5757:
330:. This is because, unlike the more common Thomson scattering that happens at the low-energy limit, the energy in the scattered photon in Compton scattering is less than the energy of the incident photon. As the electron is typically weakly bound to the atom, the scattering can be viewed from either the perspective of an electron in a potential well, or as an atom with a small ionization energy. In the former perspective, energy of the incident photon is transferred to the recoil particle, but only as kinetic energy. The electron gains no internal energy, respective masses remain the same, the mark of an
42:
232:
302:. Thus, if we are to explain low-intensity Compton scattering, light must behave as if it consists of particles. Or the assumption that the electron can be treated as free is invalid resulting in the effectively infinite electron mass equal to the nuclear mass (see e.g. the comment below on elastic scattering of X-rays being from that effect). Compton's experiment convinced physicists that light can be treated as a stream of particle-like objects (quanta called photons), whose energy is proportional to the light wave's frequency.
4250:(NICS) is the scattering of multiple low-energy photons, given by an intense electromagnetic field, in a high-energy photon (X-ray or gamma ray) during the interaction with a charged particle, such as an electron. It is also called non-linear Compton scattering and multiphoton Compton scattering. It is the non-linear version of inverse Compton scattering in which the conditions for multiphoton absorption by the charged particle are reached due to a very intense electromagnetic field, for example the one produced by a
5254:
2615:
374:
1028:
5793:
5817:
216:
5769:
5805:
5781:
2354:
4079:
1074:
At the conclusion of
Compton's 1923 paper, he reported results of experiments confirming the predictions of his scattering formula, thus supporting the assumption that photons carry momentum as well as quantized energy. At the start of his derivation, he had postulated an expression for the momentum
504:
that explained the X-ray shift by attributing particle-like momentum to light quanta (Einstein had proposed light quanta in 1905 in explaining the photo-electric effect, but
Compton did not build on Einstein's work). The energy of light quanta depends only on the frequency of the light. In his paper,
297:
scattered by charged particles, cannot explain shifts in wavelength at low intensity: classically, light of sufficient intensity for the electric field to accelerate a charged particle to a relativistic speed will cause radiation-pressure recoil and an associated
Doppler shift of the scattered light,
4257:
Non-linear inverse
Compton scattering is an interesting phenomenon for all applications requiring high-energy photons since NICS is capable of producing photons with energy comparable to the charged particle rest energy and higher. As a consequence NICS photons can be used to trigger other phenomena
2262:
Equation (1) relates the various energies associated with the collision. The electron's momentum change involves a relativistic change in the energy of the electron, so it is not simply related to the change in energy occurring in classical physics. The change of the magnitude of the momentum of
3878:
Magnetic
Compton scattering is an extension of the previously mentioned technique which involves the magnetisation of a crystal sample hit with high energy, circularly polarised photons. By measuring the scattered photons' energy and reversing the magnetisation of the sample, two different Compton
813:
Compton found that some X-rays experienced no wavelength shift despite being scattered through large angles; in each of these cases the photon failed to eject an electron. Thus the magnitude of the shift is related not to the
Compton wavelength of the electron, but to the Compton wavelength of the
261:
In
Compton's original experiment (see Fig. 1), the energy of the X ray photon (â 17 keV) was significantly larger than the binding energy of the atomic electron, so the electrons could be treated as being free after scattering. The amount by which the light's wavelength changes is
3273:
4881:
S. Chen; H. Avakian; V. Burkert; L. Vandenaweele; P. Eugenio; the CLAS collaboration; Ambrozewicz; Anghinolfi; Asryan; Bagdasaryan; Baillie; Ball; Baltzell; Barrow; Batourine; Battaglieri; Beard; Bedlinskiy; Bektasoglu; Bellis; Benmouna; Berman; Biselli; Bonner; Bouchigny; Boiarinov; Bosted;
2610:{\displaystyle {\begin{aligned}p_{e'}^{\,2}&=\mathbf {p} _{e'}\cdot \mathbf {p} _{e'}=(\mathbf {p} _{\gamma }-\mathbf {p} _{\gamma '})\cdot (\mathbf {p} _{\gamma }-\mathbf {p} _{\gamma '})\\&=p_{\gamma }^{\,2}+p_{\gamma '}^{\,2}-2p_{\gamma }\,p_{\gamma '}\cos \theta .\end{aligned}}}
2866:
505:
Compton derived the mathematical relationship between the shift in wavelength and the scattering angle of the X-rays by assuming that each scattered X-ray photon interacted with only one electron. His paper concludes by reporting on experiments which verified his derived relation:
310:
of the system is also conserved. If the scattered photon still has enough energy, the process may be repeated. In this scenario, the electron is treated as free or loosely bound. Experimental verification of momentum conservation in individual
Compton scattering processes by
3927:
305:
As shown in Fig. 2, the interaction between an electron and a photon results in the electron being given part of the energy (making it recoil), and a photon of the remaining energy being emitted in a different direction from the original, so that the overall
2257:
1018:
817:
In
Compton's original experiments the wavelength shift given above was the directly measurable observable. In modern experiments it is conventional to measure the energies, not the wavelengths, of the scattered photons. For a given incident energy
3570:
3417:
4184:(there is no phase relationship between the scattered photons), the MCP is representative of the bulk properties of the sample and is a probe of the ground state. This means that the MCP is ideal for comparison with theoretical techniques such as
1935:
4601:
Ridwan, S. M., El-Tayyeb, F., Hainfeld, J. F., & Smilowitz, H. M. (2020). Distributions of intravenous injected iodine nanoparticles in orthotopic U87 human glioma xenografts over time and tumor therapy. Nanomedicine, 15(24), 2369â2383.
1067:Ⲡdenote the electron after the collision. Compton allowed for the possibility that the interaction would sometimes accelerate the electron to speeds sufficiently close to the velocity of light as to require the application of Einstein's
3054:
3819:
494:
predicted that the wavelength of scattered rays should be equal to the initial wavelength, multiple experiments had found that the wavelength of the scattered rays was longer (corresponding to lower energy) than the initial wavelength.
2339:
1453:
334:. From this perspective, Compton scattering could be considered elastic because the internal state of the electron does not change during the scattering process. In the latter perspective, the atom's state is change, constituting an
188:), at the nucleus, or with just an electron. Pair production and the Compton effect occur at the level of the electron. When a high frequency photon scatters due to an interaction with a charged particle, there is a decrease in the
3686:
585:
2081:
1792:
4238:
Some synchrotron radiation facilities scatter laser light off the stored electron beam. This
Compton backscattering produces high energy photons in the MeV to GeV range subsequently used for nuclear physics experiments.
1264:
for all photon momentum terms which arise in course of the derivation below. The derivation which appears in Compton's paper is more terse, but follows the same logic in the same sequence as the following derivation.
365:. Compton scattering is the most important interaction in the intervening energy region, at photon energies greater than those typical of the photoelectric effect but less than the pair-production threshold.
1371:
3078:
5514:
4192:
magnetometry), can be used to isolate both the spin and orbital contributions to the total moment of a system. The shape of the MCP also yields insight into the origin of the magnetism in the system.
899:
2706:
2359:
3922:
1676:
After scattering, the possibility that the electron might be accelerated to a significant fraction of the speed of light, requires that its total energy be represented using the relativistic
4175:
4137:
4074:{\displaystyle J_{\text{mag}}(\mathbf {p} _{z})={\frac {1}{\mu }}\iint _{-\infty }^{\infty }(n_{\uparrow }(\mathbf {p} )-n_{\downarrow }(\mathbf {p} ))d\mathbf {p} _{x}d\mathbf {p} _{y}}
1574:
1671:
3468:
1590:
Before the scattering event, the electron is treated as sufficiently close to being at rest that its total energy consists entirely of the mass-energy equivalence of its (rest) mass
860:
345:
through soft X-rays, a photon can be completely absorbed and its energy can eject an electron from its host atom, a process known as the photoelectric effect. High-energy photons of
5551:
3879:
profiles are generated (one for spin up momenta and one for spin down momenta). Taking the difference between these two profiles gives the magnetic Compton profile (MCP), given by
814:
entire atom, which can be upwards of 10000 times smaller. This is known as "coherent" scattering off the entire atom since the atom remains intact, gaining no internal excitation.
894:
3716:
266:. Although nucleus Compton scattering exists, Compton scattering usually refers to the interaction involving only the electrons of an atom. The Compton effect was observed by
4216:
is presumed to produce a thermal spectrum. The lower energy photons produced from this spectrum are scattered to higher energies by relativistic electrons in the surrounding
2109:
1527:
635:
420:
3477:
2648:
1615:
690:
1171:
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1209:
1109:
608:
395:
3284:
1485:
742:
508:
488:
468:
440:
2910:
1250:
2698:
4099:
2900:
2671:
1132:
1289:
716:
657:
4574:
1948:
1803:
123:
158:, usually an electron. Specifically, when the photon hits electrons, it releases loosely bound electrons from the outer valence shells of atoms or molecules.
4188:. The area under the MCP is directly proportional to the spin moment of the system and so, when combined with total moment measurements methods (such as
5568:
2272:
1386:
450:
with matter was well under way. It was observed that when X-rays of a known wavelength interact with atoms, the X-rays are scattered through an angle
5029:
4321:
341:
Compton scattering is one of four competing processes when photons interact with matter. At energies of a few eV to a few keV, corresponding to
1685:
200:
the lost energy from the photon is transferred to the recoiling particle (such an electron would be called a "Compton Recoil electron").
3268:{\displaystyle (hf-hf'+m_{\text{e}}c^{2})^{2}-m_{\text{e}}^{\,2}c^{4}=\left(hf\right)^{2}+\left(hf'\right)^{2}-2h^{2}ff'\cos {\theta },}
116:
5609:
203:
This implies that if the recoiling particle initially carried more energy than the photon, the reverse would occur. This is known as
338:. Whether Compton scattering is considered elastic or inelastic depends on which perspective is being used, as well as the context.
