Abstract

Relativistic and correlation effects cause several inversions of the triplet and singlet J = 1 levels in the 2s3p configuration of berylliumlike ions. We have studied these effects in the range of atomic number Z = 6–54 by using both relativistic and nonrelativistic multiconfiguration wave functions. Theoretical predictions of energies of these levels with respect to the 2s2 1S0 ground level are compared with experimental data, and we conclude that overall the predictions for the ions having Z ≥ 15 are probably more accurate than the available measurements. Calculated oscillator strengths for these resonance transitions are also reported. Near cadmium (Z = 48), we confirm still another inversion that is due to the complete dominance of relativistic effects, which was reported previously. The 2p3s (1/2,1/2)1 level, a doubly excited state, goes below the 2s3p (1/2,3/2)1 level, owing to relativistic hydrogenic ordering. This type of level crossing due to hydrogenic ordering is anticipated in other sequences as well, contrary to our usual experience in atomic spectroscopy.

© 1988 Optical Society of America

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References

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  1. D. G. Ellis, Phys. Rev. A 28, 1223 (1983).
    [CrossRef]
  2. V. A. Boiko, S. A. Pikuz, U. I. Safranova, A. Ya. Faenov, J. Phys. B 10, 1253 (1977).
    [CrossRef]
  3. D. H. Sampson, R. E. H. Clark, S. J. Goett, Phys. Rev. A 24, 2979 (1981);D. H. Sampson, S. J. Goett, R. E. H. Clark, At. Data Nucl. Data Tables 30, 125 (1984).
    [CrossRef]
  4. A. K. Bhatia, H. E. Mason, Astron. Astrophys. 103, 324 (1981).
  5. H. Odabasi, J. Opt. Soc. Am. 59, 583 (1969).
    [CrossRef]
  6. R. Glass, J. Phys. B 12, 1633 (1979).
    [CrossRef]
  7. A. Hibbert, J. Phys. B 12, L661 (1979).
    [CrossRef]
  8. A. W. Weiss, Adv. At. Mol. Phys. 9, 1 (1973).
    [CrossRef]
  9. O. Gorceix, P. Indelicato, J. P. Desclaux, J. Phys. B 20, 639 (1987).
    [CrossRef]
  10. J. P. Desclaux, Comput. Phys. Commun. 9, 31 (1975).
    [CrossRef]
  11. P. J. Mohr, Ann. Phys. (NY) 88, 26, 52 (1974);Phys. Rev. A 26, 2388 (1982);At. Data Nucl. Data Tables 29, 453 (1983).
    [CrossRef]
  12. E. A. Uehling, Phys. Rev. 48, 55 (1935).
    [CrossRef]
  13. G. Hose, U. Kaldor, Phys. Rev. A 30, 2932 (1984).
    [CrossRef]
  14. C. F. Bunge, Phys. Scr. 21, 328 (1980).
    [CrossRef]
  15. C. E. Moore, Selected Tables of Atomic Spectra, Natl. Stand. Ref. Data Ser. Natl. Bur. Stand. 3, Sec. 3 (C iii) (1970);Selected Tables of Atomic Spectra Sec. 4 (N iv) (1971);Selected Tables of Atomic Spectra Sec. 9 (O v) (1980).
  16. P. O. Lowdin, Phys. Rev. 97, 1509 (1955).
    [CrossRef]
  17. D. Layzer, Ann. Phys. (NY) 8, 271 (1959).
    [CrossRef]
  18. E. P. Ivanova, U. I. Safranova, J. Phys. B 8, 1591 (1975).
    [CrossRef]
  19. K. T. Cheng, C. Froese Fischer, Y.-K. Kim, J. Phys. B 15, 181 (1982).
    [CrossRef]
  20. W. C. Martin, R. Zalubas, J. Phys. Chem. Ref. Data 9, 1 (Mg ix) (1980);J. Phys. Chem. Ref. Data 8, 817 (Al x) (1979);J. Phys. Chem. Ref. Data 12, 323 (Si xi) (1983).
    [CrossRef]
  21. W. C. Martin, R. Zalubas, A. Musgrove, J. Phys. Chem. Ref. Data 14, 751 (1985).
    [CrossRef]
  22. B. C. Fawcett, R. W. Hayes, Phys. Scr. 8, 244 (1973).
    [CrossRef]
  23. B. C. Fawcett, At. Data Nucl. Data Tables 30, 1 (1984);At. Data Nucl. Data Tables 33, 479(E) (1985).
    [CrossRef]
  24. G. E. Bromage, R. D. Cowan, B. C. Fawcett, A. Ridgeley, J. Opt. Soc. Am. 68, 48 (1978).
    [CrossRef]
  25. V. A. Boiko, A. Y. Faenov, S. A. Pikuz, J. Quant. Spectrosc. Radiat. Transfer 19, 11 (1978).
    [CrossRef]
  26. B. C. Fawcett, A. Ridgeley, T. P. Hughes, Mon. Not. R. Astron. Soc. 188, 365 (1979).
  27. B. Edlén, in Handbuch der Physik, S. Flügge, ed. (Springer-Verlag, Berlin, 1964), Vol. 27, p. 165.
  28. J. Sucher, Phys. Rev. A 22, 348 (1980).
    [CrossRef]
  29. G. E. Brown, D. G. Ravenhall, Proc. R. Soc. London Ser. A 208, 552 (1951).
    [CrossRef]
  30. A. W. Weiss, in Beam Foil Spectroscopy, I. A. Sellin, D. L. Pegg, eds. (Plenum, New York, 1976), Vol. 1, p. 51.
    [CrossRef]
  31. E. Ya. Kononov, U. I. Safronova, Opt. Spectrosc. (USSR) 43, 1 (1977).

