- Email: [email protected]
Angular distribution and spin polarization of Xe 5s → εp photoelectrons
Volume 66A, number 3
PHYSICS LE1’TERS
15 May 1978
ANGULAR DISTRIBUTION AND SPIN POLARIZATION OF Xe Ss
-~
£p PHOTOELECTRONS
N.A. CHEREPKOV A.F. loffe Physico-Technical Institute, Academy of Sciences of the USSR, 194021 Leningrad, USSR Received 22 June 1977
2 subshells from the It is shown that the deviation of the angular distribution asymmetry parameter (3 for the outer ns value 2, expected in the LS coupling scheme, is a combined effect of many-electron correlations and spin—orbit interaction.
The photoionization cross section of heavy alkali atoms near the ionization threshold has a Cooper minimum, where the dipole matrix element d(w) changes sign. After taking into account the spin—orbit interaction, the dipole matrix elements for the transitions ns -÷ep 112 (d1) and ns -÷ep312 (d3) pass through zero at different photon Owing to this fact the photoionization crossenergies section w. in the Cooper minimum does not become zero, and the asymmetry parameter13 of the photoelectron angular distribution proves to be different from 2 [1], the value which follows for s electrons in the absence of spin—orbit interaction. In addition, irradiation of alkali atoms by circularly polarized light in the region of the Cooper minimum yields photoelectrons [2]). Thepolarized same effects must appear(Fano in theeffect photoionization of ns2 subshells [3]. As is well known, the angular distribution of photoelectrons for unpolarized or circularly polarized light has the form du(w)/d~= (u(w)/4ir) [1
—
1 ~ 13(o.~)P
2(cosi)],
-
(1)
where o(w) is the total photoionization cross section. When spin—orbit interaction is taken into account, the asymmetry parameter 13 for s electrons is given by the expression (2’ 2—2d2)I(24 4-d2)= (2a2+4x)/(2a2+1),
13 = (2Id3+d~I where a
=
1
1
expression [2] 2 5a2 —4 1 a = 3d~ ~ 12d3 + d11 = CE (3) 2d~+ d~ 3(2a2 + 1) For the case d 3 = d1 it follows that a = 0, i.e. the polarization is a consequence of the spin—orbit interaction. It should be noted that the difference between the phases in the ~P1/2 and ep312 states was neglected in eqs. (2), (3) since it gives a negligible contribution [21. 1 and Expressions (2), (3) are equally applied to ns ns2 subshells [3]. As was shown in ref. [5], due to the strong influence of the many-electron correlations the Cooper minima appear in the photoionization cross section of the outer ns2 subshells of Ar, Kr and Xe above the thresholds. Therefore the phenomena con—
—
— —_________
sidered above must be observed here too. Let us consider the particular case of the 5~2subshell of Xe. In the Hartree—Fock approximation the Cooper minimum for this subshell lies in the region of the discrete spectrum. The of correlational interaction with the 5p6 andinclusion 4d10 subshells [5] moves the Cooper mimmum into the contmuous spectrum. The final
d
3/d1. If spin—orbit interaction is neglected then d3 = d1 and it follows from eq. (2) that 13 = 2. For ionization by circularly polarized light photoelectrons near the Cooper minimum are spin polarized. The general expression for the angular distribution of elec204
trons with spin orientation along an arbitrarily chosen direction was given earlier [3,41. In the particular case of electron spin orientation along the polarization vector of the photon the degree of polarization in this direction of the total electron current is given by the
cross section calculated in ref. [5] is presented in fig. 1 a. The experimental measurements [6] confirm the calculated results. However the spin—orbit interaction was not taken into account in ref. [5]. The matrix elements d1 (~) and d3 (~) in the Dirac—Slater approximation
Volume 66A, number 3
PHYSICS LETTERS
periment [8], where at w = 304A(3 Ry) it was found
0.5
5~
0.4 ~O.3 ~0.2 0.
2 ~ —_~
//
/
J3
/
I/
,-\
-
.
