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X-ray and Auger transition rates and energies of 3l 3l ′ states of two-electron ions
__ __ EB
& *H
Nuclear Instruments
and Methods in Physics Research B 99 (1995) 66-67
KIONIB
Beam Interactions with Materials 6 Atoms
ELSEVIER
X-ray and Auger transition rates and energies of 3/3/’ states of two-electron ions K.R. Karim * Physics Department,
Illinois State Uniuersiry, Normal, Illinois 61790-4560, USA
Abstract X-ray and Auger transition rates and transition energies are calculated for helium-like iron ions in the 3/3/ configurations. This work is an extension of our previous studies on the atomic parameters of doubly-excited two-electron atoms. The calculations have been performed using the Hartree-Fock-Slater atomic model. The effects of configuration interaction, spin-orbit coupling, and relativity have been included in the calculation. The autoionizing channel 3/3/’ + 2pc/ is seen to be the most favored mode of deexcitation.
1. Introduction The structure and spectra of doubly-excited heliumlike ions in 3/3/l configurations have been reported by Ho [l], Lipsky and Conneely [2], Bachau [3], and Lin [4] for Z I 10 and by Karim and Bhalla [5-71 for Z = 10, 14, 18, 20, and 22. These systems are interesting from both theoretical and applied points of view. The doubly-excited heliumlike ions are produced in ion-atom collision experiments, and in high-tempertaure laboratory and astrophysical plasmas. Since an exact solution of the dynamics of systems with three or more interacting particles has not yet been found, these simplest 3-body systems are of great interest to many-body theorists. The study of the structure and decay of such systems provide delicate tests of existing theories. In the present paper we list all the prominent decay channels of 3/3/” configurations of heliumlike iron ions with the corresponding transition energies, transition rates. and branching ratios.
2. Theory The transition dent perturbation given by
rates were calculated from time-depentheory. The Auger transition rates are
* Tel. + 1 309 438 507, [email protected]. 0168-583X/95/$09.50
fax
+ 1 309
438
5413,
e-mail
where +i and I+?, are, respectively, the antisymmetrized many-electron wave functions of the initial and final states, p(Ef) is the density of the final states, and V,, = l/rij is two-electron interaction operator. The X-ray transition rates are given as
where w is the angular frequency of the radiated photon, yJ and y’J’ represent, respectively, the initial and final states of the system, D is the electric dipole operator, and (y’J’ I] D I]rJ> is the reduced matrix element. The expressions of relevant reduced matrix elements are given in our earlier paper [S].
3. Results and discussion In Table 1 we list Auger and X-ray transition rates, transition energies, fluorescence yields and nonradiative branching ratios for all possible states of 3/3/’ configurations of heliumlike iron. The states are grouped according to parity and are listed in increasing order of the total angular momentum quantum number. The decay channels with probabilities of less than 20% are not included in the table. A complete listing can be obtained from the author on request. We note that radiative channels are generally much weaker in comparison with the nonradiative channels. The dominant X-ray channels include the transitions 3p3d 3F4 + ls3d 3D3, 3d2 3P,, --) 2p3d ‘D,, 3d* ‘Se+ ls3p ‘P,, 3p3d ‘PO + ls3d 3D,, 3p3d ‘D, -+ ls3d ‘Da, and 3p3d 3F, -+ ls3d 3D2 with fluorescence yields of 0.64, 0.61, 0.35, 0.34, 0.34, and 0.31, respectively. For nonradiative