5672:
5619:
223:
target on the left. The slit passes X-ray photons scattered at the selected angle and their average energy rate is measured using
5291:
4585:
5531:
5852:
5546:
5022:
4666:
4630:
4326:
4247:
4224:
2861:{\displaystyle p_{e'}^{\,2}c^{2}=p_{\gamma }^{\,2}c^{2}+p_{\gamma '}^{\,2}c^{2}-2c^{2}p_{\gamma }\,p_{\gamma '}\cos \theta .}
109:
3851:, as it is the most probable interaction of gamma rays and high energy X-rays with atoms in living beings and is applied in
1297:
5629:
5624:
4882:
Bradford; Branford; et al. (2006). "Measurement of Deeply Virtual Compton Scattering with a Polarized Proton Target".
4652:
Barbiellini, B., Bansil, A. (2020). Scattering Techniques, Compton. Materials Science and Materials Engineering, Elsevier.
4235:. Observations of the SunyaevâZel'dovich effect provide a nearly redshift-independent means of detecting galaxy clusters.
4177:
are the three-dimensional electron momentum distributions for the majority spin and minority spin electrons respectively.
5702:
5687:
5556:
4311:
271:
3882:
5257:
4555:
4519:
4494:
4469:"Observation of the Transition from Thomson to Compton Scattering in Optical Multiphoton Interactions with Electrons"
4451:
4220:. This is surmised to cause the power law component in the X-ray spectra (0.2â10 keV) of accreting black holes.
4571:
5857:
5842:
5604:
5583:
5129:
5015:
4232:
4142:
243:
value for the process on the right becomes larger than the cross section for the process on the left. For calcium (
5756:
5052:
4104:
4980:
Stuewer, Roger H. (1975), The Compton Effect: Turning Point in Physics (New York: Science History Publications)
1013:{\displaystyle E_{\gamma ^{\prime }}={\frac {E_{\gamma }}{1+(E_{\gamma }/m_{\text{e}}c^{2})(1-\cos \theta )}}.}
17:
1623:
5634:
5599:
4468:
4286:
4276:
821:
5697:
5667:
5526:
5499:
1677:
865:
5677:
5644:
5614:
5578:
5284:
5179:
5062:
3426:
5747:
5723:
5563:
5451:
5002:
2252:{\displaystyle {\frac {1}{c}}{\sqrt {(hf-hf'+m_{e}c^{2})^{2}-m_{e}^{2}c^{4}}}>{\frac {hf-hf'}{c}}~.}
1211:. The photon's momentum is then simply this effective mass times the photon's frame-invariant velocity
491:
177:
and quantum mechanics to explain the interaction between high frequency photons and charged particles.
1533:
349:
and above may bombard the nucleus and cause an electron and a positron to be formed, a process called
5862:
5200:
5139:
5067:
4996:
4974:
4396:
4281:
4185:
3565:{\displaystyle {\frac {c}{f'}}-{\frac {c}{f}}={\frac {h}{m_{\text{e}}c}}\left(1-\cos \theta \right).}
4347:
2263:
the photon is not just related to the change of its energy; it also involves a change in direction.
1496:
5390:
4990:
4231:. The CMB photons are scattered to higher energies by the electrons in this gas, resulting in the
2099:
Note that this magnitude of the momentum gained by the electron (formerly zero) exceeds the energy/
1377:
327:
4833:"Quantum effects of the interaction of elementary particles with an intense electromagnetic field"
2623:
1593:
668:
173:
in 1927. The Compton effect significantly deviated from dominating classical theories, using both
5847:
5093:
5038:
4884:
4263:
240:
3412:{\displaystyle 2hfm_{\text{e}}c^{2}-2hf'm_{\text{e}}c^{2}=2h^{2}ff'\left(1-\cos \theta \right).}
5692:
5541:
5277:
1269:
1137:
615:
400:
279:
197:
170:
5215:
4306:
1176:
1078:
593:
380:
5837:
5652:
5521:
5329:
3814:{\displaystyle \cot \varphi =\left(1+{\frac {hf}{m_{\text{e}}c^{2}}}\right)\tan(\theta /2)~.}
1940:
This expression can be used to find the magnitude of the momentum of the scattered electron,
1461:
727:
473:
453:
425:
285:
The effect is significant because it demonstrates that light cannot be explained purely as a
2266:
Solving the conservation of momentum expression for the scattered electron's momentum gives
1218:
5489:
5421:
5354:
4954:
4903:
4805:
4750:
4408:
4301:
2676:
294:
267:
181:
54:
5225:
4084:
2902:, we get a second expression for the magnitude of the momentum of the scattered electron,
2874:
8:
5821:
5441:
5416:
5395:
5169:
4181:
3867:
1930:{\displaystyle hf+m_{\text{e}}c^{2}=hf'+{\sqrt {(p_{e'}c)^{2}+(m_{\text{e}}c^{2})^{2}}}.}
362:
335:
185:
92:
4958:
4907:
4809:
4754:
4412:
3278:
which, after evaluating the square and canceling and rearranging terms, further yields
2653:
1114:
5809:
5797:
5682:
5461:
5359:
5235:
5134:
4927:
4893:
4860:
4774:
4740:
4424:
4316:
3859:
1797:
Substituting these quantities into the expression for the conservation of energy gives
1274:
1068:
775:
701:
693:
642:
397:
comes in from the left, collides with a target at rest, and a new photon of wavelength
290:
174:
66:
41:
4728:
1031:
Fig. 3: Energies of a photon at 500 keV and an electron after Compton scattering.
5730:
5662:
5657:
5484:
5456:
5349:
5195:
5164:
4919:
4864:
4852:
4778:
4766:
4653:
4626:
4582:
4551:
4515:
4490:
4447:
4428:
4420:
3852:
1075:
of a photon from equating Einstein's already established mass-energy relationship of
442:. The target recoils, carrying away an angle-dependent amount of the incident energy.
331:
231:
144:
4931:
4683:
3708:
of the outgoing electron with the direction of the incoming photon is specified by
1047:
in an atom, which is treated as being at rest. The collision causes the electron to
298:
but the effect would become arbitrarily small at sufficiently low light intensities
219:
Fig. 1: Schematic diagram of Compton's experiment. Compton scattering occurs in the
5773:
5446:
5324:
5230:
5113:
4962:
4911:
4844:
4813:
4758:
4416:
4377:
4259:
224:
155:
4915:
5718:
5573:
5436:
5400:
5319:
5174:
5159:
5057:
4945:
4616:
4589:
4578:
4291:
4205:
3681:{\displaystyle \lambda '-\lambda ={\frac {h}{m_{\text{e}}c}}(1-\cos {\theta })~.}
2334:{\displaystyle \mathbf {p} _{e'}=\mathbf {p} _{\gamma }-\mathbf {p} _{\gamma '}.}
1584:
1448:{\displaystyle \mathbf {p} _{\gamma }=\mathbf {p} _{\gamma '}+\mathbf {p} _{e'},}
660:
500:
350:
85:
4704:
580:{\displaystyle \lambda '-\lambda ={\frac {h}{m_{\text{e}}c}}(1-\cos {\theta }),}
5761:
5205:
4762:
4228:
4217:
4209:
3049:{\displaystyle p_{e'}^{\,2}c^{2}=(hf)^{2}+(hf')^{2}-2(hf)(hf')\cos {\theta }~.}
2345:
719:
358:
162:
4832:
4793:
4729:"Extremely high-intensity laser interactions with fundamental quantum systems"
5831:
5494:
4856:
4770:
4727:
Di Piazza, A.; MĂźller, C.; Hatsagortsyan, K. Z.; Keitel, C. H. (2012-08-16).
4547:
3866:, as it is possible for the gamma rays to scatter out of the detectors used.
342:
312:
5785:
5536:
5431:
5344:
5334:
4967:
4940:
4923:
4201:
3863:
3848:
99:
5007:
4880:
5385:
5154:
5144:
5108:
5083:
4296:
2076:{\displaystyle p_{e'}^{\,2}c^{2}=(hf-hf'+m_{e}c^{2})^{2}-m_{e}^{2}c^{4}.}
316:
4603:
1787:{\displaystyle E_{e'}={\sqrt {(p_{e'}c)^{2}+(m_{\text{e}}c^{2})^{2}}}~.}
227:
from the crystal on the right in conjunction with an ionization chamber.
5509:
5375:
5220:
5149:
4898:
4848:
4622:
4213:
320:
193:
151:
3870:
is used to detect stray scatter gamma rays to counteract this effect.
235:
Plot of photon energies calculated for a given element (atomic number
4817:
4369:
4262:, and can be used to probe non-linear quantum effects and non-linear
373:
319:
as well as by Compton and Simon has been important in disproving the
275:
4487:
An Introduction to the Passage of Energetic Particles through Matter
4381:
353:; even-higher-energy photons (beyond a threshold energy of at least
5380:
5103:
5088:
1027:
307:
220:
4745:
4726:
4667:"Comptonization mechanisms in hot coronae in AGN. The NuSTAR view"
5504:
5269:
4941:"A Quantum Theory of the Scattering of X-Rays by Light Elements"
1291:
merely equates the sum of energies before and after scattering.
803:) and at most twice the Compton wavelength of the electron (for
5339:
5098:
1048:
189:
148:
1380:, the momenta of the particles should be similarly related by
1376:
Compton postulated that photons carry momentum; thus from the
5314:
5300:
4251:
4189:
3924:â a one-dimensional projection of the electron spin density.
447:
215:
166:
446:
By the early 20th century, research into the interaction of
357:, depending on the nuclei involved), can eject a nucleon or
3072:
Equating the alternate expressions for this momentum gives
286:
180:
Photons can interact with matter at the atomic level (e.g.
5780:
4514:(2nd ed.). Singapore: World Scientific. p. 271.
4581:
in Pazdur R, Wagman LD, Camphausen KA, Hoskins WJ (Eds)
4357:. University of Warwick: 10 – via Warwick Library.
4242:
4101:
is the number of spin-unpaired electrons in the system,
1487:) is omitted on the assumption it is effectively zero.
