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One-electron and two-electron one-photon transitions in atomic systems with two K-shell vacancies
Volume 66A, number 3
PHYSICS LETTERS
15 May 1978
ONE-ELECTRON AND TWO-ELECTRON ONE-PHOTON TRANSITIONS IN ATOMIC SYSTEMS WITh TWO K-SHELL VACANCIES U.I. SAFRONOVA Institute of Spectroscopy, Academy of Sciences of the USSR, Moscow, Podolsky rayon, Academgorodok, 142092, USSR
and V.S. SENASHENKO Institute ofNuclear Physics, Moscow State University, Moscow, USSR Received 31 May 1977
The probabilities for the radiative one- and two-electron one-photon transitions into the doubly ionized K shell for ions of the isoelectronic sequence Ne have been calculated in first-order perturbation theory in the interelectron interaction as a function of the atomic number. The stability of the results of these calculations to the inclusion of corrections for the electrostatic and relativistic interaction of electrons is investigated.
At the moment we are witnessing rapid progress in experimental studies of the energy spectra of X-rays produced in ion—atom collisions. In particular several workshave been published on one- and two-electron single-photon transitions in atomic systems with fully ionized K shell [1—4]. Their publication stimulated the development of theoretical investigations. Thus, the radiative decay of excited states of a number of atoms and ions with two K-shell vacancies has been investigated quite recently on the basis of the “shakedown” model [5—9] and also in first-order perturbation theory in the interelectron interaction [10—13]. The present paper discusses the results of calculations of the probabilities of one-electron, W(K~),and two-electron, W(K~~), single-photon transitions of L electrons into the K shell for ions of the isoelectronic sequence Ne with two is vacancies. The stability of the probability ratio for one- and two-electron onephoton transitions to the inclusion of corrections for the electrostatic and relativistic interaction of electrons is investigated. The transition probabilities and energies have been calculated using the wave functions for the initial and final states obtained in first-order perturbation theory in the interelectronic interaction. The relativistic corrections have been evaluated in the Breit approximation.
The results of the calculations for ions with Z 10—60 are given in table 1. The transition probability ratios W(Kha)/W(Kac~)calculated here, as well as the experimental data [1,2,4] and calculations by other authors, are presented in table 2. Confming oneself to the first nonvanishing order in Z, one readily obtains the asymptotic formula for the single- and doubleelectron transition probability ratio (1) W(Kh)/W(K ) = 8 303z2 =
a
OCCS
A full calculation involving first-order wave functions modifies somewhat the above formula: W(Kh\ITAKK ~ = 8 303Z2F ‘Z’F Z 2 ‘
~
cia)
1’~ 1 2
where F 2 defines the cor1(Z)= 1 + 2/Z 83619/Z transition energy rection for the oneand+two-electron ratio and F 2 gives the correc= (1 1.08016/Z) tion for the2(Z) one-electron transition matrix element. We note that formula (1) qualitatively reproduces the available experimental data and its form is independent of the number of electrons in the p shell. A comparison of the results of the present calculations with those of refs. [10,13] indicates that the ratio W(K~)/W(K~~) is little sensitive to the degree of ionization of the electron shell. Thus, the ratios calcu—
185
Volume 66A, number 3
PHYSICS LET1TERS
15 May 1978