1987 (1)

O. Gorceix, P. Indelicato, J. P. Desclaux, J. Phys. B 20, 639 (1987).
[CrossRef]

1985 (1)

W. C. Martin, R. Zalubas, A. Musgrove, J. Phys. Chem. Ref. Data 14, 751 (1985).
[CrossRef]

1984 (2)

B. C. Fawcett, At. Data Nucl. Data Tables 30, 1 (1984);At. Data Nucl. Data Tables 33, 479(E) (1985).
[CrossRef]

G. Hose, U. Kaldor, Phys. Rev. A 30, 2932 (1984).
[CrossRef]

1983 (1)

D. G. Ellis, Phys. Rev. A 28, 1223 (1983).
[CrossRef]

1982 (1)

K. T. Cheng, C. Froese Fischer, Y.-K. Kim, J. Phys. B 15, 181 (1982).
[CrossRef]

1981 (2)

D. H. Sampson, R. E. H. Clark, S. J. Goett, Phys. Rev. A 24, 2979 (1981);D. H. Sampson, S. J. Goett, R. E. H. Clark, At. Data Nucl. Data Tables 30, 125 (1984).
[CrossRef]

A. K. Bhatia, H. E. Mason, Astron. Astrophys. 103, 324 (1981).

1980 (3)

C. F. Bunge, Phys. Scr. 21, 328 (1980).
[CrossRef]

W. C. Martin, R. Zalubas, J. Phys. Chem. Ref. Data 9, 1 (Mg ix) (1980);J. Phys. Chem. Ref. Data 8, 817 (Al x) (1979);J. Phys. Chem. Ref. Data 12, 323 (Si xi) (1983).
[CrossRef]

J. Sucher, Phys. Rev. A 22, 348 (1980).
[CrossRef]

1979 (3)

B. C. Fawcett, A. Ridgeley, T. P. Hughes, Mon. Not. R. Astron. Soc. 188, 365 (1979).

R. Glass, J. Phys. B 12, 1633 (1979).
[CrossRef]

A. Hibbert, J. Phys. B 12, L661 (1979).
[CrossRef]

1978 (2)

G. E. Bromage, R. D. Cowan, B. C. Fawcett, A. Ridgeley, J. Opt. Soc. Am. 68, 48 (1978).
[CrossRef]

V. A. Boiko, A. Y. Faenov, S. A. Pikuz, J. Quant. Spectrosc. Radiat. Transfer 19, 11 (1978).
[CrossRef]

1977 (2)

