[PDF]    http://dx.doi.org/10.3952/lithjphys.44303

Open access article / Atviros prieigos straipsnis

Lith. J. Phys. 44, 199–218 (2004)


ATOMIC THEORY METHODS FOR THE POLARIZATION IN PHOTON AND ELECTRON INTERACTIONS WITH ATOMS
A. Kupliauskienė
Vilnius University Research Institute of Theoretical Physics and Astronomy, A. Goštauto 12, LT-01108 Vilnius, Lithuania
E-mail: akupl@itpa.lt

Received 20 February 2004

Dedicated to the 100th anniversary of Professor A. Jucys

An alternative method to the density matrix formalism for the derivation of general expressions for the cross-sections of the interaction of polarized atoms with polarized photons and electrons is presented. The expression for the cross-section describing the polarization states of all particles taking part in the process are obtained in the form of the expansion via irreducible tensors that have the simplest possible behaviour under changes of directions. The ways of the application of the general expressions suitable for the specific experimental conditions are outlined by deriving asymmetry parameters of the angular distributions of photoelectrons and Auger electrons following photoionization as well as the parameters of the angular correlations between photo- and Auger electrons.
Keywords: photon interactions with atoms, electron scattering
PACS: 32.80.–t, 34.80.–i


ATOMO TEORIJOS METODAI ATOMŲ SĄVEIKAI SU FOTONAIS IR ELEKTRONAIS TIRTI
A. Kupliauskienė
VU Teorinės fizikos ir astronomijos institutas, Vilnius, Lietuva


Sklaidos uždaviniuose sklaidomosios dalelės kryptis yra apibrėžta, todėl reakcijos produktų būsenų užpildai būdinga asimetrija šios krypties atžvilgiu. Iki šiol tokia poliarizacija ir asimetrija buvo tiriamos tankio matricos metodais. Prieš ketvertą metų poliarizacijos reiškiniams, kai atomai ir jonai sąveikauja su elektronais ir fotonais, nagrinėti buvo pritaikyti atomo teorijos metodai, kurie iki šiol buvo taikomi izoliuotiems atomams tirti, neatsižvelgiant į išskirtą kryptį erdvėje. Apžvelgti darbai, skirti poliarizuotų atomų sąveikos su poliarizuotais fotonais ir elektronais skerspjūvių bendriausioms išraiškoms nereliatyvistiniu artėjimu surasti. Judėjimo kiekio momento grafinė technika pritaikyta šuolio operatorių matricinių elementų kvadratams integruoti kampinių ir sumuoti sukininių kintamųjų atžvilgiu. Skerspjūvių išraiškos užrašytos daugialypiais sferinių multipolių skleidiniais, kadangi sferiniai tenzoriai transformuojasi paprasčiausiai, keičiant matavimo kryptis. Pateiktas būdas fotonų ar elektronų spinduliuotei po atomo ar jono jonizacijos, sužadinimo ar rekombinacijos dvipakopiu artėjimu nagrinėti.
Išnagrinėti svarbiausi plazmoje vykstantys vyksmai: atomų ir jonų sužadinimas ir jonizacija fotonais bei elektronais, jono ir elektrono fotorekombinacija, spinduliavimo ir Auger šuoliai sužadintuose ir jonizuotuose atomuose. Dvipakopį vyksmą iliustruoja dvielektronė rekombinacija. Taip pat parodyta, kaip galima surasti skerspjūvių išraiškas konkretiems eksperimentams aprašyti. Visų išraiškų forma paprasta, patogi kompiuterinėms programoms rašyti.


