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Calculation of spectator satellite lines of nickel-like gold ions in high density thermonuclear plasma
._ElII
.H J&3 g
Nuclear Instruments
and Methods in Physics Research B 98 (1995) 98-99
NIOMI B
Beam Interactions with Materials B Atoms
EISEVIER
Calculation of spectator satellite lines of nickel-like gold ions in high density thermonuclear plasma Fumihiro Koike Physics Laboratory, School of Medicine, Kitasato University, Kitasato l-15-1, Sagamihara, Kanagawa 228, Japan
Abstract X-ray emissions and absorptions by highly charged ions play an important role in high density thermonuclear fusion plasma. Transition energies and oscillator strengths have been calculated for many combinations of the states of nickel-like gold ions with one or two spectator electrons. A relativistic atomic structure calculation has been carried out. Although the size of the calculation is quite large, a line by line analysis for such a system is well tractable.
2. Basic feature of Ni-like gold ions with one or two spectator electrons
1. Introduction A highly charged ion may accept a number of electrons in its higher-lying loosely-bound orbitals. These electrons give a number of satellites for X-ray emission lines due to the electronic transitions between the lower-lying tightlybound orbitals of ions, and further may cause an effective broadening of the emission lines. The line groups corresponding to those transitions form a quasi-continuum in a 2-4 keV photon energy range for the case of 3d-4f transitions of nickel-like gold ions [l]. These quasi-continuum lines are important for the radiation transport in high Z hot dense plasmas. The emission lines and opacity profiles have been analyzed extensively [2,3] using approximations called Unresolved Transition Array (UTA) and/or Super Transition Array (STA). These approximations are. powerful and reduce computation time significantly. However, when the population of the configurations is not in the thermal equilibrium, we have to employ a more sophisticated method for the spectral analysis. In this report, we examine the feasibility of a line by line calculation which enables us to evaluate the X-ray spectral profiles for arbitrary spectator electron population. We use a computer program called General Purpose Atomic Structure Program 2 (GRASP’) [4] for our atomic structure calculation. The program allows us to include a number of non-relativistic open shells and to include thousands of configuration state functions (CSFs) in the calculation. This feature of the program is quite advantageous for the present brute force calculation. In Section 2, we investigate the basic feature of the ionic system consisting of Au” + + one or two electrons. In Section 3, we show a couple of numerical examples of the line by line calculation and discuss the possible application to the radiation transport problem. 0168-583X/95/$09.50
Generally speaking, a single-electron orbital must be orthogonal to all the lower-lying orbitals with the same symmetry; we must include all the lower-lying orbitals in a multi-configuration atomic structure calculation if we want to safely satisfy the orthogonality constraint charged to the atomic orbitals. This situation makes the size of the calculation large when we want to obtain the Rydberg orbitals of atoms or ions. To obtain the Rydberg orbitals of Au”+ + e up to a principal quantum number n = 7 and up to an angular momentum quantum number I = n - 1, we included all the configurations composed by one of the nl orbitals with n = 4,5,6,7 and I= O,l,. . , n - 1 and an ionic configuration ls”2s22p63s23p63d”‘. Fortunately, we need not to shell ionic configuration include an open ls22s’2p63s23p”3d94f1 in the calculation. Before going into a full size calculation, we examined the need of such a configuration using smaller nl orbitals; the single electron Dirac-Fock orbitals are well defined and they are scarcely affected by the presence of such an open shell ionic configuration. The resulting outcome for the number of the CSFs for the full size calculation is 40, which is well tractable using a currently available small computer. We found that s and p orbitals very strongly exhibit a relativistic nature even in the higher-most orbitals, whereas in others the relativistic nature is moderate. Because an electron with a lower angular momentum may come close to the atomic nucleus, the relativistic effect appears even for higher Rydberg orbitals. Examining the quantum defect, we also found that the orbital nature is well coulombic outside the ion core. We are interested in the 3d-4f transition under the
0 1995 Elsevier Science B.V. All rights reserved
SSDI 0168-583X(95)00081-X
99
F. Koike / Nucl. Instr. and Meth. in Phys. Rex B 98 (1995) 98-99
presence of one or two spectator electrons. In this transition, there is, in principle, a chance for the spectator electrons to be shaken up or down into different spectator orbitals. However, it is quite rare in the present case, because the single electron orbitals are well defined and therefore the effect of electron correlation is small. This was confirmed by a couple of reduced size calculations; the transitions with the shake processes are weaker, typically by almost a factor of 10’ compared with the corresponding lines without them. We can regard the spectator electrons as the “real” spectators; they watch the 3d-4f transition with no interaction. We are allowed to employ a two-state approximation for the calculation of oscillator strengths for the spectator satellite lines. Finally, we have examined the effect of electron correlation between two spectator electrons. Using ns2, II = 4, 5, 6, 7 configurations, we compared the GRASP’ calculations with MCDF optimization (AL option of GRASP’) and without the MCDF optimization (CI option of GRASP’). We found no significant differences between the two calculations. We concluded again that the spectator Dirac-Fock orbitals are well defined, and that there is no need for further MCDF optimization, once we obtain the orbitals with single spectator electron configurations.
