferred to the states due to multiphoton resonance, these states are coupled through continuum c and the population is trapped in the

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We mention the theoretical calculation that incomplete ionization occurs whenever there is parallel resonant excitation into a common level with ionization loss. We consider a state such as 6f of Xe which consists of 7 quasi-degnerate levels in the range of the laser bandwidth. These levels along

4932:(table salt) into sodium and chlorine ions. Although it may seem as a case of ionization, in reality the ions already exist within the crystal lattice. When salt is dissociated, its constituent ions are simply surrounded by water molecules and their effects are visible (e.g. the solution becomes 4150:

The re-scattering model in Kuchiev's version (Kuchiev's model) is quantum mechanical. The basic idea of the model is illustrated by Feynman diagrams in figure a. First both electrons are in the ground state of an atom. The lines marked a and b describe the corresponding atomic states. Then the

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In general, the analytic solutions are not available, and the approximations required for manageable numerical calculations do not provide accurate enough results. However, when the laser intensity is sufficiently high, the detailed structure of the atom or molecule can be ignored and analytic

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is the time-dependent energy difference between the two dressed states. In interaction with a short pulse, if the dynamic resonance is reached in the rising or the falling part of the pulse, the population practically remains in the ground state and the effect of multiphoton resonances may be

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The Kramers–Henneberger frame is the non-inertial frame moving with the free electron under the influence of the harmonic laser pulse, obtained by applying a translation to the laboratory frame equal to the quiver motion of a classical electron in the laboratory frame. In other words, in the

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of the device. If the electric field is strong enough, the free electron gains sufficient energy to liberate a further electron when it next collides with another molecule. The two free electrons then travel towards the anode and gain sufficient energy from the electric field to cause impact

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laser was reported by Augst et al. Later, systematically studying the NSI of all rare gas atoms, the quadruple NSI of Xe was observed. The most important conclusion of this study was the observation of the following relation between the rate of NSI to any charge state and the rate of tunnel

209:, i.e. experiments in which the complete momentum vector of all collision fragments (the scattered projectile, the recoiling target-ion, and the ejected electron) are determined, have contributed to major advances in the theoretical understanding of the few-body problem in recent years. 2179:{\displaystyle {\begin{aligned}w_{m}(x)&=e^{-x^{2}}\int _{0}^{x}(x^{2}-y^{2})^{m}e^{y^{2}}\,dy\\\alpha (\gamma )&=2\left(\sinh ^{-1}(\gamma )-{\frac {\gamma }{\sqrt {1+\gamma ^{2}}}}\right)\\v&={\frac {E_{i}}{\omega }}\left(1+{\frac {2}{\gamma ^{2}}}\right)\end{aligned}}} 4438: 184:

Avalanche effect in an electric field created between two electrodes. The original ionization event liberates one electron, and each subsequent collision liberates a further electron, so two electrons emerge from each collision: the ionizing electron and the liberated

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methods where the wave function is expanded in a finite basis set. There are numerous options available e.g. B-splines or Coulomb wave packets. Another non-perturbative method is to solve the corresponding Schrödinger equation fully numerically on a lattice.

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The interaction of atoms and molecules with sufficiently strong laser pulses or with other charged particles leads to the ionization to singly or multiply charged ions. The ionization rate, i.e. the ionization probability in unit time, can be calculated using

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without going into the details of wave functions or the ionization process. An example is presented in the figure to the right. The periodic abrupt decrease in ionization potential after rare gas atoms, for instance, indicates the emergence of a new shell in

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evolution of laser intensity, due to different Stark shift of the ground and excited states there is a possibility that some excited state go into multiphoton resonance with the ground state. Within the dressed atom picture, the ground state dressed by

2799:{\displaystyle W_{KRA}=\sum _{n=N}^{\infty }2\pi \omega ^{2}p\left(n-n_{\mathrm {osc} }\right)^{2}\int \mathrm {d} \Omega \left|FT\left(I_{KAR}\Psi \left(\mathbf {r} \right)\right)\right|^{2}J_{n}^{2}\left(n_{f},{\frac {n_{\mathrm {osc} }}{2}}\right)} 3979: 196:

Positively charged ions are produced by transferring an amount of energy to a bound electron in a collision with charged particles (e.g. ions, electrons or positrons) or with photons. The threshold amount of the required energy is known as