—1~~ Q
‘
I
2
3
w (Ry)
Fig. 1. (a) The photoionization cross section of the Xe 5~2 subshell. Solid line: calculations from ref. [5], experimental points from ref. [6]. (b) The angular distribution asymmetry parameter (3, calculated in the present work (solid line), in the Dirac—Slater approximation [7] (dashed line); the square: experimental point [8]. Dot-dashed line: the degree of polarization a for circularly polarized light, calculated in present work.
were calculated in ref. [7], but without account of many-electron correlations. To find the parameters a and (3 taking into account both the many-electron correlations and spin—orbit interaction the following procedure was performed. From the cross section calculated in ref. [5] the dipole matrix element d(w) was found under the assumption that it is real. After that, based on calculations in the Dirac—Slater approximation [7], it was supposed that d1 (w) = d(w + ~ ~)‘ d~(w) = 0.75 d(w ~~)‘ (4) i.e. d3(w) = 0.75 d1 (w ~) where ~ = 0.35 Ry. The absolute values of d3 and d1, as follows from eqs. (2), (3), are unimportant. The asymmetry parameter (3 calculated with these matrix elements is presented in fig. lb. As is seen from this figure, the weak spin—orbit interaction gives rise to sharp changes in the asymmetry parameter, which otherwise should be constant equal to 2. This behaviour explains the result of a recent ex—
—
that = 1.4 ±0.1. The results of ref. [7] differ from ours 13due to the wrong position of the Cooper minimum in the Dirac—Slater approximation. It is worth noting that near the ionization threshold the contribution of the quadrupole component may be significant [9]. In fig. lb the degree of polarization of photoelectron is also shown as a function of photon energy w for circularly polarized light. Like the alkali atoms, it is large only near the Cooper minimum. In contrast to the alkali atoms, the photoionization of the ns2 subshell produces ions which are also spin-polarized in a direction opposite to the direction of the electron spin polarization. The ionization potential of the Xe 5~2 subshell is rather high, and this subshell is not the outer one. It is much more promising to study outer ns2 subshells, for
‘ —
-~
15 May 1978
minima thresholds, which are exampleabove in autoionization Ba the andionization Hg, where there are[10]. also Cooper masked by transitions Formulae (2), (3) are applicable in autoionization resonances too, and the values of a and 13 give information about the partial amplitudes d 1 and d3. If both parameters a and (3 are known in addition to the total cross section, it enables one to find the amplitudes d1 and d3 separately. In Hg the Cooper minimum for the 6s ep transition is found at w 1 Ry [10], therefore the measured value of ~3 1.68 ±0.1[11] at w= 584A(1.S6Ry)is in agreement with the behaviour of (3 above the Cooper minimum, as shown in fig. lb, which is typical for all ns ep transitions having a Cooper minimum. The large difference between values of ~ in3D the 9 6s2(2D autoionization resonance Sd 312 )6p( 1) (8 = 1.25 ±0.1 at w = 1066 A) and far on its wing (8 = 2.15 ±0.1 at w = 1048 A) demonstrates that this resonance decays preferably through one of two possible channels. To deduce which channel is preferable it is necessary to know in addition the degree of polarization of photoelectrons a in the resonance. From the ratio of the cross sections at these points and the measured values of (3 it is more likely that this autoionization state decays completely through the ns ~Pi/2 channel (a = 0.35) while the ns -÷ep312 transition cross section changes smoothly in this region. —~
-+
—~
The author is grateful to Dr. M.Ya. Amusia for useful discussions. 205
Volume 66A,
number 3
PHYSICS LETTERS
References [1] U. Heinzmann, J. Kessler and J. Lorenz, Z. Phys. 240 [2] [3] [4]
[5]
206
(1970) 42. U. Fano, Phys. Rev. 178 (1969) 131; 184 (1969) 250. N.A. Cherepkov, Zh. Eksp. Teor. Fiz. 65 (1973) 933; Soy. Phys. JETP 38 (1974) 463. B. Brehm, Z. Phys. 242 (1971) 195. M.Ya. Amusia, V.K. Ivanov, N.A. Cherepkov and L.V. Chernysheva, Zh. Eksp. Teor. Fiz. 66 (1974) 1537; M.Ya. Amusia and N.A. Cherepkov, Case Studies in Atomic Physics 5 (1975) 47.
[6] J.A.R. Samson and J.L. Gardner, Phys. (1974) 671.
15 May 1978
Rev. Lett. 33
[7] T.E.H. Walker and J.T. Waber, J. Phys. B7 (1974) 674. [8] J.L. Dehmer and D. Dill, Phys. Rev. Lett. 37 (1976) 1049. [9] M.Ya. Amusia, A.S. Baltenkov, A.A. Grinberg and S.G. Shapiro, Zh. Eksp. Teor. Fiz. 68 (1975) 28. [101 R.B. Cairns, H. Harrison and RI. Schoen, J. Chem. Phys. 53 (1970) 96; B. Brehm, Z. Naturforsch. 21a (1966) 196. [11] A. Niechaus and M.W. Ruf, Z. Phys. 252 (1972) 84.
