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The influence of inner shells upon the angular distribution of Kr 4p-photoelectrons
Volume 82A, number 4
PHYSICS LETTERS
23 March 1981
ThE INFLUENCE OF INNER SHELLS UPON THE ANGULAR DISTRIBUTION OF Kr 4p-PHOTOELECTRONS M.Ya. AMUSIA, L.V. CHERNYSHEVA and S.A. SHEINERMAN A.F. Joffe Physical-Technical Institute of the Academy of Sciences of the USSR, Leningrad, USSR
Received 18 August 1980 Revised manuscript received 17 November 1980
The influence of inner shells upon the anisotropy parameter of the 4p-photoelectrons angular distribution in Kr is investigated in the frame of the random phase approximation with exchange (RPAE). The comparison with experimental data and other calculationsdemonstrates an essential role of intershell correlations, the account of which allows to achieve a satisfactory agreement between theoretical and experimental data.
The aim of this letter is to study the variations of the energy dependence of the angular distribution anisotropy parameter (3(e) for 4p-photoelectrons in Kr and to learn, whether these variations exist due to intershell correlations only or, besides, due to relativistic effects. The calculation of /3(e) performed in this paper takes into account the intershell correlations in nonrelativistic approximation and is of interest in connection with essential differences between existing experimental data [1—3] The comparison of our and other calculations [4,5] serves as an additional argument in clarifying the question of which experimental data are more reliable. In the previous calculation ofj3(e) [4] (e is aphotoelectron energy) only intrashell correlations of Kr 4p6 -electrons in the random phase approximation with exchange (RPAE) were taken into account. The values of/3(e) obtained for the region near the threshold (e < I Ry) appeared to be in satisfactory agreement with the experimental data existing at that time as well as with single-particle Hartree—Fock calculations. However for higher photon energies w (w = e + I, I is the ionisation potential), the calculational and experimental data disagree, the measured value of /3(e) decreasing with increase of co much faster than the calculated one. It was assumed that this discrepancy is determined by essential influence of inter-
shell correlation, in particular by strong action of many-electron 3d10-subshell upon the ionized 4p6 one. This assumption was supported by the calculation of /3 performed later [6] for 5p6-subshell in Xe, where the account of inner 4d10-shell influence demonstrates the essential role of intershell correlations and leads to a prominent extra variation of /3, which was confirmed experimentally. Evidently, the strong effect of inner d10-shell upon the outer p6-electrons should be essential in Kr too and it must be taken into account in calculations of the 4p-photoelectrons angular distribution. The measurements of/3(e) performed recently [1, 2] have confirmed the previous data only at small energies, contradicting it essentially for w > 2 Ry. On the other hand, the dependence /3(e), calculated recently using the relativistic version of RPAE-RRPA [5] ,with inclusion of(4s + 4p + 3d) electron interactions is in satisfactory agreement with latest measurements [2] for the whole energy region considered in calculations [5]. To provide the possibility of understanding the role of intershell correlations only (without relativistic effects) we have calculated /3(e) for Kr 4p-electrons in nonrelativistic RPAE taking into consideration the effect of 4~2 and 3d10-subshells upon the ionized 4p6 -shell. The function /3(e) is determined by
o 03 1—9163/81/0000—0000/s 02.50 © North-Holland Publishing Company
171
Volume 82A, number 4
PHYSICS LETTERS
ed and 4p es transition amplitudes and by elastic scattering phases of the photoelectron in the remainder ion field [41: —~
electron value. The amplitude is determined by the sum: ‘2 n d4~+ ~.D3d + ~j~4s
-~
—
‘—“1±1 — 1±1
~_____i___~____
—
23 March 1981
1±1
1±1’
where d~jis the transition 1
~—~—
—~
1 ±1 matrix element,