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and collision-mediated ionization. In these cases, during the ionization process, the energy of the electron exceeds the energy difference of the potential barrier it is trying to pass. The classical description, however, cannot describe

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The ionization of inner valence electrons are responsible for the fragmentation of polyatomic molecules in strong laser fields. According to a qualitative model the dissociation of the molecules occurs through a three-step mechanism:

2484:{\displaystyle W_{ADK}=\left|C_{n^{*}l^{*}}\right|^{2}{\sqrt {\frac {6}{\pi }}}f_{lm}E_{i}\left({\frac {2}{F}}\left(2E_{i}\right)^{\frac {3}{2}}\right)^{2n^{*}-|m|-{\frac {3}{2}}}e^{-{\frac {2}{3F}}\left(2E_{i}\right)^{\frac {3}{2}}}} 1874:{\displaystyle A_{m}(\omega ,\gamma )={\frac {4}{3\pi }}{\frac {1}{|m|!}}{\frac {\gamma ^{2}}{1+\gamma ^{2}}}\sum _{n>v}^{\infty }e^{-(n-v)\alpha (\gamma )}w_{m}\left({\sqrt {{\frac {2\gamma }{\sqrt {1+\gamma ^{2}}}}(n-v)}}\right)} 261:

ionization when the next collisions occur; and so on. This is effectively a chain reaction of electron generation, and is dependent on the free electrons gaining sufficient energy between collisions to sustain the avalanche.

2547:-gauge, which emphasizes the particle nature of light (absorbing multiple photons during ionization). This approach was adopted by Krainov model based on the earlier works of Faisal and Reiss. The resulting rate is given by 334:. (There are classical methods available also, like the Classical Trajectory Monte Carlo Method (CTMC) ,but it is not overall accepted and often criticized by the community.) There are two quantum mechanical methods exist, 4660:

The utility of the KH frame lies in the fact that in this frame the laser-atom interaction can be reduced to the form of an oscillating potential energy, where the natural parameters describing the electron dynamics are

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without necessarily producing ions. As an example, the molecules of table sugar dissociate in water (sugar is dissolved) but exist as intact neutral entities. Another subtle event is the dissociation of

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Negatively charged ions are produced when a free electron collides with an atom and is subsequently trapped inside the electric potential barrier, releasing any excess energy. The process is known as

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laser pulse. Subsequent evolution of the laser pulse did not completely ionize these states, leaving behind some highly excited atoms. We shall refer to this phenomenon as "population trapping".

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In the dipole approximation, the quiver motion of a classical electron in the laboratory frame for an arbitrary field can be obtained from the vector potential of the electromagnetic field:

3688: 4036: 3785: 3690:, then the excited state is populated. After being populated, since the ionization potential of the excited state is small, it is expected that the electron will be instantly ionized. 6156:

Sharifi, S. M.; Talebpour, A; Yang, J.; Chin, S. L. (2010). "Quasi-static tunnelling and multiphoton processes in the ionization of Ar and Xe using intense femtosecond laser pulses".

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the system reduces to the so-called ‘structure equation’, which has the form of a typical energy-eigenvalue Schrödinger equation containing the ‘dressed potential’

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Walker, B.; Sheehy, B.; Dimauro, L. F.; Agostini, P.; Schafer, K. J.; Kulander, K. C. (1994). "Precision Measurement of Strong Field Double Ionization of Helium".

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Krainov, Vladimir P. (1997). "Ionization rates and energy and angular distributions at the barrier-suppression ionization of complex atoms and atomic ions".

5622:"Recommendations for Nomenclature and Symbolism for Mass Spectroscopy (including an appendix of terms used in vacuum technology)(IUPAC Recommendations 1991)" 4188:

Kramers–Henneberger frame the classical electron is at rest. Starting in the lab frame (velocity gauge), we may describe the electron with the Hamiltonian:

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Augst, S.; Talebpour, A.; Chin, S. L.; Beaudoin, Y.; Chaker, M. (1995). "Nonsequential triple ionization of argon atoms in a high-intensity laser field".

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The quasi-static tunneling (QST) is the ionization whose rate can be satisfactorily predicted by the ADK model, i.e. the limit of the PPT model when

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L’Huillier, A.; Lompre, L. A.; Mainfray, G.; Manus, C. (1983). "Multiply charged ions induced by multiphoton absorption in rare gases at 0.53 μm".

