Abstract

The fine-structure splitting between the 3p63d2DJ, J = 3/2 and J = 5/2 levels of K-like ions, Ti3+ to U73+, are calculated by means of Dirac–Fock single-configuration and multiconfiguration wave functions. The multi-configuration calculation includes jj configurations arising from some selected nonrelativistic configurations in the M-shell Coulomb complex; these include all the Dirac–Fock configurations with the principal quantum number n = 3, which are degenerate in the pure jj coupling limit for infinite nuclear charge Z, along with other configurations such that the calculated energy is correct to order Z2 and Z asymptotically. The difference between known experimental and calculated multiconfiguration Dirac–Fock fine-structure splittings is almost independent of Z, thus allowing us to predict unknown values reliably. From this plot and a comparison of theoretical and experimental results we conclude that the observed fine-structure splitting of Ag28+ [ J. Opt. Soc. Am. B 2, 1661 ( 1985)] is too small. We present splittings in high-Z K-like ions for which experimental values are unknown.

© 1992 Optical Society of America

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    [CrossRef]
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  40. J. Sugar, V. Kaufman, W. L. Rowan, J. Opt. Soc. Am. B 8, 913 (1991).
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    [CrossRef]

1991

Y.-K. Kim, D. H. Baik, P. Indelicato, J. P. Desclaux, Phys. Rev. A 44, 148 (1991).
[CrossRef] [PubMed]

J. Sugar, V. Kaufman, W. L. Rowan, J. Opt. Soc. Am. B 8, 913 (1991).
[CrossRef]

1990

1989

V. Kaufman, J. Sugar, W. L. Rowan, J. Opt. Soc. B 6, 142 (1989).
[CrossRef]

V. Kaufman, J. Sugar, W. L. Rowan, J. Opt. Soc. Am. B 6, 1444 (1989).
[CrossRef]

1988

Y.-K. Kim, W. C. Martin, A. W. Weiss, J. Opt. Soc. Am. B 5, 2215 (1988).
[CrossRef]

Y.-K. Kim, J. Sugar, V. Kaufman, M. A. Ali, J. Opt. Soc. Am. B 5, 2225 (1988).
[CrossRef]

M. A. Ali, Y.-K. Kim, Phys. Rev. A 38, 3992 (1988); Bull. Am. Phys. Soc. 35, 1191 (1990).
[CrossRef] [PubMed]

T. Brage, C. Froese-Fischer, J. Phys. B 21, 2563 (1988).
[CrossRef]

E. B. Saloman, Y.-K. Kim, Phys. Rev. A 38, 577 (1988).
[CrossRef] [PubMed]

1986

K.-N. Huang, At. Data Nucl. Data Tables 34, 1 (1986).
[CrossRef]

C. Froese-Fischer, M. Godefroid, J. Phys. B 19, 137 (1986).
[CrossRef]

B. P. Das, I. P. Grant, J. Phys. B 19, L7 (1986).
[CrossRef]

1985

C. Froese-Fischer, H. P. Saha, Phys. Scr. 32, 181 (1985).
[CrossRef]

K.-N. Huang, At. Data Nucl. Data Tables 32, 503 (1985).
[CrossRef]

B. Denne, E. Hinnov, S. Cohen, J. Timberlake, J. Opt. Soc. Am. B 2, 1661 (1985).
[CrossRef]

1984

K.-N. Huang, At. Data Nucl. Data Tables 30, 313 (1984).
[CrossRef]

M. Godefroid, C. Froese-Fischer, J. Phys. B 17, 681 (1984).
[CrossRef]

1983

J. Hata, I. P. Grant, B. P. Das, J. Phys. B 16, L189 (1983); J. Hata, I. P. Grant, J. Phys. B 16, 915 (1983); B. P. Das, J. Hata, I. P. Grant, J. Phys. B 17, L1 (1984).
[CrossRef]

C. Froese-Fischer, H. P. Saha, Phys. Rev. A 28, 3169 (1983).
[CrossRef]

K.-N. Huang, Y.-K. Kim, K. T. Cheng, J. P. Desclaux, At. Data Nucl. Data Tables 28, 355 (1983).
[CrossRef]