PHYSICS LE1’TERS
15 May 1978
ANGULAR DISTRIBUTION AND SPIN POLARIZATION OF Xe Ss
-~
£p PHOTOELECTRONS
N.A. CHEREPKOV A.F. loffe Physico-Technical Institute, Academy of Sciences of the USSR, 194021 Leningrad, USSR Received 22 June 1977
2 subshells from the It is shown that the deviation of the angular distribution asymmetry parameter (3 for the outer ns value 2, expected in the LS coupling scheme, is a combined effect of many-electron correlations and spin—orbit interaction.
The photoionization cross section of heavy alkali atoms near the ionization threshold has a Cooper minimum, where the dipole matrix element d(w) changes sign. After taking into account the spin—orbit interaction, the dipole matrix elements for the transitions ns -÷ep 112 (d1) and ns -÷ep312 (d3) pass through zero at different photon Owing to this fact the photoionization crossenergies section w. in the Cooper minimum does not become zero, and the asymmetry parameter13 of the photoelectron angular distribution proves to be different from 2 [1], the value which follows for s electrons in the absence of spin—orbit interaction. In addition, irradiation of alkali atoms by circularly polarized light in the region of the Cooper minimum yields photoelectrons [2]). Thepolarized same effects must appear(Fano in theeffect photoionization of ns2 subshells [3]. As is well known, the angular distribution of photoelectrons for unpolarized or circularly polarized light has the form du(w)/d~= (u(w)/4ir) [1
—
1 ~ 13(o.~)P
2(cosi)],
-
(1)
where o(w) is the total photoionization cross section. When spin—orbit interaction is taken into account, the asymmetry parameter 13 for s electrons is given by the expression (2’ 2—2d2)I(24 4-d2)= (2a2+4x)/(2a2+1),
13 = (2Id3+d~I where a
=
1
1
expression [2] 2 5a2 —4 1 a = 3d~ ~ 12d3 + d11 = CE (3) 2d~+ d~ 3(2a2 + 1) For the case d 3 = d1 it follows that a = 0, i.e. the polarization is a consequence of the spin—orbit interaction. It should be noted that the difference between the phases in the ~P1/2 and ep312 states was neglected in eqs. (2), (3) since it gives a negligible contribution [21. 1 and Expressions (2), (3) are equally applied to ns ns2 subshells [3]. As was shown in ref. [5], due to the strong influence of the many-electron correlations the Cooper minima appear in the photoionization cross section of the outer ns2 subshells of Ar, Kr and Xe above the thresholds. Therefore the phenomena con—
—
— —_________
sidered above must be observed here too. Let us consider the particular case of the 5~2subshell of Xe. In the Hartree—Fock approximation the Cooper minimum for this subshell lies in the region of the discrete spectrum. The of correlational interaction with the 5p6 andinclusion 4d10 subshells [5] moves the Cooper mimmum into the contmuous spectrum. The final
d
3/d1. If spin—orbit interaction is neglected then d3 = d1 and it follows from eq. (2) that 13 = 2. For ionization by circularly polarized light photoelectrons near the Cooper minimum are spin polarized. The general expression for the angular distribution of elec204
trons with spin orientation along an arbitrarily chosen direction was given earlier [3,41. In the particular case of electron spin orientation along the polarization vector of the photon the degree of polarization in this direction of the total electron current is given by the
cross section calculated in ref. [5] is presented in fig. 1 a. The experimental measurements [6] confirm the calculated results. However the spin—orbit interaction was not taken into account in ref. [5]. The matrix elements d1 (~) and d3 (~) in the Dirac—Slater approximation
Volume 66A, number 3
PHYSICS LETTERS
periment [8], where at w = 304A(3 Ry) it was found
0.5
5~
0.4 ~O.3 ~0.2 0.
2 ~ —_~
//
/
J3
/
I/
,-\
-
.