Oscillator Strength
Dlsfributian ofSp6d
Satellites
25
saten1te dlngrnm 20
15
10
5
, 0 1460
,].I,, , , 2480
2500
2560 2520 2540 Transition Energy
2580
2600
2620
2640
(eV)
Fig ,?. Two-spectator
electron satellites for transitions: AU”+ IS’ 2s ‘2p63s’3p63d94f’5p16d’ + Au5’+ ls22s22ph3s”3p63d1” Sp’6d’. The 3d-4f diagram lines are also presented by dots for comparison. 1
together with the diagram lines corresponding tions:
to the transi-
Au=+ ls22s’2p63s’3p63d94f’ + AL+‘+ ls22s22p63s23p63d”‘.
(2)
Fig. 2 shows an example of the oscillator strength distribution for two-spectator-electron satellites corresponding to the transitions:
3. Results and discussion Fig. 1 shows an example of the oscillator strength distribution for one-spectator-electron satellites corresponding to the transitions: Au’“+ ls22s22p63s23p63dy4f’nd’(n
= 4, 5, 6, 7)
+ Au5”+ ls22s22p63s23p63d1”nd~, Osctltator Strength Distribution
1
-----.
of One
(1) nd Sntellltes
9
7
satellitediagram
..
AI?‘+ ls22s’2p63s’3p63dy4f’5p’6d’ + Au5’+ ls22s22p63s23p63d”5p16d,
(3) together with the diagram lines. The energy positions of the diagram lines agree with experiment [l] to almost three digits. The accuracy of the satellite lines cannot be compared with experiment, because the experimental spectra form a continuum due to the mess of the emission lines. We expect the accuracy of the present satellite energy positions to be more or less the same as for the diagram lines. By assuming a certain distribution for the population of spectator states, we can construct spectral profiles of a real plasma. The calculation based on the LTE (local thermal equilibrium) model is now in progress and will be issued elsewhere.
References
I 2460
2480
2500
2560 2520 2540 Trsns,,ton Energy
Fig. 1. One-spectator-electron satellites
2580 (eV)
2600
2620
2640
for transitions: AU”+ (n = 4, 5, 6, 7) + Au5’+ ls22s’2p63s23p63d94f’nd’ ls22s22p63s23p63d”nd’. The 3d-4f diagram lines are also presented by dots for comparison.
[l] M. Busquet, P. Pain, J. Bauche, E. Luc-Koenig, Phys. Scripta 31 (1985) 137. [2] C. Bauche-Arnoult, J. Bauche and M. Klapisch, Phys. Rev. A 31 (1985) 2248. [3] J. Bauche, C. Bauche-Arnoult and M. Klapisch, Adv. At. Molec. Phys. 23 (1987) 132. [4] K.G. Dyall, I.P. Grant, C.T. Johnson, F.A. Parpia and E.P. Plummer, Comp. Phys. Commun. 55 (1989) 425.