References / Nuorodos


[1] A.P. Jucys and A.A. Bandzaitis, Theory of Angular Momentum in Quantum Mechanics (Mintis, Vilnius, 1965) [in Russian]
[2] A.P. Jucys and A.J. Savukynas, Mathematical Foundations of the Atomic Theory (Mintis, Vilnius, 1972) [in Russian]
[3] J.H. Macek, Alignment and orientation: Opening remarks, in: Atomic Physics, Vol. 16, eds. W.E. Baylis and G.W.F. Drake (American Institute of Physics, New York, 1999) pp. 234–236,
http://dx.doi.org/10.1063/1.59359
[4] U. Heinzmann, Experimental determination of the phase difference of continuum wavefunctions describing the photoionization process of xenon atoms, II. Evaluation of the matrix elements and their phase differences and their comparison with data in the discrete spectral range in application of the multichannel quantum defect theory, J. Phys. B 13, 4367–4381 (1980),
http://dx.doi.org/10.1088/0022-3700/13/22/011
[5] S.A. Kazantsev and J.-C. Henoux, Polarization Spectroscopy of Ionized Gases (Kluwer, Dordrecht/Boston/London, 1995),
http://dx.doi.org/10.1007/978-94-017-2708-2
[6] A.M. Urnov, Historical overview of plasma polarization spectroscopy, in: Proceedings of the Japan–US Workshop on Plasma Polarization Spectroscopy and the International Seminar on Plasma Polarization Spectroscopy (Research International Center, Nagoya, 1998) pp. 1–8
[7] J.C. Kieffer, J.P. Matte, H. Pèpin, M. Chaker, Y. Beoudain, T.W. Johnston, C.H. Chien, S. Coe, G. Moorou, and J. Dubou, Electron distribution anisotropy in laser-produced plasmas from X-ray line polarization measurements, Phys. Rev. Lett. 68, 480–483 (1992),
http://dx.doi.org/10.1103/PhysRevLett.68.480
[8] T. Fujimoto, H. Sahara, T. Kawachi, T. Kallstenius, M. Goto, H. Kawase, T. Furukubo, T. Mackawa, and Y. Terumichi, Polarization of impurity emission lines from tokamak plasma, Phys. Rev. E 54, R2240–R2243 (1996),
http://dx.doi.org/10.1103/PhysRevE.54.R2240
[9] V.A. Veretennikov, A.E. Gurei, A.N. Dolgov, V.V. Korneev, and O.G. Semenov, The polarization of line X-ray radiation from impulse discharge plasma, Pis'ma Zh. Eksp. Teor. Fiz. 47, 29–31 (1988)
[10] S.A. Kazantsev, The application of the self-alignment for the astrophysical and laboratory plasma, Uspekhi Fiz. Nauk 139, 621–666 (1983),
http://dx.doi.org/10.3367/UFNr.0139.198304c.0621
[11] A. von dem Borne, T. Dohrmann, A. Verweyen, and B. Sonntag, Dichroism in the 3p photoionization of polarized Cr atoms, Phys. Rev. Lett. 78, 4019–4022 (1997),
http://dx.doi.org/10.1103/PhysRevLett.78.4019
[12] G. Prümper, O. Geßner, B. Zimmermann, J. Viefhaus, R. Hentger, H. Kleinpoppen, and U. Becker, Absorption of circularly polarized VUV radiation in polarized iron vapor, J. Phys. B 34, 2707–2714 (2001),
http://dx.doi.org/10.1088/0953-4075/34/13/312
[13] N.A. Cherepkov, V.V. Kuznetsov, and V.A. Verbitskii, Photoionization of polarized atoms, J. Phys. B 28, 1221–1239 (1995),
http://dx.doi.org/10.1088/0953-4075/28/7/016
[14] U. Fano, Description of states in quantum mechanics by density matrix and operator technique, Rev. Mod. Phys. 29, 74–93 (1957),
http://dx.doi.org/10.1103/RevModPhys.29.74
[15] U. Fano and J.H. Macek, Impact excitation and polarization of the emitted light, Rev. Mod. Phys. 45, 553–573 (1973),
http://dx.doi.org/10.1103/RevModPhys.45.553
[16] V.L. Jacobs, Theory of atomic polarization measurements, J. Phys. B 5, 2257–2271 (1972),