1982

S. Suckewer, E. Hinnov, S. Cohen, M. Finkenthal, K. Sato, Phys. Rev. A 26, 1161 (1982).
[CrossRef]

C. Froese-Fischer, J. Phys. B 16, 157 (1982).
[CrossRef]

K.-N. Huang, Y.-K. Kim, K. T. Cheng, J. P. Desclaux, Phys. Rev. Lett. 48, 1245 (1982).
[CrossRef]

Y.-K. Kim, K.-N. Huang, Phys. Rev. A 26, 1984 (1982).
[CrossRef]

1980

C. P. Wood, N. C. Pyper, Mol. Phys. 41, 149 (1980); N. C. Pyper, J. Phys. B 16, L211 (1983).
[CrossRef]

I. P. Grant, B. J. McKenzie, P. H. Norrington, D. F. Mayers, N. C. Pyper, Comput. Phys. Commun. 21, 207 (1980).
[CrossRef]

B. J. McKenzie, I. P. Grant, P. H. Norrington, Comput. Phys. Commun. 21, 233 (1980).
[CrossRef]

A. A. Ramonas, A. N. Ryabtsev, Opt. Spectros. (USSR) 48, 348 (1980).

S. Suckewer, R. Fonck, E. Hinnov, Phys. Rev. A 21, 924 (1980).
[CrossRef]

1979

K. T. Cheng, Y.-K. Kim, J. P. Desclaux, At. Data Nucl. Data Tables 24, 111 (1979).
[CrossRef]

S. Suckewer, E. Hinnov, Phys. Rev. A 20, 578 (1979).
[CrossRef]

1978

S. Suckewer, E. Hinnov, Phys. Rev. Lett. 41, 756 (1978).
[CrossRef]

1977

1975

J. P. Desclaux, Comput. Phys. Commun. 9, 31 (1975).
[CrossRef]

1974

J. Swensson, B. Edlén, Phys. Scr. 9, 335 (1974).
[CrossRef]

1973

J. O. Ekberg, Phys. Scr. 8, 35 (1973).
[CrossRef]

1969

H. T. Doyle, Adv. At. Mol. Phys. 5, 337 (1969).
[CrossRef]

1962

D. Layzer, J. Bahcall, Ann. Phys. 17, 177 (1962).
[CrossRef]

1959

D. Layzer, Ann. Phys. 8, 271 (1959).
[CrossRef]

Ali, M. A.

M. A. Ali, Y.-K. Kim, Phys. Rev. A 38, 3992 (1988); Bull. Am. Phys. Soc. 35, 1191 (1990).
[CrossRef] [PubMed]

Y.-K. Kim, J. Sugar, V. Kaufman, M. A. Ali, J. Opt. Soc. Am. B 5, 2225 (1988).
[CrossRef]

Bahcall, J.

D. Layzer, J. Bahcall, Ann. Phys. 17, 177 (1962).
[CrossRef]

Baik, D. H.

Y.-K. Kim, D. H. Baik, P. Indelicato, J. P. Desclaux, Phys. Rev. A 44, 148 (1991).
[CrossRef] [PubMed]

Brage, T.

T. Brage, C. Froese-Fischer, J. Phys. B 21, 2563 (1988).
[CrossRef]

Brown, C. M.

Cheng, K. T.

K.-N. Huang, Y.-K. Kim, K. T. Cheng, J. P. Desclaux, At. Data Nucl. Data Tables 28, 355 (1983).
[CrossRef]

K.-N. Huang, Y.-K. Kim, K. T. Cheng, J. P. Desclaux, Phys. Rev. Lett. 48, 1245 (1982).
[CrossRef]

K. T. Cheng, Y.-K. Kim, J. P. Desclaux, At. Data Nucl. Data Tables 24, 111 (1979).
[CrossRef]

Cohen, S.