E. Ya. Kononov, U. I. Safronova, Opt. Spectrosc. (USSR) 43, 1 (1977).

V. A. Boiko, S. A. Pikuz, U. I. Safranova, A. Ya. Faenov, J. Phys. B 10, 1253 (1977).
[CrossRef]

1975 (2)

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

E. P. Ivanova, U. I. Safranova, J. Phys. B 8, 1591 (1975).
[CrossRef]

1974 (1)

P. J. Mohr, Ann. Phys. (NY) 88, 26, 52 (1974);Phys. Rev. A 26, 2388 (1982);At. Data Nucl. Data Tables 29, 453 (1983).
[CrossRef]

1973 (2)

A. W. Weiss, Adv. At. Mol. Phys. 9, 1 (1973).
[CrossRef]

B. C. Fawcett, R. W. Hayes, Phys. Scr. 8, 244 (1973).
[CrossRef]

1970 (1)

C. E. Moore, Selected Tables of Atomic Spectra, Natl. Stand. Ref. Data Ser. Natl. Bur. Stand. 3, Sec. 3 (C iii) (1970);Selected Tables of Atomic Spectra Sec. 4 (N iv) (1971);Selected Tables of Atomic Spectra Sec. 9 (O v) (1980).

1969 (1)

1959 (1)

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

1955 (1)

P. O. Lowdin, Phys. Rev. 97, 1509 (1955).
[CrossRef]

1951 (1)

G. E. Brown, D. G. Ravenhall, Proc. R. Soc. London Ser. A 208, 552 (1951).
[CrossRef]

1935 (1)

E. A. Uehling, Phys. Rev. 48, 55 (1935).
[CrossRef]

Bhatia, A. K.

A. K. Bhatia, H. E. Mason, Astron. Astrophys. 103, 324 (1981).

Boiko, V. A.

V. A. Boiko, A. Y. Faenov, S. A. Pikuz, J. Quant. Spectrosc. Radiat. Transfer 19, 11 (1978).
[CrossRef]

V. A. Boiko, S. A. Pikuz, U. I. Safranova, A. Ya. Faenov, J. Phys. B 10, 1253 (1977).
[CrossRef]

Bromage, G. E.

Brown, G. E.

G. E. Brown, D. G. Ravenhall, Proc. R. Soc. London Ser. A 208, 552 (1951).
[CrossRef]

Bunge, C. F.

C. F. Bunge, Phys. Scr. 21, 328 (1980).
[CrossRef]

Cheng, K. T.

K. T. Cheng, C. Froese Fischer, Y.-K. Kim, J. Phys. B 15, 181 (1982).
[CrossRef]

Clark, R. E. H.

D. H. Sampson, R. E. H. Clark, S. J. Goett, Phys. Rev. A 24, 2979 (1981);D. H. Sampson, S. J. Goett, R. E. H. Clark, At. Data Nucl. Data Tables 30, 125 (1984).
[CrossRef]

Cowan, R. D.

Desclaux, J. P.

O. Gorceix, P. Indelicato, J. P. Desclaux, J. Phys. B 20, 639 (1987).
[CrossRef]

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

Edlén, B.

B. Edlén, in Handbuch der Physik, S. Flügge, ed. (Springer-Verlag, Berlin, 1964), Vol. 27, p. 165.

Ellis, D. G.

D. G. Ellis, Phys. Rev. A 28, 1223 (1983).
[CrossRef]

Faenov, A. Y.

V. A. Boiko, A. Y. Faenov, S. A. Pikuz, J. Quant. Spectrosc. Radiat. Transfer 19, 11 (1978).
[CrossRef]

Faenov, A. Ya.

V. A. Boiko, S. A. Pikuz, U. I. Safranova, A. Ya. Faenov, J. Phys. B 10, 1253 (1977).
[CrossRef]

Fawcett, B. C.

B. C. Fawcett, At. Data Nucl. Data Tables 30, 1 (1984);At. Data Nucl. Data Tables 33, 479(E) (1985).
[CrossRef]

B. C. Fawcett, A. Ridgeley, T. P. Hughes, Mon. Not. R. Astron. Soc. 188, 365 (1979).

G. E. Bromage, R. D. Cowan, B. C. Fawcett, A. Ridgeley, J. Opt. Soc. Am. 68, 48 (1978).
[CrossRef]

B. C. Fawcett, R. W. Hayes, Phys. Scr. 8, 244 (1973).
[CrossRef]

Froese Fischer, C.