http://dx.doi.org/10.1088/0022-3700/5/12/019
[17] N.M. Kabachnik and I.P. Sazhina, Angular distribution and polarization of photoelectrons in the region of resonances, J. Phys. B 9, 1681–1697 (1976),
http://dx.doi.org/10.1088/0022-3700/9/10/014
[18] H. Klar, Polarization of fluorescence radiation following atomic photoionization, J. Phys. B 13, 2037–2049 (1980),
http://dx.doi.org/10.1088/0022-3700/13/10/011
[19] H. Klar and H. Kleinpoppen, Angular distribution of photoelectrons from polarized atoms exposed to polarized radiation, J. Phys. B 15, 933–950 (1982),
http://dx.doi.org/10.1088/0022-3700/15/6/019
[20] S. Baier, A.N. Grum-Grzhimailo, and N.M. Kabachnik, Angular distribution of photoelectrons in resonant photoionization of polarized atoms, J. Phys. B 27, 3363–3388 (1994),
http://dx.doi.org/10.1088/0953-4075/27/15/014
[21] A.N. Grum-Grzhimailo, K. Bartschat, N. Feuerstein, and W. Mehlhorn, Near threshold structure in electron-collision-induced alignment of excited atomic states, Phys. Rev. A 60, R1751–R1754 (1994),
http://dx.doi.org/10.1103/PhysRevA.60.R1751
[22] A.N. Grum-Grzhimailo and N.M. Kabachnik, Linear magnetic dichroism in fluorescence spectra, Phys. Lett. A 264, 192–197 (1999),
http://dx.doi.org/10.1016/S0375-9601(99)00800-2
[23] V.V. Balashov, A.N. Grum-Grzhimailo, and N.M. Kabachnik, Polarization and Correlation Phenomena in Atomic Collisions. A Practical Theory Course (Kluwer, New York, 2000),
http://dx.doi.org/10.1007/978-1-4757-3228-3
[24] K. Blum, Density Matrix Theory and Applications, 2nd edn. (Plenum, New York, 1996),
http://dx.doi.org/10.1007/978-1-4757-4931-1
[25] A. Kupliauskienė, N. Rakštikas, and V. Tutlys, General expression of the photoionization cross-section of an atom in polarized LS state, Lithuanian J. Phys. 40, 311–320 (2000)
[26] A. Kupliauskienė, N. Rakštikas, and V. Tutlys, Polarization studies in the photoionization of atoms using a graphical technique, J. Phys. B 34, 1783–1803 (2001),
http://dx.doi.org/10.1088/0953-4075/34/9/314
[27] Z. Rudzikas, Theoretical Atomic Spectroscopy (Many-Electron Atoms) (Cambridge University Press, Cambridge, 1997),
http://dx.doi.org/10.1017/CBO9780511524554
[28] U. Fano and D. Dill, Angular momentum transfer in the theory of angular distributions, Phys. Rev. A 6, 185–192 (1972),
http://dx.doi.org/10.1103/PhysRevA.6.185
[29] B. Cleff and W. Mehlhorn, On the angular distribution of Auger electrons following impact ionization, J. Phys. B 7, 593–604 (1974),
http://dx.doi.org/10.1088/0022-3700/7/5/009
[30] I.B. Levinson, Sums of the products of Wigner coefficients and their graphical representation, Proc. Inst. Phys. Techn. 2, 17–29 (1956) [in Russian]
[31] D.M. Brink and G.R. Satchler, Angular Momentum (Oxford University Press, Oxford, 1968),
[32] J.S. Briggs, Evaluation of matrix elements from a graphical representation of the angular integrals, Rev. Mod. Phys. 43, 189–230 (1971),
http://dx.doi.org/10.1103/RevModPhys.43.189
[33] E. El-Baz and B. Castel, Graphical Methods of Spin Algebras in Atomic, Nuclear and Particle Physics (Marcel Dekker, Oxford, 1972),
[34] K.-N. Huang, Graphical evaluation of relativistic matrix elements, Rev. Mod. Phys. 51, 215–236 (1979),
http://dx.doi.org/10.1103/RevModPhys.51.215
[35] G. Merkelis, Graphical method of evaluation of matrix elements in the second quantization representation, Physica Scripta 63, 289–305 (2001),