Table 1 Probabilities W (s~)and wavelengths A (A) of one- and two-electron one-photon transitions. 22p6 —÷ 1s2s22p5 2s22p6 -+ 1s22s2p5 Z 2s 1S
3P 0—3~ 1
A
W(K~)
10 15 20 25 30 40 50
12.6883 5.6359 3.1449
60
0.3245
2.552 x 14.30 x 46.92 x 108.9 x 191.6 x 171.1 x 143 x 3347 x
1.9961 1.3754 0.7585 0.4767
A
1S ‘So~P1
W(K~)
10~~12.6415
x 10l~
iO’~, 5.6159
X 1O’~ x 1O~~ x 10~~ x i0’~ x i0’~ x io’~ io~~
0.851 0.617 io’~ 3.1356 1.42 10~~ 1.9908 14.9 io’~ 1.3713 75.7 i0’~ 0.7625 433.3 io’~ 13 0.4808 1849 0.3286 922
3P 0+
1
A
W(K~)
A
W(K~)
6.9102 2.9737 1.6355 1.0295 0.7056 0.3886 0.1655 0.2442
3.075 7.617 14.43 23.25 32.86 46.37 98.36 56.92
6.8660 2.9600 1.6297 1.0267 0.7039 0.3875 0.1665 0.2431
0.678 X 0.429 X 0.683 x 0.553 X 2.82 x 21.34 x 73.02 XX 55.30
X iO~° x 1O~~ x 1O~~ X 10~° X 10~ X 10~~ xX 10”~ 10~°
10~ 1O~ iO~ 10~ 10~° 1O~° 1O’°
to
Table 2 Branching ratios of one- and two-electron one-photon transitions. Z
Present calculation
Experiment
10 13
851 1422
18 20
2702 3334
1000 ± 1000 [4] 2570± 38013]
26
5628
4100±400[3]
28
6523
5000± 600[3]
965
±
180 [3]
Calculations by other authors 500 1020 1950 2400 1570 4060 2.4 x 1870 4710 3140
[121 a); [11] b);
547 [7] 740 [6]; 682 [7] [11]; 1310 [6] [11] [6]; 1240 [7] [11]; 5700 [101; iO~[9]; 2600 [61; [7] [11]; 2.5x i05 [9]; [6]; 2120 [7];
a) In paper [12] the ratio 2 W(K~)/W(K~~) was calculated. b) In paper [11] the imaginary part of the matrix element of the two-electron transition was not taken into account and a multiplier 2 was omitted.
lated in this work for Fe+18 are close to the corresponding values obtained in ref. [10] for Fe~2and in ref. [13] for Fe~23.Taking account of the relativistic corrections also affects the magnitude of ratio (1) only wealdy; even for Z = 60, the inclusion of the relativistic effects increases the ratio W(K~)/W(K~~) by not more than 1—2%. In conclusion, it should be noted that the experimental data, with which the results of the calculations are compared, have been averaged not only over the electron configurations of an ion, but also over a certam interval of charge states. An essential improvement in the energy resolution in the registration of 186
X-ray spectra and a detailed examination of X-ray spectra pertaining to ions in a definite charge state will enable a fuller estimation of the potentialities of the theoretical model employed. Especially valuable will be experiments with detection of coincidence of ions and X-rays formed in the decay of excited states of ions with several inner-shell vacancies. References [1] W. Wölfli, Ch. Stoller, G. Bonani, M. Suter and M. Stöckli, Phys. Rev. Lett. 35 (1975) 656. [2]V.V. Afrosimov, Yu.S. Gordeev, V.M. Dukelsky, A.N. Zinoviev and A.P. Shergin, Zh. Eksp. Teor. Fiz. Pis’ma 24 (1976) 273.
Volume 66A, number 3
PHYSICS LETFERS
[3]Ch. Stoller, W. Wölfli, G. Bonani, M. Stdckli and M. Suter, Phys. Lett. 58A (1976) 18. [4] A.R. Knudson, K.W. Hill, P.G. Burkhalter and D.J. Nagel, Phys. Rev. Lett. 37 (1976) 679. [5] Th.P. Hoogkamer, P. Woerlee, F.W. Saris and M. Gavrila, J. Phys. 9B (1976) L145. [6] T. Aberg, K.A. Jamison and P. Richard, Phys. Rev. Lett. 37~(1976)63.
15 May 1978
[7]M. Gavrila and J.E. Hansen, Phys. Lett. 58A (1976) 158. [8] N. Moiseyev and J. Katriel, Phys. Lett. 58A (1976) 303. [9] H. Nussbaumer, J. Phys. 9B (1976) 1757. [10] H.R. Kelly, Phys. Rev. Lett. 37 (1976) 37. [11] S.V. Khristenko, Phys. Lett. 59A (1976) 202. [12] M.Ya. Amusia, I.S. Lee and A.N. Zinoviev, Phys. Lett. 60A (1977) 300. [13] U.I. Safronova and V.S. Senashenko, J. Phys. B, to be published.