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MPI of electrons from the inner orbitals of the molecule which results in a molecular ion in ro-vibrational levels of an excited electronic state;

297:. In addition, the local maximums in the ionization energy plot, moving from left to right in a row, are indicative of s, p, d, and f sub-shells. 4742:

From here one can apply Floquet theory to calculate quasi-stationary solutions of the TDSE. In high frequency Floquet theory, to lowest order in

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Mehdi Sharifi, S.; Talebpour, A.; Chin, S. L. (2008). "Ultra-fast laser pulses provide an ion source for highly selective mass spectroscopy".

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Becker, A.; Faisal, F. H. M. (1999). "S-matrix analysis of ionization yields of noble gas atoms at the focus of Ti:sapphire laser pulses".

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of atoms is often used to demonstrate the periodic behavior of atoms with respect to the atomic number, as summarized by ordering atoms in

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Talebpour, A; Bandrauk, A D; Vijayalakshmi, K; Chin, S L (2000). "Dissociative ionization of benzene in intense ultra-fast laser pulses".

5715:"Comparison of single-electron removal processes in collisions of electrons, positrons, protons, and antiprotons with hydrogen and helium" 6654:

Larochelle, S.; Talebpour, A.; Chin, S. L. (1998). "Non-sequential multiple ionization of rare gas atoms in a Ti:Sapphire laser field".

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which is the main contribution to the production of doubly charged ions at lower intensities. The first observation of triple NSI in

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the Coulomb potential is negligible compared to the potential of the laser field. The electron emerges from under the barrier at

335: 7157: 6809: 6518:"Photoelectron spectra and high Rydberg states of lithium generated by intense lasers in the over-the-barrier ionization regime" 5411:"The effect of an ion generator on indoor air quality in a residential room: Effect of an ion generator on indoor air in a room" 6387:

De Boer, M.; Muller, H. (1992). "Observation of large populations in excited states after short-pulse multiphoton ionization".

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Schafer, K. J.; Yang, B.; DiMauro, L.F.; Kulander, K.C. (1992). "Above threshold ionization beyond the high harmonic cutoff".

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Story, J.; Duncan, D.; Gallagher, T. (1994). "Landau-Zener treatment of intensity-tuned multiphoton resonances of potassium".

5346: 5246: 5165: 4433:{\displaystyle \mathbf {\alpha } (t)\equiv {\frac {1}{c}}\int _{0}^{t}\mathbf {A} (t')dt'=(\alpha _{0}/E_{0})\mathbf {E} (t)} 236:

is a good example of the creation of positive ions and free electrons due to ion impact. It is a cascade reaction involving

907: 5001: 4446: 7023:"Multiphoton ionization of inner-valence electrons and fragmentation of ethylene in an intense Ti:sapphire laser pulse" 3427: 2867: 2543:-gauge, meaning that the laser field is taken as electromagnetic waves. The ionization rate can also be calculated in 5608: 5395: 5379: 5321: 5296: 5271: 5221: 4775: 206: 100:, often in conjunction with other chemical changes. The resulting electrically charged atom or molecule is called an 7271: 5855:"Wave-packet continuum-discretization approach to single ionization of helium by antiprotons and energetic protons" 3649: 5183:"Current status of antiproton impact ionization of atoms and molecules: theoretical and experimental perspectives" 7568: 3987: 3723: 7638: 7563: 7294: 5068: 172:). It is also widely used for air purification, though studies have shown harmful effects of this application. 4158: 7750: 7578: 5099: 6517: 4853: 4534: 1597: 264:

Ionization efficiency is the ratio of the number of ions formed to the number of electrons or photons used.

7760: 7633: 7378: 7053: 6097: 4711: 4502: 4041: 3974:{\displaystyle W_{NS}(A^{n+})=\sum _{i=1}^{n-1}\alpha _{n}\left(\lambda \right)W_{ADK}\left(A^{i+}\right)} 2815: 7831: 190: 5182: 7841: 7836: 7821: 7806: 4945: 4171:

Rapid radiationless transition to the high-lying ro-vibrational levels of a lower electronic state; and

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Becker, Andreas; Faisal, Farhad H M (1996). "Mechanism of laser-induced double ionization of helium".

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coupling the two states. According to Story et al., the probability of remaining in the ground state,

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since the process involves the passage of electron through a classically forbidden potential barrier.