B. Denne, E. Hinnov, S. Cohen, J. Timberlake, J. Opt. Soc. Am. B 2, 1661 (1985).
[CrossRef]

S. Suckewer, E. Hinnov, S. Cohen, M. Finkenthal, K. Sato, Phys. Rev. A 26, 1161 (1982).
[CrossRef]

Cowan, R. D.

R. D. Cowan, The Theory of Atomic Structure and Spectra (U. California Press, Berkeley, 1981).

Das, B. P.

B. P. Das, I. P. Grant, J. Phys. B 19, L7 (1986).
[CrossRef]

J. Hata, I. P. Grant, B. P. Das, J. Phys. B 16, L189 (1983); J. Hata, I. P. Grant, J. Phys. B 16, 915 (1983); B. P. Das, J. Hata, I. P. Grant, J. Phys. B 17, L1 (1984).
[CrossRef]

Denne, B.

Desclaux, J. P.

Y.-K. Kim, D. H. Baik, P. Indelicato, J. P. Desclaux, Phys. Rev. A 44, 148 (1991).
[CrossRef] [PubMed]

K.-N. Huang, Y.-K. Kim, K. T. Cheng, J. P. Desclaux, At. Data Nucl. Data Tables 28, 355 (1983).
[CrossRef]

K.-N. Huang, Y.-K. Kim, K. T. Cheng, J. P. Desclaux, Phys. Rev. Lett. 48, 1245 (1982).
[CrossRef]

K. T. Cheng, Y.-K. Kim, J. P. Desclaux, At. Data Nucl. Data Tables 24, 111 (1979).
[CrossRef]

J. P. Desclaux, Comput. Phys. Commun. 9, 31 (1975).
[CrossRef]

Doyle, H. T.

H. T. Doyle, Adv. At. Mol. Phys. 5, 337 (1969).
[CrossRef]

Edlén, B.

J. Swensson, B. Edlén, Phys. Scr. 9, 335 (1974).
[CrossRef]

Ekberg, J. O.

Feldman, U.

Finkenthal, M.

S. Suckewer, E. Hinnov, S. Cohen, M. Finkenthal, K. Sato, Phys. Rev. A 26, 1161 (1982).
[CrossRef]

Fonck, R.

S. Suckewer, R. Fonck, E. Hinnov, Phys. Rev. A 21, 924 (1980).
[CrossRef]

Froese-Fischer, C.

T. Brage, C. Froese-Fischer, J. Phys. B 21, 2563 (1988).
[CrossRef]

C. Froese-Fischer, M. Godefroid, J. Phys. B 19, 137 (1986).
[CrossRef]

C. Froese-Fischer, H. P. Saha, Phys. Scr. 32, 181 (1985).
[CrossRef]

M. Godefroid, C. Froese-Fischer, J. Phys. B 17, 681 (1984).
[CrossRef]

C. Froese-Fischer, H. P. Saha, Phys. Rev. A 28, 3169 (1983).
[CrossRef]

C. Froese-Fischer, J. Phys. B 16, 157 (1982).
[CrossRef]

Godefroid, M.

C. Froese-Fischer, M. Godefroid, J. Phys. B 19, 137 (1986).
[CrossRef]

M. Godefroid, C. Froese-Fischer, J. Phys. B 17, 681 (1984).
[CrossRef]

Grant, I. P.

B. P. Das, I. P. Grant, J. Phys. B 19, L7 (1986).
[CrossRef]

J. Hata, I. P. Grant, B. P. Das, J. Phys. B 16, L189 (1983); J. Hata, I. P. Grant, J. Phys. B 16, 915 (1983); B. P. Das, J. Hata, I. P. Grant, J. Phys. B 17, L1 (1984).
[CrossRef]

I. P. Grant, B. J. McKenzie, P. H. Norrington, D. F. Mayers, N. C. Pyper, Comput. Phys. Commun. 21, 207 (1980).
[CrossRef]

B. J. McKenzie, I. P. Grant, P. H. Norrington, Comput. Phys. Commun. 21, 233 (1980).
[CrossRef]

Hata, J.

J. Hata, I. P. Grant, B. P. Das, J. Phys. B 16, L189 (1983); J. Hata, I. P. Grant, J. Phys. B 16, 915 (1983); B. P. Das, J. Hata, I. P. Grant, J. Phys. B 17, L1 (1984).
[CrossRef]

Hinnov, E.

B. Denne, E. Hinnov, S. Cohen, J. Timberlake, J. Opt. Soc. Am. B 2, 1661 (1985).
[CrossRef]

S. Suckewer, E. Hinnov, S. Cohen, M. Finkenthal, K. Sato, Phys. Rev. A 26, 1161 (1982).
[CrossRef]

S. Suckewer, R. Fonck, E. Hinnov, Phys. Rev. A 21, 924 (1980).
[CrossRef]

S. Suckewer, E. Hinnov, Phys. Rev. A 20, 578 (1979).
[CrossRef]

S. Suckewer, E. Hinnov, Phys. Rev. Lett. 41, 756 (1978).
[CrossRef]

Huang, K.-N.

K.-N. Huang, At. Data Nucl. Data Tables 34, 1 (1986).
[CrossRef]

K.-N. Huang, At. Data Nucl. Data Tables 32, 503 (1985).
[CrossRef]

K.-N. Huang, At. Data Nucl. Data Tables 30, 313 (1984).
[CrossRef]

K.-N. Huang, Y.-K. Kim, K. T. Cheng, J. P. Desclaux, At. Data Nucl. Data Tables 28, 355 (1983).
[CrossRef]

Y.-K. Kim, K.-N. Huang, Phys. Rev. A 26, 1984 (1982).
[CrossRef]

K.-N. Huang, Y.-K. Kim, K. T. Cheng, J. P. Desclaux, Phys. Rev. Lett. 48, 1245 (1982).
[CrossRef]

Indelicato, P.

Y.-K. Kim, D. H. Baik, P. Indelicato, J. P. Desclaux, Phys. Rev. A 44, 148 (1991).
[CrossRef] [PubMed]

Kaufman, V.

Kim, Y.-K.

Y.-K. Kim, D. H. Baik, P. Indelicato, J. P. Desclaux, Phys. Rev. A 44, 148 (1991).
[CrossRef] [PubMed]

Y.-K. Kim, A. W. Weiss, Bull. Am. Phys. Soc. 35, 1188 (1990).

M. A. Ali, Y.-K. Kim, Phys. Rev. A 38, 3992 (1988); Bull. Am. Phys. Soc. 35, 1191 (1990).
[CrossRef] [PubMed]

Y.-K. Kim, J. Sugar, V. Kaufman, M. A. Ali, J. Opt. Soc. Am. B 5, 2225 (1988).
[CrossRef]

Y.-K. Kim, W. C. Martin, A. W. Weiss, J. Opt. Soc. Am. B 5, 2215 (1988).
[CrossRef]

E. B. Saloman, Y.-K. Kim, Phys. Rev. A 38, 577 (1988).
[CrossRef] [PubMed]

K.-N. Huang, Y.-K. Kim, K. T. Cheng, J. P. Desclaux, At. Data Nucl. Data Tables 28, 355 (1983).
[CrossRef]

K.-N. Huang, Y.-K. Kim, K. T. Cheng, J. P. Desclaux, Phys. Rev. Lett. 48, 1245 (1982).
[CrossRef]

Y.-K. Kim, K.-N. Huang, Phys. Rev. A 26, 1984 (1982).
[CrossRef]

K. T. Cheng, Y.-K. Kim, J. P. Desclaux, At. Data Nucl. Data Tables 24, 111 (1979).
[CrossRef]

Layzer, D.

D. Layzer, J. Bahcall, Ann. Phys. 17, 177 (1962).
[CrossRef]

D. Layzer, Ann. Phys. 8, 271 (1959).
[CrossRef]

Martin, W. C.

Mayers, D. F.

I. P. Grant, B. J. McKenzie, P. H. Norrington, D. F. Mayers, N. C. Pyper, Comput. Phys. Commun. 21, 207 (1980).
[CrossRef]

McKenzie, B. J.

I. P. Grant, B. J. McKenzie, P. H. Norrington, D. F. Mayers, N. C. Pyper, Comput. Phys. Commun. 21, 207 (1980).
[CrossRef]

B. J. McKenzie, I. P. Grant, P. H. Norrington, Comput. Phys. Commun. 21, 233 (1980).
[CrossRef]

Norrington, P. H.

B. J. McKenzie, I. P. Grant, P. H. Norrington, Comput. Phys. Commun. 21, 233 (1980).
[CrossRef]

I. P. Grant, B. J. McKenzie, P. H. Norrington, D. F. Mayers, N. C. Pyper, Comput. Phys. Commun. 21, 207 (1980).
[CrossRef]

Pyper, N. C.

I. P. Grant, B. J. McKenzie, P. H. Norrington, D. F. Mayers, N. C. Pyper, Comput. Phys. Commun. 21, 207 (1980).
[CrossRef]

C. P. Wood, N. C. Pyper, Mol. Phys. 41, 149 (1980); N. C. Pyper, J. Phys. B 16, L211 (1983).
[CrossRef]

Ramonas, A. A.

A. A. Ramonas, A. N. Ryabtsev, Opt. Spectros. (USSR) 48, 348 (1980).

Reader, J.

Rowan, W. L.

Ryabtsev, A. N.

A. A. Ramonas, A. N. Ryabtsev, Opt. Spectros. (USSR) 48, 348 (1980).

Saha, H. P.

C. Froese-Fischer, H. P. Saha, Phys. Scr. 32, 181 (1985).
[CrossRef]

C. Froese-Fischer, H. P. Saha, Phys. Rev. A 28, 3169 (1983).
[CrossRef]

Saloman, E. B.

E. B. Saloman, Y.-K. Kim, Phys. Rev. A 38, 577 (1988).
[CrossRef] [PubMed]

Sato, K.

S. Suckewer, E. Hinnov, S. Cohen, M. Finkenthal, K. Sato, Phys. Rev. A 26, 1161 (1982).
[CrossRef]

Seely, J. F.

Suckewer, S.

S. Suckewer, E. Hinnov, S. Cohen, M. Finkenthal, K. Sato, Phys. Rev. A 26, 1161 (1982).
[CrossRef]

S. Suckewer, R. Fonck, E. Hinnov, Phys. Rev. A 21, 924 (1980).
[CrossRef]

S. Suckewer, E. Hinnov, Phys. Rev. A 20, 578 (1979).
[CrossRef]

S. Suckewer, E. Hinnov, Phys. Rev. Lett. 41, 756 (1978).
[CrossRef]

Sugar, J.

Swensson, J.

J. Swensson, B. Edlén, Phys. Scr. 9, 335 (1974).
[CrossRef]

Timberlake, J.

Van Deurzen, C. H. H.

Weiss, A. W.

Y.-K. Kim, A. W. Weiss, Bull. Am. Phys. Soc. 35, 1188 (1990).

Y.-K. Kim, W. C. Martin, A. W. Weiss, J. Opt. Soc. Am. B 5, 2215 (1988).
[CrossRef]

Wood, C. P.

C. P. Wood, N. C. Pyper, Mol. Phys. 41, 149 (1980); N. C. Pyper, J. Phys. B 16, L211 (1983).
[CrossRef]

Adv. At. Mol. Phys.

H. T. Doyle, Adv. At. Mol. Phys. 5, 337 (1969).
[CrossRef]

Ann. Phys.