0 1995 Elsevier Science B.V. All rights reserved
SSDI 0168-583X(94)00554-0
K.R. Karim / Nucl. instr. and Meth. in Phys. Res. B 99 (1995166-67 Table 1 Auger and X-ray transition rates (in units of 10’” /s), transition energies (in eV), radiative branching ratios (fluorescence yields), and nonradiative branching ratios (Auger yields) for doubly cited He-like iron. In column 2 the states 2~,,~ and Zp,,, written. respectively, as 2p_ and 2p+ Initial State
y I s,,
3s-
3p? is,, 3d’ ‘S,, 3p: ‘P(, 3d’ ‘P,, 3pz 3P, 3s3d ‘D, 3pz 3P, 3d2 3Pz 3~’ ’ D, 3d’ ’ D, 3s3d ’ bZ
3d’ ‘F1 3s3d ‘D, 3d’ ‘F3 3s3d ‘D, 3d”F, 3d2 ‘G,
Final state
Transition energies
Transition rates
Branching ration X 100
?SE/ 2p_ EJ’ 2p+ EL’ ls3p ‘P, 2p3d ’ P,
300.3 300.1 307.6 8269.3 1285.8 310.7 8221.9 1268.5 312.8 292.1 318.2 297.3 296.2 1275.7 310.2 289.5 327.3 328.2 328.0 307.3 331.7 311.0 319.4 298.5 332.7 312.0 320. I 334.1 313.4 341.2 320.5 301 .o 300.x 8220.5 309.9 8232.9 302. I 281.2 8221.6 3 10.0 315.5 315.2 294.5 _35’ _A.0 331.3 325.0 8227.3 305.9 285.0 8225.3
13.4 7.3 79.0 4.3 4.0 26.1 11.‘7 5.0 15.0 15.0 2.5 2.3 25.:! 2.0 15.2 18.5 17.9 26.7 18.4 30.:! 8.5 17.1 2.5 2.7 x.9 15.7 2.5 10.3 15.6 44.5 100.1 6.9 8.(l 6.9 5.2 7.2 7.0 8.9 6.5 11.1 22.4 19.5 33.7 11.1 17.3 10.3 6.8 6.3 10.4 6.4
44 24 61 35 32 55 25 61 32 32 31 29 55 21 29 35 44 32 22 36 26 51 27 29 29 51 32 32 49 24 55 27 32 27 25 34 25 32 23 42 26 23 39 28 43 38 25 23 39 24
2p_ eI ls3p ‘P, 2p3d “D, 2p.. EI: 2p+ E/ ki
2p+ E/’ ?p+ e/ 7p3d ’ Pz 7p_ EC‘ 2p+ E/‘ 2p+ t/‘
2srt 2p_ E/ ?p+ l/’ 2p_ EL’ 2p+ EL’ 2seL’ 2p+ e/’ 2p_e/’ 2p+ l!’ 2se/ 2p_ E/ zp, l/ ‘p_ E/ 2P+ l(
3s3p ‘Pi,
3p3d ‘P,, 3s3p IP,
3p3d ‘P, 3s3p ‘P,
3p3d
’ P,
3p3d ‘D, 3s3p IP,
k/’
2p+ ek‘ ls3s ?, 2p+ ce’ ls3d .‘D, 2se/’ 2p+et ls3s ?s, zp, EL‘ 2sec 2p_ G/’ 2p+ El’ Ip_c/ 2p+ E/’ 2p_ EL’ ls3d “D, 2ser 2p+ EL’ ls3s !S,
exare
Table 1 (continued) Initial State
Final state
Transition energies
3p3d ’ Pz 3p3d ’ Fz
2p-e/
ls3d ‘Dz
8221.5
4.5
.il
3p3d ‘D? 3p3d ’ Dz 3p3d ‘F3
2p+ E! ls3d ’ D, 2p3p ‘D, ls3d “D,
307.8 8220.1 1283.3 8221.6
13.2 4.5 3.3 3.4
47 34 25 26
3p3d ‘D,
2~~6
327.6
_
2p+ EY
3p3d ’ F3 3p3d ’ FJ
2pc/ zp, E/ 2s3d ’ D, ls3d ‘D,
Transition rates 6.2
Branching ration X 100 29
329.0
7.6
1:
308.3
14.3
42
341.0 320.3 1280.5 8223.9
23.0 55.8 2.5 7.6
71 52 21 64
transitions, the weakest are the 3/3/’ + Iset’ channels and the strongest are the 3/3/“’ -+ 2p~/ channels. The transition rates and energies have been found to be greatly affected by configuration mixing. A few relatively strong lines arise from electric-dipole-forbidden transitions such as 3s’ -+ ls3p. The relative widths of the states from the present calculation agree with the general systematics of autoionization widths of doubly excited states as predicted by Chen and Lin [s].
Acknowledgement This work was supported Corporation.
by a grant from Research
References [I] Y.K. Ho, Phys. Rev. A 35 (1987) 2035: 27 (1983) 1887: J. Phys. B 12 (1979) 387. [2] L. Lipsky and A.R. Conneely, Atom. Dat. Nucl. Data Tables 20 (1977) 127. [3] H. Bachau, .I. Phys. B 17 (1984) 1771. [4] C.D. Lin and S. Watanabe, Phys. Rev. A 35 (1987) 4499. [S] K.R. Karim and C.P. Bhalla, Phys. Scripta 38 (1988) 795. [6] K.R. Karim and C.P. Bhalla. .I. Ouant. Spectrosc. Radiat. Transfer 36 ( 1986) SOS. [7] K.R. Karim, Phys. Scripta 49 (1994) 565. [81 Z. Chen and C.D. Lin. Phys. Rev. A 40 (1989) 6717.