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Faisal, F. H. M.; Becker, A. (1997). "Nonsequential double ionization: Mechanism and model formula".

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Subsequent dissociation of the ion to different fragments through various fragmentation channels.

217:

Adiabatic ionization is a form of ionization in which an electron is removed from or added to an

5683: 3014: 1070: 164:. The ionization process is widely used in a variety of equipment in fundamental science (e.g., 132:

can result in the formation of ion pairs. Ionization can occur through radioactive decay by the

7704: 7694: 7444: 7439: 6116:"Tunnel ionization of complex atoms and of atomic ions in an alternating electromagnetic field" 5815: 4146:

Feynman diagram for the process of double ionization in an atom through re-scattering mechanism

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Hioe, F. T.; Carrol, C. E. (1988). "Coherent population trapping in N-level quantum systems".

5745: 3615:{\displaystyle P_{g}=\exp \left(-{\frac {2\pi W_{m}^{2}}{\mathrm {d} W/\mathrm {d} t}}\right)} 31: 6293:

Reiss, Howard (1980). "Effect of an intense electromagnetic field on a weakly bound system".

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Glenn F Knoll. Radiation Detection and Measurement, third edition 2000. John Wiley and sons,

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is as follows: in the oscillating frame, the nucleus has an oscillatory motion of trajectory

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are some constants depending on the wavelength of the laser (but not on the pulse duration).

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Peng, Jiahui; Puskas, Noah; Corkum, Paul B.; Rayner, David M.; Loboda, Alexandre V. (2012).

6135: 5942: 1040: 7623: 7383: 7122: 7079: 7037: 6987: 6944: 6872: 6821: 6774: 6710: 6663: 6620: 6585: 6532: 6482: 6439: 6396: 6345: 6302: 6259: 6216: 6165: 6127: 6073: 6036: 6028: 5994: 5986: 5915: 5866: 5827: 5523: 5484: 5125: 4887: 4826: 4650:{\displaystyle H_{KH}={\frac {1}{2}}\mathbf {P} ^{2}+V(\mathbf {r} +\mathbf {\alpha } (t))} 4290:{\displaystyle H_{lab}={\frac {1}{2}}(\mathbf {P} +{\frac {1}{c}}\mathbf {A} (t))^{2}+V(r)} 4159:

Multiphoton ionization of inner-valence electrons and fragmentation of polyatomic molecules

4115: 4088: 3496: 3400: 3373: 2923: 428: 285: 198: 153: 5904:"Ionization of helium by antiprotons: Fully correlated, four-dimensional lattice approach" 5544: 288:. This is a valuable tool for establishing and understanding the ordering of electrons in 248:. Following an original ionization event, due to such as ionizing radiation, the positive 8: 7811: 7598: 7490: 7480: 7393: 7348: 6743: 6177: 5198: 4955: 4950: 133: 7126: 7083: 7041: 6991: 6948: 6876: 6825: 6778: 6714: 6667: 6624: 6589: 6536: 6486: 6443: 6400: 6349: 6306: 6263: 6220: 6169: 6131: 6077: 6032: 5990: 5919: 5870: 5831: 5527: 5488: 4823:(the cycle-average of the oscillating potential). The interpretation of the presence of 2952: 84:

specifically in Britain, Ireland, Australia and New Zealand) is the process by which an

37: 7745: 7674: 7508: 7193: 7138: 7095: 7003: 6896: 6845: 6679: 6498: 6189: 6089: 5785:"Ionization and dissociation using B-splines: photoionization of the hydrogen molecule" 5744:

Abdurakhmanov, I.B.; Plowman, C; Kadyrov, A.S.; Bray, I.; Mukhamedzhanov, A.M. (2020).

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Talebpour, A.; Chien, C. Y.; Chin, S. L. (1996). "Population trapping in rare gases".

5800: 4963:– Instrument for detecting gaseous ionization, used in ionizing radiation measurements 4911:

can be seen as the potential of the smeared out nuclear charge along its trajectory.

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photons and the resonant state undergo an avoided crossing at the resonance intensity

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and non-perturbative methods like time-dependent coupled-channel or time independent

331: 318: 305: 281: 169: 165: 7197: 6849: 6271: 5662: 5584: 4984:– The chain reaction of ionization occurring in a gas with an applied electric field 3646:

neglected. However, if the states go onto resonance at the peak of the pulse, where

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Process by which atoms or molecules acquire charge by gaining or losing electrons

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Andersen, T (2004). "Atomic negative ions: structure, dynamics and collisions".