1022:
1490:
The photon energies are related to the frequencies by
1366:{\displaystyle E_{\gamma }+E_{e}=E_{\gamma '}+E_{e'}.}
5745:
4541:
4145:
4107:
4087:
3930:
3885:
3719:
3609:
3480:
3429:
3287:
3081:
2913:
2877:
2709:
2679:
2656:
2626:
2357:
2275:
2112:
1951:
1806:
1688:
1626:
1596:
1536:
1499:
1464:
1389:
1300:
1277:
1221:
1179:
1140:
1117:
1081:
1071:
theory to properly describe its energy and momentum.
902:
868:
824:
730:
704:
671:
645:
618:
596:
511:
476:
456:
428:
403:
383:
278:
in the years following. Compton was awarded the 1927
207:, in which the scattered photon increases in energy.
4542:
Taylor, J.R.; Zafiratos, C.D.; Dubson, M.A. (2004).
4938:
4654:https://doi.org/10.1016/B978-0-323-90800-9.00107-4
4223:The effect is also observed when photons from the
4169:
4131:
4093:
4073:
3916:
3813:
3680:
3564:
3462:
3411:
3267:
3048:
2894:
2860:
2692:
2665:
2642:
2609:
2333:
2251:
2075:
1929:
1786:
1665:
1609:
1568:
1521:
1479:
1447:
1365:
1283:
1244:
1203:
1165:
1126:
1103:
1012:
888:
854:
736:
710:
684:
651:
629:
602:
579:
482:
462:
434:
414:
389:
4322:Timeline of cosmic microwave background astronomy
5829:
4512:Interactions of Photons and Neutrons with Matter
3917:{\displaystyle J_{\text{mag}}(\mathbf {p} _{z})}
470:and emerge at a different wavelength related to
368:
4583:Cancer Management: A Multidisciplinary Approach
2871:After replacing the photon momentum terms with
1134:, which Einstein had separately postulated. If
4614:
4537:
4535:
4533:
4531:
4509:
4394:
3873:
5285:
5023:
4258:such as pair production, Compton scattering,
4227:(CMB) move through the hot gas surrounding a
4195:
4170:{\displaystyle n_{\downarrow }(\mathbf {p} )}
3858:Compton scattering is an important effect in
3847:Compton scattering is of prime importance to
274:and further verified by his graduate student
117:
4510:Chen, Sow-Hsin; Kotlarchyk, Michael (2007).
326:Compton scattering is commonly described as
250:), Compton scattering starts to dominate at
196:.) This is the Compton effect. Because of
192:of the photon (and thus, an increase in its
5037:
4544:Modern Physics for Scientists and Engineers
4528:
4200:Inverse Compton scattering is important in
4132:{\displaystyle n_{\uparrow }(\mathbf {p} )}
27:Scattering of photons off charged particles
5292:
5278:
5030:
5016:
4794:"High-intensity-laser-electron scattering"
4791:
4608:
862:, the outgoing final-state photon energy,
498:In 1923, Compton published a paper in the
124:
110:
4966:
4897:
4744:
4489:. Boca Raton, FL: CRC Press. p. 61.
4441:
3151:
2929:
2830:
2788:
2754:
2725:
2575:
2553:
2529:
2377:
1967:
4466:
4345:
1666:{\displaystyle E_{e}=m_{\text{e}}c^{2}.}
1026:
372:
230:
214:
4664:
4367:
855:{\displaystyle E_{\gamma }=hc/\lambda }
14:
5830:
4672:. DIPARTIMENTO DI MATEMATICA E FISICA.
4484:
4370:"XCOM: Photon Cross Sections Database"
3704:It can further be seen that the angle
169:by light elements, and earned him the
5273:
5011:
4830:
4722:
4720:
4604:https://doi.org/10.2217/nnm-2020-0178
4327:Non-linear inverse Compton scattering
4248:Non-linear inverse Compton scattering
4243:Non-linear inverse Compton scattering
3842:
1173:, the equivalent photon mass must be
1063:from the photon's incoming path. Let
889:{\displaystyle E_{\gamma ^{\prime }}}
361:from the nucleus in a process called
161:The effect was discovered in 1923 by
5003:Derivation of Compton shift equation
4705:"Duke University TUNL HIGS Facility"
4444:Introduction to Elementary Particles
3710:
3600:
2904:
2348:yields the square of its magnitude,
1942:
1111:to the quantized photon energies of
1023:Derivation of the scattering formula
165:while researching the scattering of
4798:IEEE Journal of Quantum Electronics
4312:Resonant inelastic X-ray scattering
637:is the wavelength after scattering,
24:
4874:
4717:
4615:Malcolm Cooper (14 October 2004).
3985:
3980:
3463:{\displaystyle 2hff'm_{\text{e}}c}
913:
879:
272:Washington University in St. Louis
25:
5874:
5299:
5258:Template:Quantum mechanics topics
4984:
4572:"Principles of Radiation Therapy"
4180:Since this scattering process is
5815:
5803:
5791:
5779:
5767:
5755:
5253:
5252:
5130:Anomalous magnetic dipole moment
4973:(the original 1923 paper on the
4837:Journal of Soviet Laser Research
4348:"X-Ray and Gamma Ray Scattering"
4160:
4122:
4061:
4046:
4031:
4007:
3946:
3901:
2491:
2476:
2450:
2435:
2412:
2392:
2313:
2298:
2278:
1569:{\displaystyle E_{\gamma '}=hf'}
1427:
1407:
1392:
778:of the electron; it is equal to
154:following an interaction with a
40:
4939:Compton, Arthur H. (May 1923).
4824:
4785:
4697:
4676:
4658:
4646:
4595:
4368:Seltzer, Stephen (2009-09-17).
3837:
377:Fig. 2: A photon of wavelength
210:
4564:
4503:
4478:
4460:
4435:
4388:
4361:
4339:
4164:
4156:
4151:
4126:
4118:
4113:
4038:
4035:
4027:
4022:
4011:
4003:
3998:
3990:
3956:
3941:
3911:
3896:
3802:
3788:
3669:
3649:
3129:
3082:
3026:
3012:
3009:
3000:
2985:
2970:
2958:
2948:
2506:
2471:
2465:
2430:
2172:
2125:
2033:
1986:
1913:
1889:
1877:
1855:
1767:
1743:
1731:
1709:
1522:{\displaystyle E_{\gamma }=hf}
1001:
983:
980:
942:
571:
551:
13:
1:
4916:10.1103/PhysRevLett.97.072002
4333:
4287:Nuclear electromagnetic pulse
4277:Compton Gamma Ray Observatory
1215:. For a photon, its momentum
369:Description of the phenomenon
293:, the classical theory of an
5853:Foundational quantum physics
4570:Camphausen KA, Lawrence RC.
4397:"Nuclear Compton scattering"
2643:{\displaystyle p_{\gamma }c}
1610:{\displaystyle m_{\text{e}}}
685:{\displaystyle m_{\text{e}}}
7:
5053:EulerâHeisenberg Lagrangian
4269:
4225:cosmic microwave background
3874:Magnetic Compton scattering
3827:
3694:
3062:
2089:
10:
5879:
5564:X-Ray Fluorescence Imaging
5452:Anomalous X-ray scattering
4999:â Georgia State University
4993:â Georgia State University
4763:10.1103/RevModPhys.84.1177
4446:. Wiley. pp. 15, 91.
4421:10.1088/0305-4616/12/9/008
4196:Inverse Compton scattering
1043:collides with an electron
610:is the initial wavelength,
492:classical electromagnetism
257:and ceases at 12 MeV.
205:inverse Compton scattering
5711:
5643:
5592:
5477:
5470:
5409:
5368:
5307:
5244:
5188:
5122:
5076:
5068:Path integral formulation
5045:
4792:Meyerhofer, D.D. (1997).
4733:Reviews of Modern Physics
4442:Griffiths, David (1987).
4346:Pattison, Philip (1975).
4233:SunyaevâZel'dovich effect
4186:density functional theory
2673:, multiply both sides by
1166:{\displaystyle mc^{2}=hf}
630:{\displaystyle \lambda '}
415:{\displaystyle \lambda '}
147:theory of high frequency
5391:Synchrotron light source
5236:Photon-photon scattering
4618:X-Ray Compton Scattering
3862:which gives rise to the
1678:energyâmomentum relation
1378:conservation of momentum
1204:{\displaystyle hf/c^{2}}
1104:{\displaystyle E=mc^{2}}
744:is the scattering angle.
603:{\displaystyle \lambda }
390:{\displaystyle \lambda }
300:regardless of wavelength
35:Lightâmatter interaction
5858:Quantum electrodynamics
5843:Observational astronomy
5410:Interaction with matter
5369:Sources and instruments
5180:WardâTakahashi identity
5063:GuptaâBleuler formalism
5039:Quantum electrodynamics
4997:Compton Scattering Data
4885:Physical Review Letters
4395:P. Christillin (1986).
3422:Dividing both sides by
1480:{\displaystyle {p_{e}}}
1258:can be substituted for
786:. The wavelength shift
737:{\displaystyle \theta }
483:{\displaystyle \theta }
463:{\displaystyle \theta }
435:{\displaystyle \theta }
171:Nobel Prize for Physics
5542:Diffraction tomography
4968:10.1103/PhysRev.21.483
4665:Dr. Tortosa, Alessia.
4401:J. Phys. G: Nucl. Phys
4171:
4133:
4095:
4075:
3918:
3815:
3682:
3566:
3464:
3413:
3269:
3050:
2896:
2862:
2694:
2667:
2644:
2611:
2335:
2253:
2077:
1931:
1788:
1667:
1611:
1570:
1523:
1481:
1449:
1367:
1285:
1270:conservation of energy
1246:
1245:{\displaystyle p=hf/c}
1205:
1167:
1128:
1105:
1032:
1014:
890:
856:
796:is at least zero (for
738:
712:
686:
653:
631:
604:
581:
484:
464:
443:
436:
416:
391:
280:Nobel Prize in Physics
258:
228:
198:conservation of energy
80:High-energy phenomena:
5653:X-ray crystallography
5522:Soft x-ray microscopy
5490:Panoramic radiography
5330:Synchrotron radiation
5201:BreitâWheeler process
5140:KleinâNishina formula
4831:Ritus, V. I. (1985).