2. PLASMAS/STRONG
FIELDS
.H J&3 g
Nuclear Instruments
and Methods in Physics Research B 98 (1995) 98-99
NIOMI B
Beam Interactions with Materials B Atoms
EISEVIER
Calculation of spectator satellite lines of nickel-like gold ions in high density thermonuclear plasma Fumihiro Koike Physics Laboratory, School of Medicine, Kitasato University, Kitasato l-15-1, Sagamihara, Kanagawa 228, Japan
Abstract X-ray emissions and absorptions by highly charged ions play an important role in high density thermonuclear fusion plasma. Transition energies and oscillator strengths have been calculated for many combinations of the states of nickel-like gold ions with one or two spectator electrons. A relativistic atomic structure calculation has been carried out. Although the size of the calculation is quite large, a line by line analysis for such a system is well tractable.
2. Basic feature of Ni-like gold ions with one or two spectator electrons
1. Introduction A highly charged ion may accept a number of electrons in its higher-lying loosely-bound orbitals. These electrons give a number of satellites for X-ray emission lines due to the electronic transitions between the lower-lying tightlybound orbitals of ions, and further may cause an effective broadening of the emission lines. The line groups corresponding to those transitions form a quasi-continuum in a 2-4 keV photon energy range for the case of 3d-4f transitions of nickel-like gold ions [l]. These quasi-continuum lines are important for the radiation transport in high Z hot dense plasmas. The emission lines and opacity profiles have been analyzed extensively [2,3] using approximations called Unresolved Transition Array (UTA) and/or Super Transition Array (STA). These approximations are. powerful and reduce computation time significantly. However, when the population of the configurations is not in the thermal equilibrium, we have to employ a more sophisticated method for the spectral analysis. In this report, we examine the feasibility of a line by line calculation which enables us to evaluate the X-ray spectral profiles for arbitrary spectator electron population. We use a computer program called General Purpose Atomic Structure Program 2 (GRASP’) [4] for our atomic structure calculation. The program allows us to include a number of non-relativistic open shells and to include thousands of configuration state functions (CSFs) in the calculation. This feature of the program is quite advantageous for the present brute force calculation. In Section 2, we investigate the basic feature of the ionic system consisting of Au” + + one or two electrons. In Section 3, we show a couple of numerical examples of the line by line calculation and discuss the possible application to the radiation transport problem. 0168-583X/95/$09.50
Generally speaking, a single-electron orbital must be orthogonal to all the lower-lying orbitals with the same symmetry; we must include all the lower-lying orbitals in a multi-configuration atomic structure calculation if we want to safely satisfy the orthogonality constraint charged to the atomic orbitals. This situation makes the size of the calculation large when we want to obtain the Rydberg orbitals of atoms or ions. To obtain the Rydberg orbitals of Au”+ + e up to a principal quantum number n = 7 and up to an angular momentum quantum number I = n - 1, we included all the configurations composed by one of the nl orbitals with n = 4,5,6,7 and I= O,l,. . , n - 1 and an ionic configuration ls”2s22p63s23p63d”‘. Fortunately, we need not to shell ionic configuration include an open ls22s’2p63s23p”3d94f1 in the calculation. Before going into a full size calculation, we examined the need of such a configuration using smaller nl orbitals; the single electron Dirac-Fock orbitals are well defined and they are scarcely affected by the presence of such an open shell ionic configuration. The resulting outcome for the number of the CSFs for the full size calculation is 40, which is well tractable using a currently available small computer. We found that s and p orbitals very strongly exhibit a relativistic nature even in the higher-most orbitals, whereas in others the relativistic nature is moderate. Because an electron with a lower angular momentum may come close to the atomic nucleus, the relativistic effect appears even for higher Rydberg orbitals. Examining the quantum defect, we also found that the orbital nature is well coulombic outside the ion core. We are interested in the 3d-4f transition under the
0 1995 Elsevier Science B.V. All rights reserved
SSDI 0168-583X(95)00081-X
99
F. Koike / Nucl. Instr. and Meth. in Phys. Rex B 98 (1995) 98-99
presence of one or two spectator electrons. In this transition, there is, in principle, a chance for the spectator electrons to be shaken up or down into different spectator orbitals. However, it is quite rare in the present case, because the single electron orbitals are well defined and therefore the effect of electron correlation is small. This was confirmed by a couple of reduced size calculations; the transitions with the shake processes are weaker, typically by almost a factor of 10’ compared with the corresponding lines without them. We can regard the spectator electrons as the “real” spectators; they watch the 3d-4f transition with no interaction. We are allowed to employ a two-state approximation for the calculation of oscillator strengths for the spectator satellite lines. Finally, we have examined the effect of electron correlation between two spectator electrons. Using ns2, II = 4, 5, 6, 7 configurations, we compared the GRASP’ calculations with MCDF optimization (AL option of GRASP’) and without the MCDF optimization (CI option of GRASP’). We found no significant differences between the two calculations. We concluded again that the spectator Dirac-Fock orbitals are well defined, and that there is no need for further MCDF optimization, once we obtain the orbitals with single spectator electron configurations.