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Lectures on Ion-Atom Collisions: From Nonrelativistic to Relativistic Velocities

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By applying a transformation to the laboratory frame equal to the quiver motion

4112:) of the laser. Corkum's model places a cut-off limit on the minimum intensity ( 4081:

The electron rescattering model was independently developed by Kuchiev, Schafer

7518: 7513: 7470: 7403: 7398: 6544: 5927: 5878: 5761: 5150:

Springer Handbook of Atomic, Molecular, and Optical Physics. Springer Handbooks

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Machacek, J.R.; McEachran, R.P.; Stauffer, A.D. (2023). "Positron Collisions".

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is proportional to intensity) where ionization due to re-scattering can occur.

339: 241: 201:. The study of such collisions is of fundamental importance with regard to the 7134: 7816: 7800: 7755: 7735: 7658: 7618: 7553: 7485: 7408: 7236: 7181: 6892: 6632: 6597: 6562: 6451: 6365: 6357: 6322: 6314: 6279: 6236: 6185: 5730: 5661:, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) " 5583:, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) " 3708: 3424:, at the avoided crossing is proportional to the generalized Rabi frequency, 294: 46: 6228: 5670: 5638: 5621: 5592: 65:

of these particles causes them to emit light of varying color, thus forming

7780: 7653: 7648: 7643: 7608: 7558: 7475: 7189: 6964: 6841: 6794: 6730: 6416: 5746:"One-center close-coupling approach to two-center rearrangement collisions" 5553: 5436: 5104: 5087: 4933: 226: 104:. Ionization can result from the loss of an electron after collisions with 54: 7279: 6640: 6459: 6373: 6250:

Faisal, F. H. M. (1973). "Multiple absorption of laser photons by atoms".

5371: 3841:

ionization (predicted by the ADK formula) to the previous charge states;

7689: 7583: 7495: 7266: 7158:"High-Pressure Gas Phase Femtosecond Laser Ionization Mass Spectrometry" 5887: 5535: 136:

process, in which an excited nucleus transfers its energy to one of the

7628: 7530: 7500: 7434: 7413: 7249:

Gavrila, Mihai. "Atomic structure and decay in high-frequency fields."

4966: 372:, the potential of the laser can be neglected, while at distances with 309: 117: 42: 7173: 6697:

Fittinghoff, D. N.; Bolton, P. R.; Chang, B.; Kulander, K. C. (1992).

6553: 5769: 3209:{\textstyle n_{f}=2{\sqrt {n_{\mathrm {osc} }/\omega }}p\cos(\theta )} 359:

Combined potential of an atom and a uniform laser field. At distances

355: 2534: 180: 58: 7363: 6698: 4142: 7765: 7593: 5853:

Abdurakhmanov, I.B.; Kadyrov, A.S.; Bray, I; Bartschat, K. (2017).

5080: 237: 222: 109: 97: 89: 7069: 3333:{\displaystyle I_{KAR}=\left({\frac {2Z^{2}}{n^{2}Fr}}\right)^{n}} 7725: 7613: 7548: 7465: 7460: 5852: 5063: 3127:{\displaystyle p={\sqrt {2\omega (n-n_{\mathrm {osc} }-n_{i})}},} 253: 66: 7253:

edited by Mihai Gavrila, Academic Press, Inc, 1992, pp. 435-508.

7334: 5743: 5041: 4038:

is the rate of quasi-static tunneling to i'th charge state and

324: 113: 6696: 3009:

is the minimum number of photons necessary to ionize the atom,

276:

Ionization energies of neutral elements (predicted beyond 104)

30:"Ionisation" redirects here. For the musical composition, see 7343: 7329: 7021:

Talebpour, A.; Bandrauk, A. D.; Yang, J; Chin, S. L. (1999).

6575: 5036: 4936:). However, no transfer or displacement of electrons occurs. 3833: 257: 50: 6059:"Coulomb effect in multiphoton ionization of rare-gas atoms" 3837: 895:{\displaystyle \gamma ={\frac {\omega {\sqrt {2E_{i}}}}{F}}} 7217: