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Photoionization processes widely exist in the astrophysical plasma and the high temperature laboratory plasma. Compared with the traditional photoelectron energy spectrum, the photoelectron angular distribution is not only related to the amplitude of the photoionization channels, but also sensitive to the phases of these channels. So the photoelectron angular distribution contains much more quantum information about the photoionization processes and is used to provide stringent tests of our understanding of basic physical processes underlying gas- and condensed-phase interaction with radiation, as well as a tool to probe physical and chemical structure in solids and surfaces. For a long time, the dipole approximation has been the basis in the study of the photoelectron angular distribution, but with the progress of light source, such as the fourth generation synchrotron facilities, more and more attention is paid to the non-dipole effect of the photoelectron angular distribution. In thispresent work, the photoionization processes of sodium-like ions (20Z92) are studied for the different incident photon energies based on the multiconfiguration Dirac-Fock method and the density matrix theory. The influences of the non-dipole terms on the photoelectron angular distributions, which arise from the multipole expansion of the electron-photon interaction, are discussed in detail. The relationship between the dipole and non-dipole parameters of the photoelectron angular distribution along with the atomic number is given. It is found that the influence of non-dipole terms on the photoelectron angular distribution is related to the incident photon energy and the atomic number of the target ion and the subshell of the ionized electron. In general, the influences of the non-dipole terms on the photoelectron angular distribution of p subshell are larger than those of the s subshell. In the electric dipole approximation, the s subshell photoelectron angular distribution is nearly independent of the photon energy and nuclear charge number, but this situation is not for the p subshell. With the increase of photon energy, an abnormal angular distribution is found for the p subshell photoelectron. However, if the non-dipole effects are included, the abnormal photoelectron angular distribution of p subshell disappears and the photoelectron distribution has maximum values respectively near 45o and 135o with respect to the polarization vector of incident light, that is, the photoelectron distribution has an obvious forward scattering characteristic.
[1] Jablonski A, Powell C J 2015 J. Electron Spectrosc. Relat. Phenom. 199 27
[2] Ricz S, Buhr T, Kövér á, Holste K, Borovik A, Schippers S, Varga D, Müller A 2014 Phys. Rev. A 90 013410
[3] Ma K, Dong C Z, Xie L Y, Qu Y Z 2014 Chin. Phys. Lett. 31 103201
[4] Ma K, Dong C Z, Xie L Y, Ding X B, Qu Y Z 2014 Chin. Phys. Lett. 31 053201
[5] Guillemin R, Hemmers O, Lindle D W, Manson S T 2006 Radiat. Phys. Chem. 75 2258
[6] Schmidt V 1992 Rep. Prog. Phys. 55 1483
[7] Krässig B, Jung M, Gemmell D S, Kanter E P, LeBrun T, Southworth S H, Young L 1995 Phys. Rev. Lett. 75 4736
[8] Jung M, Krässig B, Gemmell D S, Kanter E P, LeBrun T, Southworth S H, Young L 1996 Phys. Rev. A 54 2127