187
PHYSICS LETTERS
15 May 1978
ONE-ELECTRON AND TWO-ELECTRON ONE-PHOTON TRANSITIONS IN ATOMIC SYSTEMS WITh TWO K-SHELL VACANCIES U.I. SAFRONOVA Institute of Spectroscopy, Academy of Sciences of the USSR, Moscow, Podolsky rayon, Academgorodok, 142092, USSR
and V.S. SENASHENKO Institute ofNuclear Physics, Moscow State University, Moscow, USSR Received 31 May 1977
The probabilities for the radiative one- and two-electron one-photon transitions into the doubly ionized K shell for ions of the isoelectronic sequence Ne have been calculated in first-order perturbation theory in the interelectron interaction as a function of the atomic number. The stability of the results of these calculations to the inclusion of corrections for the electrostatic and relativistic interaction of electrons is investigated.
At the moment we are witnessing rapid progress in experimental studies of the energy spectra of X-rays produced in ion—atom collisions. In particular several workshave been published on one- and two-electron single-photon transitions in atomic systems with fully ionized K shell [1—4]. Their publication stimulated the development of theoretical investigations. Thus, the radiative decay of excited states of a number of atoms and ions with two K-shell vacancies has been investigated quite recently on the basis of the “shakedown” model [5—9] and also in first-order perturbation theory in the interelectron interaction [10—13]. The present paper discusses the results of calculations of the probabilities of one-electron, W(K~),and two-electron, W(K~~), single-photon transitions of L electrons into the K shell for ions of the isoelectronic sequence Ne with two is vacancies. The stability of the probability ratio for one- and two-electron onephoton transitions to the inclusion of corrections for the electrostatic and relativistic interaction of electrons is investigated. The transition probabilities and energies have been calculated using the wave functions for the initial and final states obtained in first-order perturbation theory in the interelectronic interaction. The relativistic corrections have been evaluated in the Breit approximation.
The results of the calculations for ions with Z 10—60 are given in table 1. The transition probability ratios W(Kha)/W(Kac~)calculated here, as well as the experimental data [1,2,4] and calculations by other authors, are presented in table 2. Confming oneself to the first nonvanishing order in Z, one readily obtains the asymptotic formula for the single- and doubleelectron transition probability ratio (1) W(Kh)/W(K ) = 8 303z2 =
a
OCCS
A full calculation involving first-order wave functions modifies somewhat the above formula: W(Kh\ITAKK ~ = 8 303Z2F ‘Z’F Z 2 ‘
~
cia)
1’~ 1 2
where F 2 defines the cor1(Z)= 1 + 2/Z 83619/Z transition energy rection for the oneand+two-electron ratio and F 2 gives the correc= (1 1.08016/Z) tion for the2(Z) one-electron transition matrix element. We note that formula (1) qualitatively reproduces the available experimental data and its form is independent of the number of electrons in the p shell. A comparison of the results of the present calculations with those of refs. [10,13] indicates that the ratio W(K~)/W(K~~) is little sensitive to the degree of ionization of the electron shell. Thus, the ratios calcu—
185
Volume 66A, number 3
PHYSICS LET1TERS
15 May 1978
Table 1 Probabilities W (s~)and wavelengths A (A) of one- and two-electron one-photon transitions. 22p6 —÷ 1s2s22p5 2s22p6 -+ 1s22s2p5 Z 2s 1S