4282:KleinâNishina formula
4172:
4134:
4096:
4076:
3919:
3816:
3683:
3567:
3465:
3414:
3270:
3051:
2897:
2863:
2695:
2693:{\displaystyle c^{2}}
2668:
2650:being replaced with
2645:
2612:
2336:
2254:
2078:
1932:
1789:
1668:
1612:
1571:
1524:
1482:
1450:
1368:
1286:
1247:
1206:
1168:
1129:
1106:
1030:
1015:
891:
857:
739:
713:
687:
654:
632:
605:
582:
485:
465:
437:
417:
392:
376:
234:
218:
61:Mid-energy phenomena:
49:Low-energy phenomena:
5422:Photoelectric effect
5355:Characteristic X-ray
4302:Photoelectric effect
4143:
4105:
4094:{\displaystyle \mu }
4085:
3928:
3883:
3717:
3607:
3478:
3427:
3285:
3079:
2911:
2895:{\displaystyle hf/c}
2875:
2707:
2677:
2654:
2624:
2355:
2273:
2110:
2103:lost by the photon,
1949:
1804:
1686:
1624:
1594:
1534:
1497:
1462:
1387:
1298:
1275:
1219:
1177:
1138:
1115:
1079:
900:
866:
822:
728:
702:
669:
643:
616:
594:
509:
474:
454:
426:
422:emerges at an angle
401:
381:
328:inelastic scattering
295:electromagnetic wave
268:Arthur Holly Compton
182:photoelectric effect
163:Arthur Holly Compton
55:Photoelectric effect
5442:Photodisintegration
5417:Rayleigh scattering
5396:Free-electron laser
5216:DelbrĂźck scattering
5170:Vacuum polarization
5094:FaddeevâPopov ghost
4959:1923PhRv...21..483C
4908:2006PhRvL..97g2002C
4810:1997IJQE...33.1935M
4755:2012RvMP...84.1177D
4485:Carron, NJ (2007).
4413:1986JPhG...12..837C
3989:
3868:Compton suppression
3156:
2934:
2793:
2759:
2730:
2620:In anticipation of
2558:
2534:
2382:
2198:
2059:
1972:
1059:Ⲡemerges at angle
1051:, and a new photon
363:photodisintegration
336:inelastic collision
282:for the discovery.
186:Rayleigh scattering
93:Photodisintegration
5683:X-ray reflectivity
5462:X-ray fluorescence
5427:Compton scattering
5360:High-energy X-rays
5211:Compton scattering
4991:Compton Scattering
4849:10.1007/BF01120220
4588:2013-10-04 at the
4577:2009-05-15 at the
4550:. pp. 136â9.
4317:Thomson scattering
4307:Radiation pressure
4167:
4129:
4091:
4071:
3972:
3914:
3860:gamma spectroscopy
3843:Compton scattering
3811:
3678:
3562:
3460:
3409:
3265:
3141:
3046:
2914:
2892:
2858:
2773:
2744:
2710:
2690:
2666:{\displaystyle hf}
2663:
2640:
2607:
2605:
2538:
2519:
2362:
2344:Making use of the
2331:
2249:
2184:
2073:
2045:
1952:
1927:
1784:
1663:
1607:
1566:
1519:
1477:
1445:
1363:
1281:
1242:
1201:
1163:
1127:{\displaystyle hf}
1124:
1101:
1069:special relativity
1055:Ⲡwith wavelength
1033:
1010:
886:
852:
776:Compton wavelength
734:
708:
694:electron rest mass
682:
649:
627:
600:
577:
480:
460:
444:
432:
412:
387:
291:Thomson scattering
259:
229:
175:special relativity
137:Compton scattering
74:Compton scattering
67:Thomson scattering
5743:
5742:
5739:
5738:
5731:X-ray lithography
5663:Backscatter X-ray
5658:X-ray diffraction
5485:X-ray radiography
5457:X-ray diffraction
5350:Siegbahn notation
5267:
5266:
5226:Møller scattering
5196:Bhabha scattering
5165:Uehling potential
5114:Virtual particles
4804:(11): 1935â1941.
4684:"GRAAL home page"
4632:978-0-19-850168-8
4467:C. Moore (1995).
4260:nuclear reactions
3970:
3938:
3893:
3853:radiation therapy
3835:
3834:
3807:
3775:
3761:
3702:
3701:
3674:
3647:
3640:
3532:
3525:
3507:
3494:
3454:
3341:
3304:
3148:
3115:
3070:
3069:
3042:
2245:
2241:
2209:
2121:
2097:
2096:
1922:
1899:
1823:
1780:
1776:
1753:
1647:
1604:
1284:{\displaystyle E}
1005:
967:
711:{\displaystyle c}
679:
652:{\displaystyle h}
549:
542:
332:elastic collision
134:
133:
16:(Redirected from
5870:
5863:X-ray scattering
5820:
5819:
5818:
5808:
5807:
5806:
5796:
5795:
5794:
5784:
5783:
5772:
5771:
5770:
5760:
5759:
5751:
5569:X-ray holography
5475:
5474:
5447:Radiation damage
5294:
5287:
5280:
5271:
5270:
5256:
5255:
5231:Schwinger effect
5032:
5025:
5018:
5009:
5008:
4972:
4970:
4935:
4901:
4869:
4868:
4828:
4822:
4821:
4818:10.1109/3.641308
4789:
4783:
4782:
4748:
4739:(3): 1177â1228.
4724:
4715:
4714:
4712:
4711:
4701:
4695:
4694:
4692:
4691:
4680:
4674:
4673:
4671:
4662:
4656:
4650:
4644:
4643:
4641:
4639:
4612:
4606:
4599:
4593:
4568:
4562:
4561:
4546:(2nd ed.).
4539:
4526:
4525:
4507:
4501:
4500:
4482:
4476:
4475:
4473:
4464:
4458:
4457:
4439:
4433:
4432:
4392:
4386:
4385:
4365:
4359:
4358:
4355:Warwick Database
4352:
4343:
4176:
4174:
4173:
4168:
4163:
4155:
4154:
4138:
4136:
4135:
4130:
4125:
4117:
4116:
4100:
4098:
4097:
4092:
4080:
4078:
4077:
4072:
4070:
4069:
4064:
4055:
4054:
4049:
4034:
4026:
4025:
4010:
4002:
4001:
3988:
3983:
3971:
3963:
3955:
3954:
3949:
3940:
3939:
3936:
3923:
3921:
3920:
3915:
3910:
3909:
3904:
3895:
3894:
3891:
3829:
3820:
3818:
3817:
3812:
3805:
3798:
3781:
3777:
3776:
3774:
3773:
3772:
3763:
3762:
3759:
3752:
3744:
3711:
3707:
3696:
3687:
3685:
3684:
3679:
3672:
3668:
3648:
3646:
3642:
3641:
3638:
3628:
3617:
3601:
3597:
3593:
3588:
3580:
3575:Finally, since
3571:
3569:
3568:
3563:
3558:
3554:
3533:
3531:
3527:
3526:
3523:
3513:
3508:
3500:
3495:
3493:
3482:
3470:
3469:
3467:
3466:
3461:
3456:
3455:
3452:
3446:
3418:
3416:
3415:
3410:
3405:
3401:
3380:
3369:
3368:
3353:
3352:
3343:
3342:
3339:
3333:
3316:
3315:
3306:
3305:
3302:
3274:
3272:
3271:
3266:
3261:
3250:
3239:
3238:
3223:
3222:
3217:
3213:
3212:
3192:
3191:
3186:
3182:
3166:
3165:
3155:
3149:
3146:
3137:
3136:
3127:
3126:
3117:
3116:
3113:
3104:
3064:
3055:
3053:
3052:
3047:
3040:
3039:
3025:
2993:
2992:
2983:
2966:
2965:
2944:
2943:
2933:
2927:
2926:
2905:
2901:
2899:
2898:
2893:
2888:
2867:
2865:
2864:
2859:
2845:
2844:
2843:
2829:
2828:
2819:
2818:
2803:
2802:
2792:
2786:
2785:
2769:
2768:
2758:
2752:
2740:
2739:
2729:
2723:
2722:
2699:
2697:
2696:
2691:
2689:
2688:
2672:
2670:
2669:
2664:
2649:
2647:
2646:
2641:
2636:
2635:
2616:
2614:
2613:
2608:
2606:
2590:
2589:
2588:
2574:
2573:
2557:
2551:
2550:
2533:
2527:
2512:
2505:
2504:
2503:
2494:
2485:
2484:
2479:
2464:
2463:
2462:
2453:
2444:
2443:
2438:
2426:
2425:
2424:
2415:
2406:
2405:
2404:
2395:
2381:
2375:
2374:
2340:
2338:
2337:
2332:
2327:
2326:
2325:
2316:
2307:
2306:
2301:
2292:
2291:
2290:
2281:
2258:
2256:
2255:
2250:
2243:
2242:
2237:
2236:
2215:
2210:
2208:
2207:
2197:
2192:
2180:
2179:
2170:
2169:
2160:
2159:
2147:
2124:
2122:
2114:
2091:
2082:
2080:
2079:
2074:
2069:
2068:
2058:
2053:
2041:
2040:
2031:
2030:
2021:
2020:
2008:
1982:
1981:
1971:
1965:
1964:
1943:
1936:
1934:
1933:
1928:
1923:
1921:
1920:
1911:
1910:
1901:
1900:
1897:
1885:
1884:
1872:
1871:
1870:
1854:
1849:
1835:
1834:
1825:
1824:
1821:
1793:
1791:
1790:
1785:
1778:
1777:
1775:
1774:
1765:
1764:
1755:
1754:
1751:
1739:
1738:
1726:
1725:
1724:
1708:
1703:
1702:
1701:
1672:
1670:
1669:
1664:
1659:
1658:
1649:
1648:
1645:
1636:
1635:
1616:
1614:
1613:
1608:
1606:
1605:
1602:
1575:
1573:
1572:
1567:
1565:
1551:
1550:
1549:
1528:
1526:
1525:
1520:
1509:
1508:
1486:
1484:
1483:
1478:
1476:
1475:
1474:
1454:
1452:
1451:
1446:
1441:
1440:
1439:
1430:
1421:
1420:
1419:
1410:
1401:
1400:
1395:
1372:
1370:
1369:
1364:
1359:
1358:
1357:
1341:
1340:
1339:
1323:
1322:
1310:
1309:
1290:
1288:
1287:
1282:
1263:
1257:
1251:
1249:
1248:
1243:
1238:
1214:
1210:
1208:
1207:
1202:
1200:
1199:
1190:
1172:
1170:
1169:
1164:
1153:
1152:
1133:
1131:
1130:
1125:
1110:
1108:
1107:
1102:
1100:
1099:
1066:
1062:
1058:
1054:
1046:
1042:
1039:with wavelength
1038:
1019:
1017:
1016:
1011:
1006:
1004:
979:
978:
969:
968:
965:
959:
954:
953:
934:
933:
924:
919:
918:
917:
916:
895:
893:
892:
887:
885:
884:
883:
882:
861:
859:
858:
853:
848:
834:
833:
809:
802:
795:
785:
783:
774:is known as the
773:
771:
770:
759:
756:
743:
741:
740:
735:
717:
715:
714:
709:
691:
689:
688:
683:
681:
680:
677:
658:
656:
655:
650:
636:
634:
633:
628:
626:
609:
607:
606:
601:
586:
584:
583:
578:
570:
550:
548:
544:
543:
540:
530:
519:
489:
487:
486:
481:
469:
467:
466:
461:
441:
439:
438:
433:
421:
419:
418:
413:
411:
396:
394:
393:
388:
356:
348:
256:
249:
225:Bragg scattering
156:charged particle
126:
119:
112:
44:
32:
31:
21:
5878:
5877:
5873:
5872:
5871:
5869:
5868:
5867:
5828:
5827:
5826:
5816:
5814:
5804:
5802:
5792:
5790:
5778:
5768:
5766:
5754:
5746:
5744:
5735:
5719:X-ray astronomy
5707:
5639:
5588:
5574:X-ray telescope
5466:
5437:Photoionization
5405:
5401:X-ray nanoprobe
5364:
5320:Absorption edge
5308:Characteristics
5303:
5298:
5268:
5263:
5262:
5240:
5184:
5175:Vertex function
5160:Schwinger limit
5135:Furry's theorem
5118:
5072:
5058:Feynman diagram
5041:
5036:
4987:
4946:Physical Review
4877:
4875:Further reading
4872:
4829:
4825:
4790:
4786:
4725:
4718:
4709:
4707:
4703:
4702:
4698:
4689:
4687:
4682:
4681:
4677:
4669:
4663:
4659:
4651:
4647:
4637:
4635:
4633:
4613:
4609:
4600:
4596:
4590:Wayback Machine
4579:Wayback Machine
4569:
4565:
4558:
4540:
4529:
4522:
4508:
4504:
4497:
4483:
4479:
4471:
4465:
4461:
4454:
4440:
4436:
4393:
4389:
4382:10.18434/T48G6X
4366:
4362:
4350:
4344:
4340:
4336:
4331:
4292:Pair production
4272:
4245:
4206:X-ray astronomy
4198:
4159:
4150:
4146:
4144:
4141:
4140:
4121:
4112:
4108:
4106:
4103:
4102:
4086:
4083:
4082:
4065:
4060:
4059:
4050:
4045:
4044:
4030:
4021:
4017:
4006:
3997:
3993:
3984:
3976:
3962:
3950:
3945:
3944:
3935:
3931:
3929:
3926:
3925:
3905:
3900:
3899:
3890:
3886:
3884:
3881:
3880:
3876:
3845:
3840:
3794:
3768:
3764:
3758:
3754:
3753:
3745:
3743:
3736:
3732:
3718:
3715:
3714:
3705:
3664:
3637:
3633:
3632:
3627:
3610:
3608:
3605:
3604:
3595:
3586:
3582:
3576:
3538:
3534:
3522:
3518:
3517:
3512:
3499:
3486:
3481:
3479:
3476:
3475:
3451:
3447:
3439:
3428:
3425:
3424:
3423:
3385:
3381:
3373:
3364:
3360:
3348:
3344:
3338:
3334:
3326:
3311:
3307:
3301:
3297:
3286:
3283:
3282:
3257:
3243:
3234:
3230:
3218:
3205:
3201:
3197:
3196:
3187:
3175:
3171:
3170:
3161:
3157:
3150:
3145:
3132:
3128:
3122:
3118:
3112:
3108:
3097:
3080:
3077:
3076:
3035:
3018:
2988:
2984:
2976:
2961:
2957:
2939:
2935:
2928:
2919:
2918:
2912:
2909:
2908:
2884:
2876:
2873:
2872:
2836:
2835:
2831:
2824:
2820:
2814:
2810:
2798:
2794:
2787:
2778:
2777:
2764:
2760:
2753:
2748:
2735:
2731:
2724:
2715:
2714:
2708:
2705:
2704:
2684:
2680:
2678:
2675:
2674:
2655:
2652:
2651:
2631:
2627:
2625:
2622:
2621:
2604:
2603:
2581:
2580:
2576:
2569:
2565:
2552:
2543:
2542:
2528:
2523:
2510:
2509:
2496:
2495:
2490:
2489:
2480:
2475:
2474:
2455:
2454:
2449:
2448:
2439:
2434:
2433:
2417:
2416:
2411:
2410:
2397:
2396:
2391:
2390:
2383:
2376:
2367:
2366:
2358:
2356:
2353:
2352:
2318:
2317:
2312:
2311:
2302:
2297:
2296:
2283:
2282:
2277:
2276:
2274:
2271:
2270:
2229:
2216:
2214:
2203:
2199:
2193:
2188:
2175:
2171:
2165:
2161:
2155:
2151:
2140:
2123:
2113:
2111:
2108:
2107:
2064:
2060:
2054:
2049:
2036:
2032:
2026:
2022:
2016:
2012:
2001:
1977:
1973:
1966:
1957:
1956:
1950:
1947:
1946:
1916:
1912:
1906:
1902:
1896:
1892:
1880:
1876:
1863:
1862:
1858:
1853:
1842:
1830:
1826:
1820:
1816:
1805:
1802:
1801:
1770:
1766:
1760:
1756:
1750:
1746:
1734:
1730:
1717:
1716:
1712:
1707:
1694:
1693:
1689:
1687:
1684:
1683:
1654:
1650:
1644:
1640:
1631:
1627:
1625:
1622:
1621:
1601:
1597:
1595:
1592:
1591:
1585:Planck constant
1558:
1542:
1541:
1537:
1535:
1532:
1531:
1504:
1500:
1498:
1495:
1494:
1470:
1466:
1465:
1463:
1460:
1459:
1432:
1431:
1426:
1425:
1412:
1411:
1406:
1405:
1396:
1391:
1390:
1388:
1385:
1384:
1350:
1349:
1345:
1332:
1331:
1327:
1318:
1314:
1305:
1301:
1299:
1296:
1295:
1276:
1273:
1272:
1259:
1253:
1234:
1220:
1217:
1216:
1212:
1195:
1191:
1186:
1178:
1175:
1174:
1148:
1144:
1139:
1136:
1135:
1116:
1113:
1112:
1095:
1091:
1080:
1077:
1076:
1064:
1060:
1056:
1052:
1044:
1040:
1036:
1025:
974:
970:
964:
960:
955:
949:
945:
935:
929:
925:
923:
912:
908:
907:
903:
901:
898:
897:
878:
874:
873:
869:
867:
864:
863:
844:
829:
825:
823:
820:
819:
804:
797:
787:
781:
779:
766:
760:
757:
752:
751:
749:
729:
726:
725:
703:
700:
699:
676:
672:
670:
667:
666:
661:Planck constant
644:
641:
640:
619:
617:
614:
613:
595:
592:
591:
566:
539:
535:
534:
529:
512:
510:
507:
506:
501:Physical Review
475:
472:
471:
455:
452:
451:
427:
424:
423:
404:
402:
399:
398:
382:
379:
378:
371:
354:
351:pair production
346:
255:= 0.08 MeV
251:
244:
239:) at which the
213:
130:
86:Pair production
28:
23:
22:
15:
12:
11:
5:
5876:
5866:
5865:
5860:
5855:
5850:
5848:Atomic physics
5845:
5840:
5825:
5824:
5812:
5800:
5788:
5776:
5764:
5741:
5740:
5737:
5736:
5734:
5733:
5728:
5727:
5726:
5715:
5713:
5709:
5708:
5706:
5705:
5700:
5695:
5690:
5685:
5680:
5675:
5670:
5665:
5660:
5655:
5649:
5647:
5641:
5640:
5638:
5637:
5632:
5627:
5622:
5617:
5612:
5607:
5602:
5596:
5594:
5590:
5589:
5587:
5586:
5581:
5576:
5571:
5566:
5561:
5560:
5559:
5554:
5549:
5539:
5534:
5529:
5524:
5519:
5518:
5517:
5512:
5502:
5497:
5492:
5487:
5481:
5479:
5472:
5468:
5467:
5465:
5464:
5459:
5454:
5449:
5444:
5439:
5434:
5429:
5424:
5419:
5413:
5411:
5407:
5406:
5404:
5403:
5398:
5393:
5388:
5383:
5378:
5372:
5370:
5366:
5365:
5363:
5362:
5357:
5352:
5347:
5342:
5337:
5332:
5327:
5322:
5317:
5311:
5309:
5305:
5304:
5297:
5296:
5289:
5282:
5274:
5265:
5264:
5261:
5260:
5246:
5245:
5242:
5241:
5239:
5238:
5233:
5228:
5223:
5218:
5213:
5208:
5206:Bremsstrahlung
5203:
5198:
5192:
5190:
5186:
5185:
5183:
5182:
5177:
5172:
5167:
5162:
5157:
5152:
5147:
5142:
5137:
5132:
5126:
5124:
5120:
5119:
5117:
5116:
5111:
5106:
5101:
5096:
5091:
5086:
5080:
5078:
5074:
5073:
5071:
5070:
5065:
5060:
5055:
5049:
5047:
5043:
5042:
5035:
5034:
5027:
5020:
5012:
5006:
5005:
5000:
4994:
4986:
4985:External links
4983:
4982:
4981:
4978:
4953:(5): 483â502.
4936:
4899:hep-ex/0605012
4876:
4873:
4871:
4870:
4843:(5): 497â617.
4823:
4784:
4716:
4696:
4675:
4657:
4645:
4631:
4607:
4594:
4592:. 11 ed. 2008.
4563:
4556:
4527:
4520:
4502:
4495:
4477:
4459:
4452:
4434:
4407:(9): 837â851.
4387:
4360:
4337:
4335:
4332:
4330:
4329:
4324:
4319:
4314:
4309:
4304:
4299:
4294:
4289:
4284:
4279:
4273:
4271:
4268:
4244:
4241:
4229:galaxy cluster
4212:surrounding a
4210:accretion disk
4197:
4194:
4166:
4162:
4158:
4153:
4149:
4128:
4124:
4120:
4115:
4111:
4090:
4068:
4063:
4058:
4053:
4048:
4043:
4040:
4037:
4033:
4029:
4024:
4020:
4016:
4013:
4009:
4005:
4000:
3996:
3992:
3987:
3982:
3979:
3975:
3969:
3966:
3961:
3958:
3953:
3948:
3943:
3934:
3913:
3908:
3903:
3898:
3889:
3875:
3872:
3844:
3841:
3839:
3836:
3833:
3832:
3823:
3821:
3810:
3804:
3801:
3797:
3793:
3790:
3787:
3784:
3780:
3771:
3767:
3757:
3751:
3748:
3742:
3739:
3735:
3731:
3728:
3725:
3722:
3700:
3699:
3690:
3688:
3677:
3671:
3667:
3663:
3660:
3657:
3654:
3651:
3645:
3636:
3631:
3626:
3623:
3620:
3616:
3613:
3573:
3572:
3561:
3557:
3553:
3550:
3547:
3544:
3541:
3537:
3530:
3521:
3516:
3511:
3506:
3503:
3498:
3492:
3489:
3485:
3459:
3450:
3445:
3442:
3438:
3435:
3432:
3420:
3419:
3408:
3404:
3400:
3397:
3394:
3391:
3388:
3384:
3379:
3376:
3372:
3367:
3363:
3359:
3356:
3351:
3347:
3337:
3332:
3329:
3325:
3322:
3319:
3314:
3310:
3300:
3296:
3293:
3290:
3276:
3275:
3264:
3260:
3256:
3253:
3249:
3246:
3242:
3237:
3233:
3229:
3226:
3221:
3216:
3211:
3208:
3204:
3200:
3195:
3190:
3185:
3181:
3178:
3174:
3169:
3164:
3160:
3154:
3144:
3140:
3135:
3131:
3125:
3121:
3111:
3107:
3103:
3100:
3096:
3093:
3090:
3087:
3084:
3068:
3067:
3058:
3056:
3045:
3038:
3034:
3031:
3028:
3024:
3021:
3017:
3014:
3011:
3008:
3005:
3002:
2999:
2996:
2991:
2987:
2982:
2979:
2975:
2972:
2969:
2964:
2960:
2956:
2953:
2950:
2947:
2942:
2938:
2932:
2925:
2922:
2917:
2891:
2887:
2883:
2880:
2869:
2868:
2857:
2854:
2851:
2848:
2842:
2839:
2834:
2827:
2823:
2817:
2813:
2809:
2806:
2801:
2797:
2791:
2784:
2781:
2776:
2772:
2767:
2763:
2757:
2751:
2747:
2743:
2738:
2734:
2728:
2721:
2718:
2713:
2687:
2683:
2662:
2659:
2639:
2634:
2630:
2618:
2617:
2602:
2599:
2596:
2593:
2587:
2584:
2579:
2572:
2568:
2564:
2561:
2556:
2549:
2546:
2541:
2537:
2532:
2526:
2522:
2518:
2515:
2513:
2511:
2508:
2502:
2499:
2493:
2488:
2483:
2478:
2473:
2470:
2467:
2461:
2458:
2452:
2447:
2442:
2437:
2432:
2429:
2423:
2420:
2414:
2409:
2403:
2400:
2394:
2389:
2386:
2384:
2380:
2373:
2370:
2365:
2361:
2360:
2346:scalar product
2342:
2341:
2330:
2324:
2321:
2315:
2310:
2305:
2300:
2295:
2289:
2286:
2280:
2260:
2259:
2248:
2240:
2235:
2232:
2228:
2225:
2222:
2219:
2213:
2206:
2202:
2196:
2191:
2187:
2183:
2178:
2174:
2168:
2164:
2158:
2154:
2150:
2146:
2143:
2139:
2136:
2133:
2130:
2127:
2120:
2117:
2095:
2094:
2085:
2083:
2072:
2067:
2063:
2057:
2052:
2048:
2044:
2039:
2035:
2029:
2025:
2019:
2015:
2011:
2007:
2004:
2000:
1997:
1994:
1991:
1988:
1985:
1980:
1976:
1970:
1963:
1960:
1955:
1938:
1937:
1926:
1919:
1915:
1909:
1905:
1895:
1891:
1888:
1883:
1879:
1875:
1869:
1866:
1861:
1857:
1852:
1848:
1845:
1841:
1838:
1833:
1829:
1819:
1815:
1812:
1809:
1795:
1794:
1783:
1773:
1769:
1763:
1759:
1749:
1745:
1742:
1737:
1733:
1729:
1723:
1720:
1715:
1711:
1706:
1700:
1697:
1692:
1674:
1673:
1662:
1657:
1653:
1643:
1639:
1634:
1630:
1600:
1577:
1576:
1564:
1561:
1557:
1554:
1548:
1545:
1540:
1529:
1518:
1515:
1512:
1507:
1503:
1473:
1469:
1456:
1455:
1444:
1438:
1435:
1429:
1424:
1418:
1415:
1409:
1404:
1399:
1394:
1374:
1373:
1362:
1356:
1353:
1348:
1344:
1338:
1335:
1330:
1326:
1321:
1317:
1313:
1308:
1304:
1280:
1241:
1237:
1233:
1230:
1227:
1224:
1198:
1194:
1189:
1185:
1182:
1162:
1159:
1156:
1151:
1147:
1143:
1123:
1120:
1098:
1094:
1090:
1087:
1084:
1024:
1021:
1009:
1003:
1000:
997:
994:
991:
988:
985:
982:
977:
973:
963:
958:
952:
948:
944:
941:
938:
932:
928:
922:
915:
911:
906:
896:, is given by
881:
877:
872:
851:
847:
843:
840:
837:
832:
828:
764:
746:
745:
733:
723:
720:speed of light
707:
697:
675:
664:
648:
638:
625:
622:
611:
599:
576:
573:
569:
565:
562:
559:
556:
553:
547:
538:
533:
528:
525:
522:
518:
515:
479:
459:
431:
410:
407:
386:
370:
367:
359:alpha particle
355:1.670 MeV
347:1.022 MeV
212:
209:
141:Compton effect
132:
131:
129:
128:
121:
114:
106:
103:
102:
96:
95:
89:
88:
82:
81:
77:
76:
70:
69:
63:
62:
58:
57:
51:
50:
46:
45:
37:
36:
26:
18:Comptonization
9:
6:
4:
3:
2:
5875:
5864:
5861:
5859:
5856:
5854:
5851:
5849:
5846:
5844:
5841:
5839:
5836:
5835:
5833:
5823:
5813:
5811:
5801:
5799:
5789:
5787:
5782:
5777:
5775:
5765:
5763:
5758:
5753:
5752:
5749:
5732:
5729:
5725:
5722:
5721:
5720:
5717:
5716:
5714:
5710:
5704:
5701:
5699:
5696:
5694:
5691:
5689:
5686:
5684:
5681:
5679:
5676:
5674:
5671:
5669:
5666:
5664:
5661:
5659:
5656:
5654:
5651:
5650:
5648:
5646:
5642:
5636:
5633:
5631:
5628:
5626:
5623:
5621:
5618:
5616:
5613:
5611:
5608:
5606:
5603:
5601:
5598:
5597:
5595:
5591:
5585:
5582:
5580:
5577:
5575:
5572:
5570:
5567:
5565:
5562:
5558:
5555:
5553:
5550:
5548:
5545:
5544:
5543:
5540:
5538:
5535:
5533:
5530:
5528:
5525:
5523:
5520:
5516:
5513:
5511:
5508:
5507:
5506:
5503:
5501:
5498:
5496:
5495:Tomosynthesis
5493:
5491:
5488:
5486:
5483:
5482:
5480:
5476:
5473:
5469:
5463:
5460:
5458:
5455:
5453:
5450:
5448:
5445:
5443:
5440:
5438:
5435:
5433:
5430:
5428:
5425:
5423:
5420:
5418:
5415:
5414:
5412:
5408:
5402:
5399:
5397:
5394:
5392:
5389:
5387:
5384:
5382:
5379:
5377:
5374:
5373:
5371:
5367:
5361:
5358:
5356:
5353:
5351:
5348:
5346:
5343:
5341:
5338:
5336:
5333:
5331:
5328:
5326:
5325:Moseley's law
5323:
5321:
5318:
5316:
5313:
5312:
5310:
5306:
5302:
5301:X-ray science
5295:
5290:
5288:
5283:
5281:
5276:
5275:
5272:
5259:
5251:
5248:
5247:
5243:
5237:
5234:
5232:
5229:
5227:
5224:
5222:
5219:
5217:
5214:
5212:
5209:
5207:
5204:
5202:
5199:
5197:
5194:
5193:
5191:
5187:
5181:
5178:
5176:
5173:
5171:
5168:
5166:
5163:
5161:
5158:
5156:
5153:
5151:
5148:
5146:
5143:
5141:
5138:
5136:
5133:
5131:
5128:
5127:
5125:
5121:
5115:
5112:
5110:
5107:
5105:
5102:
5100:
5097:
5095:
5092:
5090:
5087:
5085:
5082:
5081:
5079:
5075:
5069:
5066:
5064:
5061:
5059:
5056:
5054:
5051:
5050:
5048:
5044:
5040:
5033:
5028:
5026:
5021:
5019:
5014:
5013:
5010:
5004:
5001:
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4995:
4992:
4989:
4988:
4979:
4976:
4969:
4964:
4960:
4956:
4952:
4948:
4947:
4942:
4937:
4933:
4929:
4925:
4921:
4917:
4913:
4909:
4905:
4900:
4895:
4892:(7): 072002.
4891:
4887:
4886:
4879:
4878:
4866:
4862:
4858:
4854:
4850:
4846:
4842:
4838:
4834:
4827:
4819:
4815:
4811:
4807:
4803:
4799:
4795:
4788:
4780:
4776:
4772:
4768:
4764:
4760:
4756:
4752:
4747:
4742:
4738:
4734:
4730:
4723:
4721:
4706:
4700:
4686:. Lnf.infn.it
4685:
4679:
4668:
4661:
4655:
4649:
4634:
4628:
4624:
4620:
4619:
4611:
4605:
4598:
4591:
4587:
4584:
4580:
4576:
4573:
4567:
4559:
4557:0-13-805715-X
4553:
4549:
4548:Prentice Hall
4545:
4538:
4536:
4534:
4532:
4523:
4521:9789810242145
4517:
4513:
4506:
4498:
4496:9781420012378
4492:
4488:
4481:
4470:
4463:
4455:
4453:0-471-60386-4
4449:
4445:
4438:
4430:
4426:
4422:
4418:
4414:
4410:
4406:
4402:
4398:
4391:
4383:
4379:
4375:
4371:
4364:
4356:
4349:
4342:
4338:
4328:
4325:
4323:
4320:
4318:
4315:
4313:
4310:
4308:
4305:
4303:
4300:
4298:
4295:
4293:
4290:
4288:
4285:
4283:
4280:
4278:
4275:
4274:
4267:
4265:
4261:
4255:
4253:
4249:
4240:
4236:
4234:
4230:
4226:
4221:
4219:
4215:
4211:
4207:
4203:
4193:
4191:
4187:
4183:
4178:
4147:
4109:
4088:
4066:
4056:
4051:
4041:
4018:
4014:
3994:
3977:
3973:
3967:
3964:
3959:
3951:
3932:
3906:
3887:
3871:
3869:
3865:
3861:
3856:
3854:
3850:
3831:
3824:
3822:
3808:
3799:
3795:
3791:
3785:
3782:
3778:
3769:
3765:
3755:
3749:
3746:
3740:
3737:
3733:
3729:
3726:
3723:
3720:
3713:
3712:
3709:
3698:
3691:
3689:
3675:
3665:
3661:
3658:
3655:
3652:
3643:
3634:
3629:
3624:
3621:
3618:
3614:
3611:
3603:
3602:
3599:
3591:
3585:
3579:
3559:
3555:
3551:
3548:
3545:
3542:
3539:
3535:
3528:
3519:
3514:
3509:
3504:
3501:
3496:
3490:
3487:
3483:
3474:
3473:
3472:
3457:
3448:
3443:
3440:
3436:
3433:
3430:
3406:
3402:
3398:
3395:
3392:
3389:
3386:
3382:
3377:
3374:
3370:
3365:
3361:
3357:
3354:
3349:
3345:
3335:
3330:
3327:
3323:
3320:
3317:
3312:
3308:
3298:
3294:
3291:
3288:
3281:
3280:
3279:
3262:
3258:
3254:
3251:
3247:
3244:
3240:
3235:
3231:
3227:
3224:
3219:
3214:
3209:
3206:
3202:
3198:
3193:
3188:
3183:
3179:
3176:
3172:
3167:
3162:
3158:
3152:
3142:
3138:
3133:
3123:
3119:
3109:
3105:
3101:
3098:
3094:
3091:
3088:
3085:
3075:
3074:
3073:
3066:
3059:
3057:
3043:
3036:
3032:
3029:
3022:
3019:
3015:
3006:
3003:
2997:
2994:
2989:
2980:
2977:
2973:
2967:
2962:
2954:
2951:
2945:
2940:
2936:
2930:
2923:
2920:
2915:
2907:
2906:
2903:
2889:
2885:
2881:
2878:
2855:
2852:
2849:
2846:
2840:
2837:
2832:
2825:
2821:
2815:
2811:
2807:
2804:
2799:
2795:
2789:
2782:
2779:
2774:
2770:
2765:
2761:
2755:
2749:
2745:
2741:
2736:
2732:
2726:
2719:
2716:
2711:
2703:
2702:
2701:
2685:
2681:
2660:
2657:
2637:
2632:
2628:
2600:
2597:
2594:
2591:
2585:
2582:
2577:
2570:
2566:
2562:
2559:
2554:
2547:
2544:
2539:
2535:
2530:
2524:
2520:
2516:
2514:
2500:
2497:
2486:
2481:
2468:
2459:
2456:
2445:
2440:
2427:
2421:
2418:
2407:
2401:
2398:
2387:
2385:
2378:
2371:
2368:
2363:
2351:
2350:
2349:
2347:
2328:
2322:
2319:
2308:
2303:
2293:
2287:
2284:
2269:
2268:
2267:
2264:
2246:
2238:
2233:
2230:
2226:
2223:
2220:
2217:
2211:
2204:
2200:
2194:
2189:
2185:
2181:
2176:
2166:
2162:
2156:
2152:
2148:
2144:
2141:
2137:
2134:
2131:
2128:
2118:
2115:
2106:
2105:
2104:
2102:
2093:
2086:
2084:
2070:
2065:
2061:
2055:
2050:
2046:
2042:
2037:
2027:
2023:
2017:
2013:
2009:
2005:
2002:
1998:
1995:
1992:
1989:
1983:
1978:
1974:
1968:
1961:
1958:
1953:
1945:
1944:
1941:
1924:
1917:
1907:
1903:
1893:
1886:
1881:
1873:
1867:
1864:
1859:
1850:
1846:
1843:
1839:
1836:
1831:
1827:
1817:
1813:
1810:
1807:
1800:
1799:
1798:
1781:
1771:
1761:
1757:
1747:
1740:
1735:
1727:
1721:
1718:
1713:
1704:
1698:
1695:
1690:
1682:
1681:
1680:
1679:
1660:
1655:
1651:
1641:
1637:
1632:
1628:
1620:
1619:
1618:
1598:
1588:
1586:
1582:
1562:
1559:
1555:
1552:
1546:
1543:
1538:
1530:
1516:
1513:
1510:
1505:
1501:
1493:
1492:
1491:
1488:
1471:
1467:
1442:
1436:
1433:
1422:
1416:
1413:
1402:
1397:
1383:
1382:
1381:
1379:
1360:
1354:
1351:
1346:
1342:
1336:
1333:
1328:
1324:
1319:
1315:
1311:
1306:
1302:
1294:
1293:
1292:
1278:
1271:
1266:
1262:
1256:
1239:
1235:
1231:
1228:
1225:
1222:
1196:
1192:
1187:
1183:
1180:
1160:
1157:
1154:
1149:
1145:
1141:
1121:
1118:
1096:
1092:
1088:
1085:
1082:
1072:
1070:
1050:
1029:
1020:
1007:
998:
995:
992:
989:
986:
975:
971:
961:
956:
950:
946:
939:
936:
930:
926:
920:
909:
904:
875:
870:
849:
845:
841:
838:
835:
830:
826:
815:
811:
807:
800:
794:
790:
777:
769:
763:
755:
748:The quantity
731:
724:
721:
705:
698:
695:
673:
665:
662:
646:
639:
623:
620:
612:
597:
590:
589:
588:
574:
567:
563:
560:
557:
554:
545:
536:
531:
526:
523:
520:
516:
513:
503:
502:
496:
493:
477:
457:
449:
429:
408:
405:
384:
375:
366:
364:
360:
352:
344:
343:visible light
339:
337:
333:
329:
324:
322:
318:
314:
309:
303:
301:
296:
292:
288:
283:
281:
277:
273:
269:
265:
264:Compton shift
254:
247:
242:
241:cross section
238:
233:
226:
222:
217:
208:
206:
201:
199:
195:
191:
187:
183:
178:
176:
172:
168:
164:
159:
157:
153:
150:
146:
142:
138:
127:
122:
120:
115:
113:
108:
107:
105:
104:
101:
98:
97:
94:
91:
90:
87:
84:
83:
79:
78:
75:
72:
71:
68:
65:
64:
60:
59:
56:
53:
52:
48:
47:
43:
39:
38:
34:
33:
30:
19:
5838:Astrophysics
5822:Solar System
5593:Spectroscopy
5537:Ptychography
5471:Applications
5432:Auger effect
5426:
5335:Water window
5249:
5210:
4950:
4944:
4889:
4883:
4840:
4836:
4826:
4801:
4797:
4787:
4736:
4732:
4708:. Retrieved
4699:
4688:. Retrieved
4678:
4660:
4648:
4636:. Retrieved
4617:
4610:
4597:
4566:
4543:
4511:
4505:
4486:
4480:
4462:
4443:
4437:
4404:
4400:
4390:
4373:
4363:
4354:
4341:
4256:
4246:
4237:
4222:
4202:astrophysics
4199:
4179:
3877:
3864:Compton edge
3857:
3849:radiobiology
3846:
3838:Applications
3825:
3703:
3692:
3589:
3583:
3577:
3574:
3421:
3277:
3071:
3060:
2870:
2619:
2343:
2265:
2261:
2100:
2098:
2087:
1939:
1796:
1675:
1589:
1580:
1578:
1489:
1457:
1375:
1267:
1260:
1254:
1073:
1034:
816:
812:
805:
798:
792:
788:
767:
761:
753:
747:
499:
497:
445:
340:
325:
304:
299:
289:phenomenon.