[9] Hemmers O, Fisher G, Glans P, Hansen D L, Wang H, Whitfield S B, Wehlitz R, Levin J C, Sellin I A, Perera R C C, Dias E W B, Chakraborty H S, Deshmukh P C, Manson S T, Lindle D W 1997 J. Phys. B 30 L727
[10] Holste K, Borovik A A, Buhr T, Ricz S, Kövér á, Bernhardt D, Schippers S, Varga D, Müller A 2014 J. Phys. Confer. Ser. 488 022041
[11] Ma K, Xie L Y, Zhang D H, Dong C Z 2015 Chin. Phys. B 24 073402
[12] Li C Y, Han X Y, Wang J G, Qu Y Z 2013 Chin. Phys. B 22 123201
[13] Grant I P 1970 Adv. Phys. 19 747
[14] Jönsson P, He X, Fischer C F, Grant I P 2007 Comput. Phys. Commun. 177 597
[15] Fritzsche S 2012 Comput. Phys. Commun. 183 1525
[16] Ma K, Xie L Y, Zhang D H, Dong C Z, Qu Y Z 2016 Acta Phys. Sci. 65 083201 (in Chinese)[马堃, 颉录有, 张登红, 董晨钟, 屈一至 2016 65 083201]
[17] Blum K 2012 Density Matrix Theory and Applications (Vol. 3) (Berlin:Springer) pp61-162
[18] Balashov V V, Grum-Grahimailo A N, Kabachnik N M 2000 Polarization and Correlation in Atomic Collisions (New York:Kluwer Academic/Plenum) pp45-97
[19] Rose M E 1957 Elementary Theory of Angular Momentum (New York:Wiley) pp32-94
[20] Derevianko A, Hemmers O, Oblad S, Glans P, Wang H, Whitfield B, Wehlitz R, Sellin I A, Johnson W R, Lindle D W 2000 Phys. Rev. Lett. 84 2116
[21] Jablonski A 2013 J. Electron Spectrosc. Relat. Phenom. 189 81
[22] Scofield J H 1989 Phys. Rev. A 40 3054
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[1] Jablonski A, Powell C J 2015 J. Electron Spectrosc. Relat. Phenom. 199 27
[2] Ricz S, Buhr T, Kövér á, Holste K, Borovik A, Schippers S, Varga D, Müller A 2014 Phys. Rev. A 90 013410
[3] Ma K, Dong C Z, Xie L Y, Qu Y Z 2014 Chin. Phys. Lett. 31 103201
[4] Ma K, Dong C Z, Xie L Y, Ding X B, Qu Y Z 2014 Chin. Phys. Lett. 31 053201
[5] Guillemin R, Hemmers O, Lindle D W, Manson S T 2006 Radiat. Phys. Chem. 75 2258
[6] Schmidt V 1992 Rep. Prog. Phys. 55 1483
[7] Krässig B, Jung M, Gemmell D S, Kanter E P, LeBrun T, Southworth S H, Young L 1995 Phys. Rev. Lett. 75 4736
[8] Jung M, Krässig B, Gemmell D S, Kanter E P, LeBrun T, Southworth S H, Young L 1996 Phys. Rev. A 54 2127
[9] Hemmers O, Fisher G, Glans P, Hansen D L, Wang H, Whitfield S B, Wehlitz R, Levin J C, Sellin I A, Perera R C C, Dias E W B, Chakraborty H S, Deshmukh P C, Manson S T, Lindle D W 1997 J. Phys. B 30 L727
[10] Holste K, Borovik A A, Buhr T, Ricz S, Kövér á, Bernhardt D, Schippers S, Varga D, Müller A 2014 J. Phys. Confer. Ser. 488 022041
[11] Ma K, Xie L Y, Zhang D H, Dong C Z 2015 Chin. Phys. B 24 073402
[12] Li C Y, Han X Y, Wang J G, Qu Y Z 2013 Chin. Phys. B 22 123201
[13] Grant I P 1970 Adv. Phys. 19 747
[14] Jönsson P, He X, Fischer C F, Grant I P 2007 Comput. Phys. Commun. 177 597
[15] Fritzsche S 2012 Comput. Phys. Commun. 183 1525
[16] Ma K, Xie L Y, Zhang D H, Dong C Z, Qu Y Z 2016 Acta Phys. Sci. 65 083201 (in Chinese)[马堃, 颉录有, 张登红, 董晨钟, 屈一至 2016 65 083201]
[17] Blum K 2012 Density Matrix Theory and Applications (Vol. 3) (Berlin:Springer) pp61-162
[18] Balashov V V, Grum-Grahimailo A N, Kabachnik N M 2000 Polarization and Correlation in Atomic Collisions (New York:Kluwer Academic/Plenum) pp45-97
[19] Rose M E 1957 Elementary Theory of Angular Momentum (New York:Wiley) pp32-94
[20] Derevianko A, Hemmers O, Oblad S, Glans P, Wang H, Whitfield B, Wehlitz R, Sellin I A, Johnson W R, Lindle D W 2000 Phys. Rev. Lett. 84 2116
[21] Jablonski A 2013 J. Electron Spectrosc. Relat. Phenom. 189 81
[22] Scofield J H 1989 Phys. Rev. A 40 3054
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