3P 0—3~ 1
A
W(K~)
10 15 20 25 30 40 50
12.6883 5.6359 3.1449
60
0.3245
2.552 x 14.30 x 46.92 x 108.9 x 191.6 x 171.1 x 143 x 3347 x
1.9961 1.3754 0.7585 0.4767
A
1S ‘So~P1
W(K~)
10~~12.6415
x 10l~
iO’~, 5.6159
X 1O’~ x 1O~~ x 10~~ x i0’~ x i0’~ x io’~ io~~
0.851 0.617 io’~ 3.1356 1.42 10~~ 1.9908 14.9 io’~ 1.3713 75.7 i0’~ 0.7625 433.3 io’~ 13 0.4808 1849 0.3286 922
3P 0+
1
A
W(K~)
A
W(K~)
6.9102 2.9737 1.6355 1.0295 0.7056 0.3886 0.1655 0.2442
3.075 7.617 14.43 23.25 32.86 46.37 98.36 56.92
6.8660 2.9600 1.6297 1.0267 0.7039 0.3875 0.1665 0.2431
0.678 X 0.429 X 0.683 x 0.553 X 2.82 x 21.34 x 73.02 XX 55.30
X iO~° x 1O~~ x 1O~~ X 10~° X 10~ X 10~~ xX 10”~ 10~°
10~ 1O~ iO~ 10~ 10~° 1O~° 1O’°
to
Table 2 Branching ratios of one- and two-electron one-photon transitions. Z
Present calculation
Experiment
10 13
851 1422
18 20
2702 3334
1000 ± 1000 [4] 2570± 38013]
26
5628
4100±400[3]
28
6523
5000± 600[3]
965
±
180 [3]
Calculations by other authors 500 1020 1950 2400 1570 4060 2.4 x 1870 4710 3140
[121 a); [11] b);
547 [7] 740 [6]; 682 [7] [11]; 1310 [6] [11] [6]; 1240 [7] [11]; 5700 [101; iO~[9]; 2600 [61; [7] [11]; 2.5x i05 [9]; [6]; 2120 [7];
a) In paper [12] the ratio 2 W(K~)/W(K~~) was calculated. b) In paper [11] the imaginary part of the matrix element of the two-electron transition was not taken into account and a multiplier 2 was omitted.
lated in this work for Fe+18 are close to the corresponding values obtained in ref. [10] for Fe~2and in ref. [13] for Fe~23.Taking account of the relativistic corrections also affects the magnitude of ratio (1) only wealdy; even for Z = 60, the inclusion of the relativistic effects increases the ratio W(K~)/W(K~~) by not more than 1—2%. In conclusion, it should be noted that the experimental data, with which the results of the calculations are compared, have been averaged not only over the electron configurations of an ion, but also over a certam interval of charge states. An essential improvement in the energy resolution in the registration of 186
X-ray spectra and a detailed examination of X-ray spectra pertaining to ions in a definite charge state will enable a fuller estimation of the potentialities of the theoretical model employed. Especially valuable will be experiments with detection of coincidence of ions and X-rays formed in the decay of excited states of ions with several inner-shell vacancies. References [1] W. Wölfli, Ch. Stoller, G. Bonani, M. Suter and M. Stöckli, Phys. Rev. Lett. 35 (1975) 656. [2]V.V. Afrosimov, Yu.S. Gordeev, V.M. Dukelsky, A.N. Zinoviev and A.P. Shergin, Zh. Eksp. Teor. Fiz. Pis’ma 24 (1976) 273.
Volume 66A, number 3
PHYSICS LETFERS
[3]Ch. Stoller, W. Wölfli, G. Bonani, M. Stdckli and M. Suter, Phys. Lett. 58A (1976) 18. [4] A.R. Knudson, K.W. Hill, P.G. Burkhalter and D.J. Nagel, Phys. Rev. Lett. 37 (1976) 679. [5] Th.P. Hoogkamer, P. Woerlee, F.W. Saris and M. Gavrila, J. Phys. 9B (1976) L145. [6] T. Aberg, K.A. Jamison and P. Richard, Phys. Rev. Lett. 37~(1976)63.
15 May 1978
[7]M. Gavrila and J.E. Hansen, Phys. Lett. 58A (1976) 158. [8] N. Moiseyev and J. Katriel, Phys. Lett. 58A (1976) 303. [9] H. Nussbaumer, J. Phys. 9B (1976) 1757. [10] H.R. Kelly, Phys. Rev. Lett. 37 (1976) 37. [11] S.V. Khristenko, Phys. Lett. 59A (1976) 202. [12] M.Ya. Amusia, I.S. Lee and A.N. Zinoviev, Phys. Lett. 60A (1977) 300. [13] U.I. Safronova and V.S. Senashenko, J. Phys. B, to be published.
187