(2! + l)[1D
lD1~1l1 X {(l l)ID 2 + (1 + 2)ID 2 + 6\/l(l + 1) 1—1 X [(ReD ReD + ImD 1+1 ImD )
1_11
which includes the 4p intrashell correlations only, whereas and are corrections including 10- and the effect of virtual and real excitations of 3d pho4s2-subshells respectively upon the 4p-electron toionization amplitude. The amplitude D 1~1is cornplex. The relation (2) is valid, because, as was demon2- and 10 -electrons is small and the corresponding correc3d strated by calculations, the mutual action of 4s
+
—
1—i
1+1
11
1+1
~ )
cost 1+1 ImD 1—1 —(ReD 1—1 i+i —ReD 1+1 ImD ~ —
S1fl~ 1+1
)
~ l—l’~‘‘
“
tions to D 1~1of(2)amplitudes may be neglected. The correlation were calculated by us
‘
where D1~1D1_1 are the reduced matrix elements of 4p ed and 4p -÷ es transitions respectively and 6shell ionization 1 = elastic 1. are the scattering phases; for 4p In the Hartree—Fock approximation transition amplitudes are given by a real dipole moment matrix element calculated with single electron wavefunctions. Dynamic polarization of 4s2- and 3d10-electrons due to absorbtion of a photon with a frequency w leads to variation of the amplitude as compared to its one-
in RPAE [7] Along with 4p-intrashell correlations the of real virtual 3d Nu3d influence e’p and 4s e’pand were takentransitions into account. merical calculations were performed using programs [8] by the computer BESM-6 in the energy w region from 4p6-subshell threshold up to S au. The results of our calculations among other theoretical values (3(w) and experimental data are given in fig. 1. According to calculations the influence of 4s2subshell upon (34p is negligible, while the many-elec-
,
.
—~
—~
—~
—~
N
_____________________________________________________I Fig. 1. Anisotropy parameter !34p for Kr. Experimental points:
and o
[2] for ~3(2P 2P 2 P 312)and ~3(2P 112) respectively (if there is no difference between subshells, + represents the common value); A and x [I] for j3( 312) and j3( 112) respectively; • [3]. Results of 2P calculations: — 2P RPAE (sip + 4s + 3d), this paper; — — RPAE (4p) [4]; ——— and —.— RRPA (4p + 4s + 3d) [5] for P( 11~)and ~3( 312)respectively.
172
+
Volume 82A, number 4
PHYSICS LETTERS
tron 3d10-shell essentially alters the values j3 for w> 1.5 au. The correlations are especially strong for w 3.5 au, that corresponds to the 3d10-subshell ionization threshold. The account of intershell correlations leads in this energy region to an essential increase of /3 which then proves to be positive for the whole energy region considered, The comparison with other calculations [4,5] demonstrates that for w <2 au, intershell correlations and relativistic corrections are negligible. In the energy region 1.8 au 1.2 au allows to conclude that the data of [3] in this region are erroneous. 6The strong influence of 3d’°-upon ionized 4pnasubshell leads to the conclusion about collective ture of 4p-photoelectrons angular distribution at least for w > 2 au. The measured /3(e) can be satisfactory described using nonrelativistic RPAE method with
23 March 1981
account of intra- and intershell correlations in the whole energy region where experimental data are available. However, the intershell correlations are especially strong for photon energies w ~ 3 au, where the 4p6-subshell photoelectron angular distribution totally appears to be subject to influence of 3d10shell. This statement is supported by the coincidence in this region between the existing experimental data [2] with the result of our calculations. References [1] J.L. Dehmer, W.A. Chypka, 1. Berkowitz and W.T. Jivery, Phys. Rev. A12 (1975) 1966. [2] D.L. Miller, J.D. Dow, R.G. Houlgate, G.V. Marr and J.B. West, J. Phys. BIG (1977) 3205. [3] G.R. Branton and C.E. Brion, J. Electr. Spectroscopy 3 (1974) 123. [4] M.Ya. Amusia, N.A. Cherepkov and L.V. Chernysheva, Phys. Lett. 40A (1972) 15.
[5] W.R. Johnson, C.D. Lin, K.T. Cheng and C.M. Lee,
Physica Scripta 21(1980) 409. V.K. Ivanov, Phys. Lett. 59A (1976) 194. [7] M.Ya. N.A. Cherepkov, Case Studies in AtomicAmusia Physicsand 5 (1975) 47.