http://dx.doi.org/10.1238/Physica.Regular.063a00289
[36] Ph. Golecki and H. Klar, (e, 2e) from laser-excited atoms with spin-polarized electrons, J. Phys. B 32, 1647–1656 (1999),
http://dx.doi.org/10.1088/0953-4075/32/7/008
[37] H. Aksela, Resonant Auger spectroscopy of atoms and molecules, J. Electr. Spectr. Relat. Phenomena 72, 235–242 (1995),
http://dx.doi.org/10.1016/0368-2048(94)02292-5
[38] K. Ueda, Y. Shimizu, H. Chiba, Y. Sato, M. Kitajima, H. Tanaka, and N.M. Kabachnik, Experimental determination of Auger-decay amplitudes from the angular correlations in Auger cascades following the 2p → 4s photoexcitation of Ar, Phys. Rev. Lett. 83, 5463–5466 (1999),
http://dx.doi.org/10.1103/PhysRevLett.83.5463
[39] B. Langer, N. Berrah, A. Farhat, M. Humphrey, D. Cubaynes, A. Menzel, and U. Becker, Angular distributions of resonant and non-resonant Auger electrons as a test case for the validity of spectator model: The argon L2MM case, J. Phys. B 30, 4255–4266 (1977),
http://dx.doi.org/10.1088/0953-4075/30/19/015
[40] P. O'Keeffe, S. Aloise, M. Meyer, and A.N. Grum-Grzhimailo, Circular polarization of ion fluorescence completing the analysis of resonant Xe 4d−1 5/26p Auger decay, Phys. Rev. Lett. 90, 023002(4) (2003),
http://dx.doi.org/10.1103/PhysRevLett.90.023002
[41] N.M. Kabachnik, I.P. Sazhina, and K. Ueda, Angular distribution of Auger electrons and fluorescence in cascades and resonantly enhanced transitions, J. Phys. B 32, 1769–1781 (1999),
http://dx.doi.org/10.1088/0953-4075/32/8/301
[42] A. Kupliauskienė, Photoexcitation of polarized atoms by polarized radiation, Lithuanian J. Phys. 44(1), 17–26 (2004),
http://dx.doi.org/10.3952/lithjphys.44102
[43] D.A. Varshalovich, A.N. Moskalev, and V.K. Khersonskii, Quantum Theory of Angular Momentum (World Scientific, Singapore, 1988),
http://dx.doi.org/10.1142/0270
[44] A. Kupliauskienė and V. Tutlys, Application of graphical technique for Auger decay following photoionization of atoms, Physica Scripta 67, 290–300 (2003),
http://dx.doi.org/10.1238/Physica.Regular.067a00290
[45] A. Kupliauskienė and V. Tutlys, Auger decay probability following photoionization of atoms, Lithuanian J. Phys. 43, 27–34 (2003)
[46] A. Kupliauskienė and K. Glemža, General expression for ionization cross-section of polarized atoms by polarized electrons, Lithuanian J. Phys. 43, 89–97 (2003)
[47] P. Serapinas and A. Kupliauskienė, On current filament formation in arc cathode plasma, J. Phys. D 27, 330–337 (1994),
http://dx.doi.org/10.1088/0022-3727/27/2/022
[48] A. Dorn, A. Elliott, J. Lower, E. Weigold, J. Berakdar, A. Engelns, and H. Klar, Orientational dichroism in the electron-impact ionization of laser-oriented atomic sodium, Phys. Rev. Lett. 80, 257–260 (1998),
http://dx.doi.org/10.1103/PhysRevLett.80.257
[49] J. Lower, E. Weigold, J. Berakdar, and S. Mazevet, Magnetic and orbital dichroism in (e, 2e) ionization of sodium, Phys. Rev. Lett. 86, 624–627 (2001),
http://dx.doi.org/10.1103/PhysRevLett.86.624
[50] S. Gelfort, H. Kerkow, P.V. Petukhov, and E.A. Romanovskii, Influence of Coster–Kroning transitions on the polarization of L-shell X-rays induced by proton impact, Zh. Eksp. Teor. Fiz. 113, 2005–2010 (1998) [in Russian]
[51] E.G. Berezhko and N.M. Kabachnik, Theoretical study of inner-shell alignment of atoms in electron impact ionization: Angular distribution and polarization of X-rays and Auger electrons, J. Phys. B 10, 2467–2477 (1977),