D. Layzer, Ann. Phys. 8, 271 (1959).
[CrossRef]

D. Layzer, J. Bahcall, Ann. Phys. 17, 177 (1962).
[CrossRef]

At. Data Nucl. Data Tables

K. T. Cheng, Y.-K. Kim, J. P. Desclaux, At. Data Nucl. Data Tables 24, 111 (1979).
[CrossRef]

K.-N. Huang, At. Data Nucl. Data Tables 34, 1 (1986).
[CrossRef]

K.-N. Huang, Y.-K. Kim, K. T. Cheng, J. P. Desclaux, At. Data Nucl. Data Tables 28, 355 (1983).
[CrossRef]

K.-N. Huang, At. Data Nucl. Data Tables 30, 313 (1984).
[CrossRef]

K.-N. Huang, At. Data Nucl. Data Tables 32, 503 (1985).
[CrossRef]

Bull. Am. Phys. Soc.

Y.-K. Kim, A. W. Weiss, Bull. Am. Phys. Soc. 35, 1188 (1990).

Comput. Phys. Commun.

J. P. Desclaux, Comput. Phys. Commun. 9, 31 (1975).
[CrossRef]

I. P. Grant, B. J. McKenzie, P. H. Norrington, D. F. Mayers, N. C. Pyper, Comput. Phys. Commun. 21, 207 (1980).
[CrossRef]

B. J. McKenzie, I. P. Grant, P. H. Norrington, Comput. Phys. Commun. 21, 233 (1980).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. B

J. Opt. Soc. B

V. Kaufman, J. Sugar, W. L. Rowan, J. Opt. Soc. B 6, 142 (1989).
[CrossRef]

J. Phys. B

C. Froese-Fischer, J. Phys. B 16, 157 (1982).
[CrossRef]

J. Hata, I. P. Grant, B. P. Das, J. Phys. B 16, L189 (1983); J. Hata, I. P. Grant, J. Phys. B 16, 915 (1983); B. P. Das, J. Hata, I. P. Grant, J. Phys. B 17, L1 (1984).
[CrossRef]

B. P. Das, I. P. Grant, J. Phys. B 19, L7 (1986).
[CrossRef]

M. Godefroid, C. Froese-Fischer, J. Phys. B 17, 681 (1984).
[CrossRef]

C. Froese-Fischer, M. Godefroid, J. Phys. B 19, 137 (1986).
[CrossRef]

T. Brage, C. Froese-Fischer, J. Phys. B 21, 2563 (1988).
[CrossRef]

Mol. Phys.

C. P. Wood, N. C. Pyper, Mol. Phys. 41, 149 (1980); N. C. Pyper, J. Phys. B 16, L211 (1983).
[CrossRef]

Opt. Spectros. (USSR)

A. A. Ramonas, A. N. Ryabtsev, Opt. Spectros. (USSR) 48, 348 (1980).

Phys. Rev. A

S. Suckewer, E. Hinnov, S. Cohen, M. Finkenthal, K. Sato, Phys. Rev. A 26, 1161 (1982).
[CrossRef]

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Figures (1)

Fig. 1
Fig. 1

Comparison of theory and experiment. The difference between theoretical and experimental fine-structure splitting in the ground state, 3d2D, of K-like ions is plotted as a function of the nuclear charge Z. The filled circles represent the difference between experiment and single-configuration Dirac–Fock (SCDF) calculations. The filled squares stand for the difference between experiment and MCDF calculations. The filled triangles are the difference between the values recommended by Sugar et al.40 and our MC calculation. The dashed curve represents a least-squares fit to the difference between experiment and our MC values (excluding the experimental value42 for Ag28+). See Tables 2 and 3 for the sources of the experimental data.

Tables (4)

Tables Icon

Table 1 Configurations of Even Parity in the (3s3p3d)9 Complex

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Table 2 Fine-Structure Splittings (cm−1) in K-like Ions, Ti3+ through Mo23+

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Table 3 Fine-Structure Splittings (cm−1) in K-like Ions, Tc24+ through Xe35+

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Table 4 Theoretical Fine-Structure Splitting (cm−1) in Other K-like Ions, Cs36+ through U73+

Equations (3)

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E = E 2 Z 2 + E 1 Z + E 0 + E - 1 / Z + E - 2 / Z 2 + ,
E = Z 2 n m E n m Z - n m ,
Δ E = 0.1526 Z + 20.3327 ( cm - 1 ) ,

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