I. ATOMIC/MOLECULAR
PHYSICS
& *H
Nuclear Instruments
and Methods in Physics Research B 99 (1995) 66-67
KIONIB
Beam Interactions with Materials 6 Atoms
ELSEVIER
X-ray and Auger transition rates and energies of 3/3/’ states of two-electron ions K.R. Karim * Physics Department,
Illinois State Uniuersiry, Normal, Illinois 61790-4560, USA
Abstract X-ray and Auger transition rates and transition energies are calculated for helium-like iron ions in the 3/3/ configurations. This work is an extension of our previous studies on the atomic parameters of doubly-excited two-electron atoms. The calculations have been performed using the Hartree-Fock-Slater atomic model. The effects of configuration interaction, spin-orbit coupling, and relativity have been included in the calculation. The autoionizing channel 3/3/’ + 2pc/ is seen to be the most favored mode of deexcitation.
1. Introduction The structure and spectra of doubly-excited heliumlike ions in 3/3/l configurations have been reported by Ho [l], Lipsky and Conneely [2], Bachau [3], and Lin [4] for Z I 10 and by Karim and Bhalla [5-71 for Z = 10, 14, 18, 20, and 22. These systems are interesting from both theoretical and applied points of view. The doubly-excited heliumlike ions are produced in ion-atom collision experiments, and in high-tempertaure laboratory and astrophysical plasmas. Since an exact solution of the dynamics of systems with three or more interacting particles has not yet been found, these simplest 3-body systems are of great interest to many-body theorists. The study of the structure and decay of such systems provide delicate tests of existing theories. In the present paper we list all the prominent decay channels of 3/3/” configurations of heliumlike iron ions with the corresponding transition energies, transition rates. and branching ratios.
2. Theory The transition dent perturbation given by
rates were calculated from time-depentheory. The Auger transition rates are
* Tel. + 1 309 438 507, [email protected]. 0168-583X/95/$09.50
fax
+ 1 309
438
5413,
where +i and I+?, are, respectively, the antisymmetrized many-electron wave functions of the initial and final states, p(Ef) is the density of the final states, and V,, = l/rij is two-electron interaction operator. The X-ray transition rates are given as
where w is the angular frequency of the radiated photon, yJ and y’J’ represent, respectively, the initial and final states of the system, D is the electric dipole operator, and (y’J’ I] D I]rJ> is the reduced matrix element. The expressions of relevant reduced matrix elements are given in our earlier paper [S].
3. Results and discussion In Table 1 we list Auger and X-ray transition rates, transition energies, fluorescence yields and nonradiative branching ratios for all possible states of 3/3/’ configurations of heliumlike iron. The states are grouped according to parity and are listed in increasing order of the total angular momentum quantum number. The decay channels with probabilities of less than 20% are not included in the table. A complete listing can be obtained from the author on request. We note that radiative channels are generally much weaker in comparison with the nonradiative channels. The dominant X-ray channels include the transitions 3p3d 3F4 + ls3d 3D3, 3d2 3P,, --) 2p3d ‘D,, 3d* ‘Se+ ls3p ‘P,, 3p3d ‘PO + ls3d 3D,, 3p3d ‘D, -+ ls3d ‘Da, and 3p3d 3F, -+ ls3d 3D2 with fluorescence yields of 0.64, 0.61, 0.35, 0.34, 0.34, and 0.31, respectively. For nonradiative