[6] M.Ya. Amusia and
[8] L.V. Chernysheva, M.Ya. Amusia and N.A. Cherepkov, preprint loffe Physical-Technical Institute 459 (1974), Leningrad.
173
PHYSICS LETTERS
23 March 1981
ThE INFLUENCE OF INNER SHELLS UPON THE ANGULAR DISTRIBUTION OF Kr 4p-PHOTOELECTRONS M.Ya. AMUSIA, L.V. CHERNYSHEVA and S.A. SHEINERMAN A.F. Joffe Physical-Technical Institute of the Academy of Sciences of the USSR, Leningrad, USSR
Received 18 August 1980 Revised manuscript received 17 November 1980
The influence of inner shells upon the anisotropy parameter of the 4p-photoelectrons angular distribution in Kr is investigated in the frame of the random phase approximation with exchange (RPAE). The comparison with experimental data and other calculationsdemonstrates an essential role of intershell correlations, the account of which allows to achieve a satisfactory agreement between theoretical and experimental data.
The aim of this letter is to study the variations of the energy dependence of the angular distribution anisotropy parameter (3(e) for 4p-photoelectrons in Kr and to learn, whether these variations exist due to intershell correlations only or, besides, due to relativistic effects. The calculation of /3(e) performed in this paper takes into account the intershell correlations in nonrelativistic approximation and is of interest in connection with essential differences between existing experimental data [1—3] The comparison of our and other calculations [4,5] serves as an additional argument in clarifying the question of which experimental data are more reliable. In the previous calculation ofj3(e) [4] (e is aphotoelectron energy) only intrashell correlations of Kr 4p6 -electrons in the random phase approximation with exchange (RPAE) were taken into account. The values of/3(e) obtained for the region near the threshold (e < I Ry) appeared to be in satisfactory agreement with the experimental data existing at that time as well as with single-particle Hartree—Fock calculations. However for higher photon energies w (w = e + I, I is the ionisation potential), the calculational and experimental data disagree, the measured value of /3(e) decreasing with increase of co much faster than the calculated one. It was assumed that this discrepancy is determined by essential influence of inter-
shell correlation, in particular by strong action of many-electron 3d10-subshell upon the ionized 4p6 one. This assumption was supported by the calculation of /3 performed later [6] for 5p6-subshell in Xe, where the account of inner 4d10-shell influence demonstrates the essential role of intershell correlations and leads to a prominent extra variation of /3, which was confirmed experimentally. Evidently, the strong effect of inner d10-shell upon the outer p6-electrons should be essential in Kr too and it must be taken into account in calculations of the 4p-photoelectrons angular distribution. The measurements of/3(e) performed recently [1, 2] have confirmed the previous data only at small energies, contradicting it essentially for w > 2 Ry. On the other hand, the dependence /3(e), calculated recently using the relativistic version of RPAE-RRPA [5] ,with inclusion of(4s + 4p + 3d) electron interactions is in satisfactory agreement with latest measurements [2] for the whole energy region considered in calculations [5]. To provide the possibility of understanding the role of intershell correlations only (without relativistic effects) we have calculated /3(e) for Kr 4p-electrons in nonrelativistic RPAE taking into consideration the effect of 4~2 and 3d10-subshells upon the ionized 4p6 -shell. The function /3(e) is determined by
o 03 1—9163/81/0000—0000/s 02.50 © North-Holland Publishing Company
171
Volume 82A, number 4
PHYSICS LETTERS
ed and 4p es transition amplitudes and by elastic scattering phases of the photoelectron in the remainder ion field [41: —~
electron value. The amplitude is determined by the sum: ‘2 n d4~+ ~.D3d + ~j~4s
-~
—
‘—“1±1 — 1±1
