Multiconfiguration Hartree-Fock study of the interaction between sp6 and s2p4d in the CI i, Br i, and I i isoelectronic sequences with particular emphasis on the neutral halogens
Jørgen E. Hansen, "Multiconfiguration Hartree-Fock study of the interaction between sp6 and s2p4d in the CI i, Br i, and I i isoelectronic sequences with particular emphasis on the neutral halogens," J. Opt. Soc. Am. 67, 754-760 (1977)
Multiconfiguration Hartree-Fock calculations for the lowest 2S term belonging to the sp62S + s2p4d configurations are presented for the first members of the Cl i, Br i, and I i isoelectronic sequences. The wave functions are used to calculate gf values for the transitions to the ground term and to calculate the hyperfine structure of the 2S terms. For the halogens the 2S term is found to be a nearly 50% mixture of sp6 and s2p4d which agrees qualitatively with results obtained by Cowan, Radziemski, and Kaufman by a series perturbation calculation. It is argued that for the purpose of isoelectronic comparison it is valid to consider the lowest 2S terms as belonging to the same isoelectronic series even though the dominant eigenvector component in one sequence (Br i) changes along the series in the MCHF approximation.
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HF and MCHF results for Cl i, Ar ii, Br i, Kr ii, I i and Xe ii. The calculated and observed values are the distances between the centers-of-gravity of the ground term s2p52P and the indicated excited term. Values are in cm−1 . The MCHF calculations are for the lowest 2S term.
Radziemski, Jr. and Kaufman, Ref. 1.
Minnhagen, Refs. 10 and 11.
R. D. Cowan (private communication).
Tech, Ref. 2.
Minnhagen et al., Ref. 18.
Minnhagen, Ref. 5; and Luc-Koenig et al., Ref. 7.
Humphreys, Ref. 13.
TABLE II
Eigenvector compositions for the lowest 2S state in the Cl i, Br i, and I i isoelectronic sequences obtained in MCHF calculations including the nsnp6 and ns2np4nd configurations.
Cl i
Ar ii
K iii
Hydrogenic limit
3s3p62S
0. 7301
0. 7918
0. 8147
0. 8732
3s23p4(1D)3d2S
0. 6834
0. 6107
0. 5799
0. 4874
Br i
Kr ii
Rb iii
Hydrogenic limit
4s4p62S
0. 6709
0. 7813
0. 8184
0. 938
4s24p4(1D)4d2S
0. 7415
0. 6241
0. 5747
0. 345
I i
Xe ii
Cs iii
Hydrogenic limit
5s5p62S
0. 7123
0. 7815
0. 8127
0. 947
5s25p4(1D)5d2S
0. 7018
0. 6239
0. 5827
0. 321
TABLE III
Calculated gf values for ground term transitions from the lowest 2S state in Cl i, Ar ii, Br i, Kr ii, I i, and Xe ii. Relative intensities (visual estimates) for the observed transitions are also shown together with (in parentheses) the intensity of the strongest ground term transition from the lowest p4s configuration.
This quantity is defined in the text. It applies to both gf values in a particular spectrum.
Radziemski, Jr. and Kaufman, Ref. 1.
Minnhagen, Ref. 16.
Boyce, Ref. 17.
Tech, Ref. 2.
Minnhagen et al., Ref. 18.
Boyce, Ref. 19.
Minnhagen, Ref. 5.
Boyce, Ref. 20.
TABLE IV
A values (s−1) for the sp6→ s2p52P transitions in Ar ii and Kr ii calculated by MCHF and C i methods. For Ar ii the “observed” A values are given. These were calculated from the observed lifetime of the sp6 level assuming the LS intensity ratio.
Observed and calculated hyperfine splittings of the lowest 2S1/2 level in Cl i, Br i, and I i. In the calculated values only the hyperfine structure associated with the unpaired s electron is considered. The method of calculation is explained in the text. Values are in cm−1.
Values taken from Kopfermann, Ref. 25. The result of the relativistic correction is an increase in the nonrelativistic value.
Br i: Tech, Ref. 2; and I i: Luc-Koenig et al., Ref. 7.
The magnetic moment used in the theoretical estimate corresponds to the natural isotope mixture.
Tables (5)
TABLE I
HF and MCHF results for Cl i, Ar ii, Br i, Kr ii, I i and Xe ii. The calculated and observed values are the distances between the centers-of-gravity of the ground term s2p52P and the indicated excited term. Values are in cm−1 . The MCHF calculations are for the lowest 2S term.
Radziemski, Jr. and Kaufman, Ref. 1.
Minnhagen, Refs. 10 and 11.
R. D. Cowan (private communication).
Tech, Ref. 2.
Minnhagen et al., Ref. 18.
Minnhagen, Ref. 5; and Luc-Koenig et al., Ref. 7.
Humphreys, Ref. 13.
TABLE II
Eigenvector compositions for the lowest 2S state in the Cl i, Br i, and I i isoelectronic sequences obtained in MCHF calculations including the nsnp6 and ns2np4nd configurations.
Cl i
Ar ii
K iii
Hydrogenic limit
3s3p62S
0. 7301
0. 7918
0. 8147
0. 8732
3s23p4(1D)3d2S
0. 6834
0. 6107
0. 5799
0. 4874
Br i
Kr ii
Rb iii
Hydrogenic limit
4s4p62S
0. 6709
0. 7813
0. 8184
0. 938
4s24p4(1D)4d2S
0. 7415
0. 6241
0. 5747
0. 345
I i
Xe ii
Cs iii
Hydrogenic limit
5s5p62S
0. 7123
0. 7815
0. 8127
0. 947
5s25p4(1D)5d2S
0. 7018
0. 6239
0. 5827
0. 321
TABLE III
Calculated gf values for ground term transitions from the lowest 2S state in Cl i, Ar ii, Br i, Kr ii, I i, and Xe ii. Relative intensities (visual estimates) for the observed transitions are also shown together with (in parentheses) the intensity of the strongest ground term transition from the lowest p4s configuration.
This quantity is defined in the text. It applies to both gf values in a particular spectrum.
Radziemski, Jr. and Kaufman, Ref. 1.
Minnhagen, Ref. 16.
Boyce, Ref. 17.
Tech, Ref. 2.
Minnhagen et al., Ref. 18.
Boyce, Ref. 19.
Minnhagen, Ref. 5.
Boyce, Ref. 20.
TABLE IV
A values (s−1) for the sp6→ s2p52P transitions in Ar ii and Kr ii calculated by MCHF and C i methods. For Ar ii the “observed” A values are given. These were calculated from the observed lifetime of the sp6 level assuming the LS intensity ratio.
Observed and calculated hyperfine splittings of the lowest 2S1/2 level in Cl i, Br i, and I i. In the calculated values only the hyperfine structure associated with the unpaired s electron is considered. The method of calculation is explained in the text. Values are in cm−1.
Values taken from Kopfermann, Ref. 25. The result of the relativistic correction is an increase in the nonrelativistic value.
Br i: Tech, Ref. 2; and I i: Luc-Koenig et al., Ref. 7.
The magnetic moment used in the theoretical estimate corresponds to the natural isotope mixture.
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