Oscillator Strength
Dlsfributian ofSp6d
Satellites
25
saten1te dlngrnm 20
15
10
5
, 0 1460
,].I,, , , 2480
2500
2560 2520 2540 Transition Energy
2580
2600
2620
2640
(eV)
Fig ,?. Two-spectator
electron satellites for transitions: AU”+ IS’ 2s ‘2p63s’3p63d94f’5p16d’ + Au5’+ ls22s22ph3s”3p63d1” Sp’6d’. The 3d-4f diagram lines are also presented by dots for comparison. 1
together with the diagram lines corresponding tions:
to the transi-
Au=+ ls22s’2p63s’3p63d94f’ + AL+‘+ ls22s22p63s23p63d”‘.
(2)
Fig. 2 shows an example of the oscillator strength distribution for two-spectator-electron satellites corresponding to the transitions:
3. Results and discussion Fig. 1 shows an example of the oscillator strength distribution for one-spectator-electron satellites corresponding to the transitions: Au’“+ ls22s22p63s23p63dy4f’nd’(n
= 4, 5, 6, 7)
+ Au5”+ ls22s22p63s23p63d1”nd~, Osctltator Strength Distribution
1
-----.
of One
(1) nd Sntellltes
9
7
satellitediagram
..
AI?‘+ ls22s’2p63s’3p63dy4f’5p’6d’ + Au5’+ ls22s22p63s23p63d”5p16d,
(3) together with the diagram lines. The energy positions of the diagram lines agree with experiment [l] to almost three digits. The accuracy of the satellite lines cannot be compared with experiment, because the experimental spectra form a continuum due to the mess of the emission lines. We expect the accuracy of the present satellite energy positions to be more or less the same as for the diagram lines. By assuming a certain distribution for the population of spectator states, we can construct spectral profiles of a real plasma. The calculation based on the LTE (local thermal equilibrium) model is now in progress and will be issued elsewhere.
References
I 2460
2480
2500
2560 2520 2540 Trsns,,ton Energy
Fig. 1. One-spectator-electron satellites
2580 (eV)
2600
2620
2640
for transitions: AU”+ (n = 4, 5, 6, 7) + Au5’+ ls22s’2p63s23p63d94f’nd’ ls22s22p63s23p63d”nd’. The 3d-4f diagram lines are also presented by dots for comparison.
[l] M. Busquet, P. Pain, J. Bauche, E. Luc-Koenig, Phys. Scripta 31 (1985) 137. [2] C. Bauche-Arnoult, J. Bauche and M. Klapisch, Phys. Rev. A 31 (1985) 2248. [3] J. Bauche, C. Bauche-Arnoult and M. Klapisch, Adv. At. Molec. Phys. 23 (1987) 132. [4] K.G. Dyall, I.P. Grant, C.T. Johnson, F.A. Parpia and E.P. Plummer, Comp. Phys. Commun. 55 (1989) 425.
2. PLASMAS/STRONG
FIELDS