~_____i___~____
—
23 March 1981
1±1
1±1’
where d~jis the transition 1
~—~—
—~
1 ±1 matrix element,
(2! + l)[1D
lD1~1l1 X {(l l)ID 2 + (1 + 2)ID 2 + 6\/l(l + 1) 1—1 X [(ReD ReD + ImD 1+1 ImD )
1_11
which includes the 4p intrashell correlations only, whereas and are corrections including 10- and the effect of virtual and real excitations of 3d pho4s2-subshells respectively upon the 4p-electron toionization amplitude. The amplitude D 1~1is cornplex. The relation (2) is valid, because, as was demon2- and 10 -electrons is small and the corresponding correc3d strated by calculations, the mutual action of 4s
+
—
1—i
1+1
11
1+1
~ )
cost 1+1 ImD 1—1 —(ReD 1—1 i+i —ReD 1+1 ImD ~ —
S1fl~ 1+1
)
~ l—l’~‘‘
“
tions to D 1~1of(2)amplitudes may be neglected. The correlation were calculated by us
‘
where D1~1D1_1 are the reduced matrix elements of 4p ed and 4p -÷ es transitions respectively and 6shell ionization 1 = elastic 1. are the scattering phases; for 4p In the Hartree—Fock approximation transition amplitudes are given by a real dipole moment matrix element calculated with single electron wavefunctions. Dynamic polarization of 4s2- and 3d10-electrons due to absorbtion of a photon with a frequency w leads to variation of the amplitude as compared to its one-
in RPAE [7] Along with 4p-intrashell correlations the of real virtual 3d Nu3d influence e’p and 4s e’pand were takentransitions into account. merical calculations were performed using programs [8] by the computer BESM-6 in the energy w region from 4p6-subshell threshold up to S au. The results of our calculations among other theoretical values (3(w) and experimental data are given in fig. 1. According to calculations the influence of 4s2subshell upon (34p is negligible, while the many-elec-
,
.
—~
—~
—~
—~
N
_____________________________________________________I Fig. 1. Anisotropy parameter !34p for Kr. Experimental points:
and o
[2] for ~3(2P 2P 2 P 312)and ~3(2P 112) respectively (if there is no difference between subshells, + represents the common value); A and x [I] for j3( 312) and j3( 112) respectively; • [3]. Results of 2P calculations: — 2P RPAE (sip + 4s + 3d), this paper; — — RPAE (4p) [4]; ——— and —.— RRPA (4p + 4s + 3d) [5] for P( 11~)and ~3( 312)respectively.
172
+
Volume 82A, number 4
PHYSICS LETTERS
tron 3d10-shell essentially alters the values j3 for w> 1.5 au. The correlations are especially strong for w 3.5 au, that corresponds to the 3d10-subshell ionization threshold. The account of intershell correlations leads in this energy region to an essential increase of /3 which then proves to be positive for the whole energy region considered, The comparison with other calculations [4,5] demonstrates that for w <2 au, intershell correlations and relativistic corrections are negligible. In the energy region 1.8 au
23 March 1981
account of intra- and intershell correlations in the whole energy region where experimental data are available. However, the intershell correlations are especially strong for photon energies w ~ 3 au, where the 4p6-subshell photoelectron angular distribution totally appears to be subject to influence of 3d10shell. This statement is supported by the coincidence in this region between the existing experimental data [2] with the result of our calculations. References [1] J.L. Dehmer, W.A. Chypka, 1. Berkowitz and W.T. Jivery, Phys. Rev. A12 (1975) 1966. [2] D.L. Miller, J.D. Dow, R.G. Houlgate, G.V. Marr and J.B. West, J. Phys. BIG (1977) 3205. [3] G.R. Branton and C.E. Brion, J. Electr. Spectroscopy 3 (1974) 123. [4] M.Ya. Amusia, N.A. Cherepkov and L.V. Chernysheva, Phys. Lett. 40A (1972) 15.
[5] W.R. Johnson, C.D. Lin, K.T. Cheng and C.M. Lee,
Physica Scripta 21(1980) 409. V.K. Ivanov, Phys. Lett. 59A (1976) 194. [7] M.Ya. N.A. Cherepkov, Case Studies in AtomicAmusia Physicsand 5 (1975) 47.
[6] M.Ya. Amusia and
[8] L.V. Chernysheva, M.Ya. Amusia and N.A. Cherepkov, preprint loffe Physical-Technical Institute 459 (1974), Leningrad.
173