http://dx.doi.org/10.1088/0022-3700/10/12/025
[52] A. Kupliauskienė and V. Tutlys, Angular distribution and polarization of radiation following photoionization of polarized atoms, Physica Scripta (accepted)
[53] Y. Hann and K.J. LaGattuta, Dielectronic recombination and related resonance processes, Physics Reports (Review Section of Physics Letters) 166, 195–268 (1988),
http://dx.doi.org/10.1016/0370-1573(88)90021-X
[54] A.V. Kupliauskiene and R.L. Furmonavichyute, Cross-sections for resonance charge exchange with electron excitation due to collisions of Ca17+ with He and H2, Opt. Spektrosk. (USSR) 71, 13–15 (1991)
[55] M. Gail, N. Grün, and W. Scheid, Angular distribution of radiation emitted after resonant transfer and excitation, J. Phys. B 31, 4645–4654 (1998),
http://dx.doi.org/10.1088/0953-4075/31/20/021
[56] V.V. Balashov, I.V. Bondarenko, V.K. Dolinov, and S.I. Strachova, Angular anisotropy of the cascade photons in the dielectronic recombination of ions, Opt. Spektrosk. 77, 801–806 (1994)
[57] S. Zakowicz, W. Scheid and N. Grün, Dielectronic recombination into hydrogen-like heavy ions with emission of two photons, J. Phys. B 37, 131–145 (2004),
http://dx.doi.org/10.1088/0953-4075/37/1/008
[58] J. Cooper and R.N. Zare, Angular distribution of photoelectrons, J. Chem. Phys. 48, 942–943 (1968),
http://dx.doi.org/10.1063/1.1668742
[59] D. Dill, A.F. Starace, and S.T. Manson, Effects of anisotropic electron–ion interactions in atomic photoelectron angular distributions, Phys. Rev. A 11, 1596–1606 (1975),
http://dx.doi.org/10.1103/PhysRevA.11.1596
[60] N.A. Cherepkov, Angular distribution of photoelectrons with specific spin orientation, Zh. Eksp. Teor. Fiz. 65, 933–946 (1973) [in Russian]
[61] O. Plotzke, G. Prümper, B. Zimmermann, U. Becker, and H. Kleinpoppen, Magnetic dichroism in the angular distribution of atomic oxygen 2p photoelectrons, Phys. Rev. Lett. 77, 2642–2645 (1996),
http://dx.doi.org/10.1103/PhysRevLett.77.2642
[62] O. Hemmers et al., Dramatic nondipole effects in low-energy photoionization: Experiment and theoretical study of Xe 5s, Phys. Rev. Lett. 91, 053002 (2003),
http://dx.doi.org/10.1103/PhysRevLett.91.053002
[63] C. Pan and A.F. Starace, Angular distributions for near-threshold (e, 2e) processes for Li and Mg, Phys. Rev. A 47, 2389–2392 (1993),
http://dx.doi.org/10.1103/PhysRevA.47.2389
[64] M. Streun et al., Spin dependence of (e, 2e) collisions on lithium at 54.4 eV, J. Phys. B 31, 4401–4411 (1998),
http://dx.doi.org/10.1088/0953-4075/31/19/022
[65] S.C. McFarlane, The polarization of characteristic X-radiation excited by electron impact, J. Phys. B 5, 1906–1915 (1972),
http://dx.doi.org/10.1088/0022-3700/5/10/020
[66] S. Flügge, W. Mehlhorn, and V. Schmidt, Angular distribution of Auger electrons following photoionization, Phys. Rev. Lett. 29, 7–9 (1972),
http://dx.doi.org/10.1103/PhysRevLett.29.7
[67] E.G. Berezhko, N.M. Kabachnik, and V.S.Rostovsky, Potential-barrier effects in inner-shell photoionization and their influence on the anisotropy of X-rays and Auger electrons, J. Phys. B 11, 1749–1758 (1978),
http://dx.doi.org/10.1088/0022-3700/11/10/012
[68] E.G. Berezhko, N.M. Kabachnik, and V.V. Sizov, The theory of coincidence experiments on electron impact ionization of inner atomic shells, J. Phys. B 11, 1819–1832 (1978),