284:
263:
260:
252:
245:
236:
211:Introduction
204:
202:
179:
160:
140:
136:
135:
100:Photofission
73:
29:
5810:Outer space
5798:Spaceflight
5386:Synchrotron
5155:Self-energy
5145:Landau pole
5109:Positronium
5084:Dual photon
4297:Peter Debye
1252:, and thus
490:. Although
270:in 1923 at
262:called the
5832:Categories
5645:Scattering
5510:Helical CT
5376:X-ray tube
5221:Lamb shift
5150:QED vacuum
4710:2021-01-31
4690:2011-11-08
4623:OUP Oxford
4334:References
4214:black hole
4182:incoherent
1458:in which (
321:BKS theory
194:wavelength
152:scattering
5774:Astronomy
5250:See also:
5189:Processes
5077:Particles
5046:Formalism
4865:121183948
4857:0270-2010
4779:118536606
4771:0034-6861
4746:1111.3886
4429:250783416
4152:↓
4114:↑
4089:μ
4023:↓
4015:−
3999:↑
3986:∞
3981:∞
3978:−
3974:∬
3968:μ
3792:θ
3786:
3727:φ
3724:
3666:θ
3662:
3656:−
3622:λ
3619:−
3612:λ
3552:θ
3549:
3543:−
3497:−
3399:θ
3396:
3390:−
3318:−
3259:θ
3255:
3225:−
3139:−
3092:−
3037:θ
3033:
2995:−
2853:θ
2850:
2838:γ
2826:γ
2805:−
2780:γ
2750:γ
2633:γ
2598:θ
2595:
2583:γ
2571:γ
2560:−
2545:γ
2525:γ
2498:γ
2487:−
2482:γ
2469:⋅
2457:γ
2446:−
2441:γ
2408:⋅
2320:γ
2309:−
2304:γ
2224:−
2182:−
2135:−
2043:−
1996:−
1544:γ
1506:γ
1414:γ
1398:γ
1334:γ
1307:γ
1035:A photon
999:θ
996:
990:−
951:γ
931:γ
914:′
910:γ
880:′
876:γ
850:λ
831:γ
784:10 m
732:θ
621:λ
598:λ
568:θ
564:
558:−
524:λ
521:−
514:λ
478:θ
458:θ
430:θ
406:λ
385:λ
276:Y. H. Woo
143:) is the
5381:Betatron
5123:Concepts
5104:Positron
5089:Electron
4977:website)
4932:15326395
4924:17026221
4586:Archived
4575:Archived
4270:See also
3615:′
3491:′
3444:′
3378:′
3331:′
3248:′
3210:′
3102:′
3023:′
2981:′
2924:′
2841:′
2783:′
2720:′
2586:′
2548:′
2501:′
2460:′
2422:′
2402:′
2372:′
2323:′
2288:′
2234:′
2145:′
2006:′
1962:′
1868:′
1847:′
1722:′
1699:′
1563:′
1547:′
1437:′
1417:′
1355:′
1337:′
624:′
517:′
409:′
308:momentum
221:graphite
139:(or the
5762:Physics
5748:Portals
5724:History
5478:Imaging
4955:Bibcode
4904:Bibcode
4806:Bibcode
4751:Bibcode
4638:4 March
4409:Bibcode
3592:′
3471:yields
1583:is the
772:
750:
718:is the
692:is the
659:is the
149:photons
145:quantum
5712:Others
5673:GISAXS
5345:L-edge
5340:K-edge
5099:Photon
4930:
4922:
4863:
4855:
4777:
4769:
4629:
4554:
4518:
4493:
4450:
4427:
4218:corona
4208:, the
4081:where
3806:
3673:
3041:
2244:
1779:
1579:where
1049:recoil
808:= 180°
587:where
448:X-rays
317:Geiger
190:energy
167:X-rays
5786:Stars
5703:EDXRD
5625:XANES
5620:EXAFS
5610:ARPES
5557:3DXRD
5315:X-ray
4928:S2CID
4894:arXiv
4861:S2CID
4775:S2CID
4741:arXiv
4670:(PDF)
4472:(PDF)
4425:S2CID
4351:(PDF)
4252:laser
4204:. In
4190:SQUID
722:, and
313:Bothe
5688:RIXS
5678:WAXS
5668:SAXS
5579:DFXM
5547:XDCT
5532:STXM
5527:XPCI
5515:XACT
4920:PMID
4853:ISSN
4767:ISSN
4640:2013
4627:ISBN
4552:ISBN
4516:ISBN
4491:ISBN
4448:ISBN
4374:NIST
4139:and
2212:>
1268:The
801:= 0°
780:2.43
315:and
287:wave
248:= 20
184:and
5693:XRS
5635:XFH
5630:EDS
5615:AES
5605:XPS
5600:XAS
5584:DXA
5552:DCT
5500:CDI
4975:APS
4963:doi
4912:doi
4845:doi
4814:doi
4759:doi
4417:doi
4378:doi
4264:QED
3937:mag
3892:mag
3783:tan
3721:cot
3659:cos
3581:=
3546:cos
3393:cos
3252:cos
3030:cos
2847:cos
2592:cos
993:cos
810:).
561:cos
5834::
5698:XS
5505:CT
4961:.
4951:21
4949:.
4943:.
4926:.
4918:.
4910:.
4902:.
4890:97
4888:.
4859:.
4851:.
4839:.
4835:.
4812:.
4802:33
4800:.
4796:.
4773:.
4765:.
4757:.
4749:.
4737:84
4735:.
4731:.
4719:^
4625:.
4621:.
4530:^
4423:.
4415:.
4405:12
4403:.
4399:.
4376:.
4372:.
4353:.
4266:.
4254:.
3855:.
3598:,
3594:=
3578:fÎť
2700:,
1617:,
1587:.
1261:pc
1255:hf
791:â
789:Îťâ˛
323:.
253:hĎ
5750::
5293:e
5286:t
5279:v
5031:e
5024:t
5017:v
4971:.
4965::
4957::
4934:.
4914::
4906::
4896::
4867:.
4847::
4841:6
4820:.
4816::
4808::
4781:.
4761::
4753::
4743::
4713:.
4693:.
4642:.
4560:.
4524:.
4499:.
4474:.
4456:.
4431:.
4419::
4411::
4384:.
4380::
4165:)
4161:p
4157:(
4148:n
4127:)
4123:p
4119:(
4110:n
4067:y
4062:p
4057:d
4052:x
4047:p
4042:d
4039:)
4036:)
4032:p
4028:(
4019:n
4012:)
4008:p
4004:(
3995:n
3991:(
3965:1
3960:=
3957:)
3952:z
3947:p
3942:(
3933:J
3912:)
3907:z
3902:p
3897:(
3888:J
3830:)
3828:4
3826:(
3809:.
3803:)
3800:2
3796:/
3789:(
3779:)
3770:2
3766:c
3760:e
3756:m
3750:f
3747:h
3741:+
3738:1
3734:(
3730:=
3706:Ď
3697:)
3695:3
3693:(
3676:.
3670:)
3653:1
3650:(
3644:c
3639:e
3635:m
3630:h
3625:=
3596:c
3590:Îť
3587:â˛
3584:f
3560:.
3556:)
3540:1
3536:(
3529:c
3524:e
3520:m
3515:h
3510:=
3505:f
3502:c
3488:f
3484:c
3458:c
3453:e
3449:m
3441:f
3437:f
3434:h
3431:2
3407:.
3403:)
3387:1
3383:(
3375:f
3371:f
3366:2
3362:h
3358:2
3355:=
3350:2
3346:c
3340:e
3336:m
3328:f
3324:h
3321:2
3313:2
3309:c
3303:e
3299:m
3295:f
3292:h
3289:2
3263:,
3245:f
3241:f
3236:2
3232:h
3228:2
3220:2
3215:)
3207:f
3203:h
3199:(
3194:+
3189:2
3184:)
3180:f
3177:h
3173:(
3168:=
3163:4
3159:c
3153:2
3147:e
3143:m
3134:2
3130:)
3124:2
3120:c
3114:e
3110:m
3106:+
3099:f
3095:h
3089:f
3086:h
3083:(
3065:)
3063:2
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3044:.
3027:)
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3010:)
3007:f
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2998:2
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2968:+
2963:2
2959:)
2955:f
2952:h
2949:(
2946:=
2941:2
2937:c
2931:2
2921:e
2916:p
2890:c
2886:/
2882:f
2879:h
2856:.
2833:p
2822:p
2816:2
2812:c
2808:2
2800:2
2796:c
2790:2
2775:p
2771:+
2766:2
2762:c
2756:2
2746:p
2742:=
2737:2
2733:c
2727:2
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2712:p
2686:2
2682:c
2661:f
2658:h
2638:c
2629:p
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2567:p
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2466:)
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2428:=
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2294:=
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2247:.
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2205:4
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2195:2
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2167:2
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2071:.
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2056:2
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2038:2
2034:)
2028:2
2024:c
2018:e
2014:m
2010:+
2003:f
1999:h
1993:f
1990:h
1987:(
1984:=
1979:2
1975:c
1969:2
1959:e
1954:p
1925:.
1918:2
1914:)
1908:2
1904:c
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1894:m
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1887:+
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1874:c
1865:e
1860:p
1856:(
1851:+
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1837:=
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1822:e
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1811:f
1808:h
1782:.
1772:2
1768:)
1762:2
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1710:(
1705:=
1696:e
1691:E
1661:.
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1642:m
1638:=
1633:e
1629:E
1603:e
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1581:h
1560:f
1556:h
1553:=
1539:E
1517:f
1514:h
1511:=
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1468:p
1443:,
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1423:+
1408:p
1403:=
1393:p
1361:.
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1325:=
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1236:/
1232:f
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1226:=
1223:p
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1197:2
1193:c
1188:/
1184:f
1181:h
1161:f
1158:h
1155:=
1150:2
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1142:m
1122:f
1119:h
1097:2
1093:c
1089:m
1086:=
1083:E
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1061:θ
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1053:Îł
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1041:Îť
1037:Îł
1008:.
1002:)
987:1
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981:)
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940:+
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921:=
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846:/
842:c
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836:=
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806:θ
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782:Ă
768:c
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758:/
754:h
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696:,
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575:,
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555:1
552:(
546:c
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537:m
532:h
527:=
246:Z
237:Z
125:e
118:t
111:v
20:)
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