—1~~ Q
‘
I
2
3
w (Ry)
Fig. 1. (a) The photoionization cross section of the Xe 5~2 subshell. Solid line: calculations from ref. [5], experimental points from ref. [6]. (b) The angular distribution asymmetry parameter (3, calculated in the present work (solid line), in the Dirac—Slater approximation [7] (dashed line); the square: experimental point [8]. Dot-dashed line: the degree of polarization a for circularly polarized light, calculated in present work.
were calculated in ref. [7], but without account of many-electron correlations. To find the parameters a and (3 taking into account both the many-electron correlations and spin—orbit interaction the following procedure was performed. From the cross section calculated in ref. [5] the dipole matrix element d(w) was found under the assumption that it is real. After that, based on calculations in the Dirac—Slater approximation [7], it was supposed that d1 (w) = d(w + ~ ~)‘ d~(w) = 0.75 d(w ~~)‘ (4) i.e. d3(w) = 0.75 d1 (w ~) where ~ = 0.35 Ry. The absolute values of d3 and d1, as follows from eqs. (2), (3), are unimportant. The asymmetry parameter (3 calculated with these matrix elements is presented in fig. lb. As is seen from this figure, the weak spin—orbit interaction gives rise to sharp changes in the asymmetry parameter, which otherwise should be constant equal to 2. This behaviour explains the result of a recent ex—
—
that = 1.4 ±0.1. The results of ref. [7] differ from ours 13due to the wrong position of the Cooper minimum in the Dirac—Slater approximation. It is worth noting that near the ionization threshold the contribution of the quadrupole component may be significant [9]. In fig. lb the degree of polarization of photoelectron is also shown as a function of photon energy w for circularly polarized light. Like the alkali atoms, it is large only near the Cooper minimum. In contrast to the alkali atoms, the photoionization of the ns2 subshell produces ions which are also spin-polarized in a direction opposite to the direction of the electron spin polarization. The ionization potential of the Xe 5~2 subshell is rather high, and this subshell is not the outer one. It is much more promising to study outer ns2 subshells, for
‘ —
-~
15 May 1978
minima thresholds, which are exampleabove in autoionization Ba the andionization Hg, where there are[10]. also Cooper masked by transitions Formulae (2), (3) are applicable in autoionization resonances too, and the values of a and 13 give information about the partial amplitudes d 1 and d3. If both parameters a and (3 are known in addition to the total cross section, it enables one to find the amplitudes d1 and d3 separately. In Hg the Cooper minimum for the 6s ep transition is found at w 1 Ry [10], therefore the measured value of ~3 1.68 ±0.1[11] at w= 584A(1.S6Ry)is in agreement with the behaviour of (3 above the Cooper minimum, as shown in fig. lb, which is typical for all ns ep transitions having a Cooper minimum. The large difference between values of ~ in3D the 9 6s2(2D autoionization resonance Sd 312 )6p( 1) (8 = 1.25 ±0.1 at w = 1066 A) and far on its wing (8 = 2.15 ±0.1 at w = 1048 A) demonstrates that this resonance decays preferably through one of two possible channels. To deduce which channel is preferable it is necessary to know in addition the degree of polarization of photoelectrons a in the resonance. From the ratio of the cross sections at these points and the measured values of (3 it is more likely that this autoionization state decays completely through the ns ~Pi/2 channel (a = 0.35) while the ns -÷ep312 transition cross section changes smoothly in this region. —~
-+
—~
The author is grateful to Dr. M.Ya. Amusia for useful discussions. 205
Volume 66A,
number 3
PHYSICS LETTERS
References [1] U. Heinzmann, J. Kessler and J. Lorenz, Z. Phys. 240 [2] [3] [4]
[5]
206
(1970) 42. U. Fano, Phys. Rev. 178 (1969) 131; 184 (1969) 250. N.A. Cherepkov, Zh. Eksp. Teor. Fiz. 65 (1973) 933; Soy. Phys. JETP 38 (1974) 463. B. Brehm, Z. Phys. 242 (1971) 195. M.Ya. Amusia, V.K. Ivanov, N.A. Cherepkov and L.V. Chernysheva, Zh. Eksp. Teor. Fiz. 66 (1974) 1537; M.Ya. Amusia and N.A. Cherepkov, Case Studies in Atomic Physics 5 (1975) 47.
[6] J.A.R. Samson and J.L. Gardner, Phys. (1974) 671.
15 May 1978
Rev. Lett. 33
[7] T.E.H. Walker and J.T. Waber, J. Phys. B7 (1974) 674. [8] J.L. Dehmer and D. Dill, Phys. Rev. Lett. 37 (1976) 1049. [9] M.Ya. Amusia, A.S. Baltenkov, A.A. Grinberg and S.G. Shapiro, Zh. Eksp. Teor. Fiz. 68 (1975) 28. [101 R.B. Cairns, H. Harrison and RI. Schoen, J. Chem. Phys. 53 (1970) 96; B. Brehm, Z. Naturforsch. 21a (1966) 196. [11] A. Niechaus and M.W. Ruf, Z. Phys. 252 (1972) 84.