http://dx.doi.org/10.1088/0022-3700/11/10/017
[69] N.M. Kabachnik and I.P. Sazhina, Angular distribution and spin polarization of Auger electrons, J. Phys. B 17, 1335–1342 (1984),
http://dx.doi.org/10.1088/0022-3700/17/7/017
[70] V.V. Balashov, A.N. Grum-Grzhimailo, and N.M. Kabachnik, Angular distribution of autoionization and Auger electrons ejected by electron impact from laser-excited and polarized atoms, J. Phys. B 30, 1269–1291 (1997),
http://dx.doi.org/10.1088/0953-4075/30/5/020
[71] K. Ueda, Y. Shimizu, H. Chiba, M. Kitajima, H. Tanaka, S. Fritzsche, and N.M. Kabachnik, Experimental and theoretical study of the Auger cascade following 2p → 4s photoexcitation in Ar, J. Phys. B 34, 107–119 (2001),
http://dx.doi.org/10.1088/0953-4075/34/1/308
[72] K. Blum, B. Lohmann, and E. Taute, Angular distribution and polarization of Auger electrons, J. Phys. B 19, 3815–3825 (1986),
http://dx.doi.org/10.1088/0022-3700/19/22/02
[73] U. Kleiman and B. Lohmann, Large dynamic spin polarization parameters for diagram L3M1M4,5 Auger transitions, J. Phys. B 33, 2653–2663 (2000),
http://dx.doi.org/10.1088/0953-4075/33/14/304
[74] K. Bartschat and A.N. Grum-Grzhimailo, Vector (e, e′γ) correlations in ionization-excitation of He by electron impact, J. Phys. B 35, 5035–5050 (2002),
http://dx.doi.org/10.1088/0953-4075/35/24/308
[75] J. Eichler, A. Ichihara, and T. Shirai, Alignment caused by photoionization and in radiative electron capture into excited states of hydrogenic high-Z ions, Phys. Rev. A 58, 2128–2135 (1998),
http://dx.doi.org/10.1103/PhysRevA.58.2128
[76] J. Eichler and A. Ichihara, Polarization of photons emitted in radiative electron capture by bare high-Z ions, Phys. Rev. A 65, 052716 (2002),
http://dx.doi.org/10.1103/PhysRevA.65.052716
[77] A. Surzhykov, S. Fritzsche, and Th. Stöhlker, Two-step radiative recombination of polarized electrons into bare, high-Z ions, Nucl. Instrum. Methods Phys. Res. B 205, 391–394 (2003),
http://dx.doi.org/10.1016/S0168-583X(03)00589-5
[78] P.D. Fainstein, L. Gulyas, F. Martin, and A. Salin, Angular asymmetry of low-energy electron emission in ion-atom collisions, Phys. Rev. A 53, 3243–3246 (1996),
http://dx.doi.org/10.1103/PhysRevA.53.3243
[79] H. Tanuma, T. Hayakawa, C. Verzani, H. Kano, H. Watanabe, B.D. DePaola, and N. Kobayashi, Polarization spectroscopy of O5+ (1s23p) states produced in the collisions of O6+ with He and H2, J. Phys. B 33, 5091–5098 (2000),
http://dx.doi.org/10.1088/0953-4075/33/22/310
[80] A. Kupliauskienė, On the application of relaxed-orbital and sudden perturbation approximations for the photoionization of atoms, J. Phys. B 34, 345–361 (2001),
http://dx.doi.org/10.1088/0953-4075/34/3/312
[81] N. Rakštikas and A. Kupliauskienė, Strong dependence of the 2p photoionization cross sections of Na atoms on valence electron state, Physica Scripta 58, 587–594 (1998),
http://dx.doi.org/10.1088/0031-8949/58/6/007
[82] A. Kupliauskienė and J. Lipinskaja, The peculiarities of the angular distribution of photoelectrons from the 2p shell of excited Na, Lithuanian J. Phys. 41, 208–212 (2001)
[83] D. Jurčiukonis and A. Kupliauskienė, Investigation of the influence of valence electron excitation on the polarization of photoelectrons from Na atoms, Lithuanian J. Phys. 41, 242–246 (2001)