0 1995 Elsevier Science B.V. All rights reserved
SSDI 0168-583X(94)00554-0
K.R. Karim / Nucl. instr. and Meth. in Phys. Res. B 99 (1995166-67 Table 1 Auger and X-ray transition rates (in units of 10’” /s), transition energies (in eV), radiative branching ratios (fluorescence yields), and nonradiative branching ratios (Auger yields) for doubly cited He-like iron. In column 2 the states 2~,,~ and Zp,,, written. respectively, as 2p_ and 2p+ Initial State
y I s,,
3s-
3p? is,, 3d’ ‘S,, 3p: ‘P(, 3d’ ‘P,, 3pz 3P, 3s3d ‘D, 3pz 3P, 3d2 3Pz 3~’ ’ D, 3d’ ’ D, 3s3d ’ bZ
3d’ ‘F1 3s3d ‘D, 3d’ ‘F3 3s3d ‘D, 3d”F, 3d2 ‘G,
Final state
Transition energies
Transition rates
Branching ration X 100
?SE/ 2p_ EJ’ 2p+ EL’ ls3p ‘P, 2p3d ’ P,
300.3 300.1 307.6 8269.3 1285.8 310.7 8221.9 1268.5 312.8 292.1 318.2 297.3 296.2 1275.7 310.2 289.5 327.3 328.2 328.0 307.3 331.7 311.0 319.4 298.5 332.7 312.0 320. I 334.1 313.4 341.2 320.5 301 .o 300.x 8220.5 309.9 8232.9 302. I 281.2 8221.6 3 10.0 315.5 315.2 294.5 _35’ _A.0 331.3 325.0 8227.3 305.9 285.0 8225.3
13.4 7.3 79.0 4.3 4.0 26.1 11.‘7 5.0 15.0 15.0 2.5 2.3 25.:! 2.0 15.2 18.5 17.9 26.7 18.4 30.:! 8.5 17.1 2.5 2.7 x.9 15.7 2.5 10.3 15.6 44.5 100.1 6.9 8.(l 6.9 5.2 7.2 7.0 8.9 6.5 11.1 22.4 19.5 33.7 11.1 17.3 10.3 6.8 6.3 10.4 6.4
44 24 61 35 32 55 25 61 32 32 31 29 55 21 29 35 44 32 22 36 26 51 27 29 29 51 32 32 49 24 55 27 32 27 25 34 25 32 23 42 26 23 39 28 43 38 25 23 39 24
2p_ eI ls3p ‘P, 2p3d “D, 2p.. EI: 2p+ E/ ki
2p+ E/’ ?p+ e/ 7p3d ’ Pz 7p_ EC‘ 2p+ E/‘ 2p+ t/‘
2srt 2p_ E/ ?p+ l/’ 2p_ EL’ 2p+ EL’ 2seL’ 2p+ e/’ 2p_e/’ 2p+ l!’ 2se/ 2p_ E/ zp, l/ ‘p_ E/ 2P+ l(
3s3p ‘Pi,
3p3d ‘P,, 3s3p IP,
3p3d ‘P, 3s3p ‘P,
3p3d
’ P,
3p3d ‘D, 3s3p IP,
k/’
2p+ ek‘ ls3s ?, 2p+ ce’ ls3d .‘D, 2se/’ 2p+et ls3s ?s, zp, EL‘ 2sec 2p_ G/’ 2p+ El’ Ip_c/ 2p+ E/’ 2p_ EL’ ls3d “D, 2ser 2p+ EL’ ls3s !S,
exare
Table 1 (continued) Initial State
Final state
Transition energies
3p3d ’ Pz 3p3d ’ Fz
2p-e/
ls3d ‘Dz
8221.5
4.5
.il
3p3d ‘D? 3p3d ’ Dz 3p3d ‘F3
2p+ E! ls3d ’ D, 2p3p ‘D, ls3d “D,
307.8 8220.1 1283.3 8221.6
13.2 4.5 3.3 3.4
47 34 25 26
3p3d ‘D,
2~~6
327.6
_
2p+ EY
3p3d ’ F3 3p3d ’ FJ
2pc/ zp, E/ 2s3d ’ D, ls3d ‘D,
Transition rates 6.2
Branching ration X 100 29
329.0
7.6
1:
308.3
14.3
42
341.0 320.3 1280.5 8223.9
23.0 55.8 2.5 7.6
71 52 21 64
transitions, the weakest are the 3/3/’ + Iset’ channels and the strongest are the 3/3/“’ -+ 2p~/ channels. The transition rates and energies have been found to be greatly affected by configuration mixing. A few relatively strong lines arise from electric-dipole-forbidden transitions such as 3s’ -+ ls3p. The relative widths of the states from the present calculation agree with the general systematics of autoionization widths of doubly excited states as predicted by Chen and Lin [s].
Acknowledgement This work was supported Corporation.
by a grant from Research
References [I] Y.K. Ho, Phys. Rev. A 35 (1987) 2035: 27 (1983) 1887: J. Phys. B 12 (1979) 387. [2] L. Lipsky and A.R. Conneely, Atom. Dat. Nucl. Data Tables 20 (1977) 127. [3] H. Bachau, .I. Phys. B 17 (1984) 1771. [4] C.D. Lin and S. Watanabe, Phys. Rev. A 35 (1987) 4499. [S] K.R. Karim and C.P. Bhalla, Phys. Scripta 38 (1988) 795. [6] K.R. Karim and C.P. Bhalla. .I. Ouant. Spectrosc. Radiat. Transfer 36 ( 1986) SOS. [7] K.R. Karim, Phys. Scripta 49 (1994) 565. [81 Z. Chen and C.D. Lin. Phys. Rev. A 40 (1989) 6717.
I. ATOMIC/MOLECULAR
PHYSICS