K. T. Cheng, C. Froese Fischer, Y.-K. Kim, J. Phys. B 15, 181 (1982).
[CrossRef]

Glass, R.

R. Glass, J. Phys. B 12, 1633 (1979).
[CrossRef]

Goett, S. J.

D. H. Sampson, R. E. H. Clark, S. J. Goett, Phys. Rev. A 24, 2979 (1981);D. H. Sampson, S. J. Goett, R. E. H. Clark, At. Data Nucl. Data Tables 30, 125 (1984).
[CrossRef]

Gorceix, O.

O. Gorceix, P. Indelicato, J. P. Desclaux, J. Phys. B 20, 639 (1987).
[CrossRef]

Hayes, R. W.

B. C. Fawcett, R. W. Hayes, Phys. Scr. 8, 244 (1973).
[CrossRef]

Hibbert, A.

A. Hibbert, J. Phys. B 12, L661 (1979).
[CrossRef]

Hose, G.

G. Hose, U. Kaldor, Phys. Rev. A 30, 2932 (1984).
[CrossRef]

Hughes, T. P.

B. C. Fawcett, A. Ridgeley, T. P. Hughes, Mon. Not. R. Astron. Soc. 188, 365 (1979).

Indelicato, P.

O. Gorceix, P. Indelicato, J. P. Desclaux, J. Phys. B 20, 639 (1987).
[CrossRef]

Ivanova, E. P.

E. P. Ivanova, U. I. Safranova, J. Phys. B 8, 1591 (1975).
[CrossRef]

Kaldor, U.

G. Hose, U. Kaldor, Phys. Rev. A 30, 2932 (1984).
[CrossRef]

Kim, Y.-K.

K. T. Cheng, C. Froese Fischer, Y.-K. Kim, J. Phys. B 15, 181 (1982).
[CrossRef]

Kononov, E. Ya.

E. Ya. Kononov, U. I. Safronova, Opt. Spectrosc. (USSR) 43, 1 (1977).

Layzer, D.

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

Lowdin, P. O.

P. O. Lowdin, Phys. Rev. 97, 1509 (1955).
[CrossRef]

Martin, W. C.

W. C. Martin, R. Zalubas, A. Musgrove, J. Phys. Chem. Ref. Data 14, 751 (1985).
[CrossRef]

W. C. Martin, R. Zalubas, J. Phys. Chem. Ref. Data 9, 1 (Mg ix) (1980);J. Phys. Chem. Ref. Data 8, 817 (Al x) (1979);J. Phys. Chem. Ref. Data 12, 323 (Si xi) (1983).
[CrossRef]

Mason, H. E.

A. K. Bhatia, H. E. Mason, Astron. Astrophys. 103, 324 (1981).

Mohr, P. J.

P. J. Mohr, Ann. Phys. (NY) 88, 26, 52 (1974);Phys. Rev. A 26, 2388 (1982);At. Data Nucl. Data Tables 29, 453 (1983).
[CrossRef]

Moore, C. E.

C. E. Moore, Selected Tables of Atomic Spectra, Natl. Stand. Ref. Data Ser. Natl. Bur. Stand. 3, Sec. 3 (C iii) (1970);Selected Tables of Atomic Spectra Sec. 4 (N iv) (1971);Selected Tables of Atomic Spectra Sec. 9 (O v) (1980).

Musgrove, A.

W. C. Martin, R. Zalubas, A. Musgrove, J. Phys. Chem. Ref. Data 14, 751 (1985).
[CrossRef]

Odabasi, H.

Pikuz, S. A.

V. A. Boiko, A. Y. Faenov, S. A. Pikuz, J. Quant. Spectrosc. Radiat. Transfer 19, 11 (1978).
[CrossRef]

V. A. Boiko, S. A. Pikuz, U. I. Safranova, A. Ya. Faenov, J. Phys. B 10, 1253 (1977).
[CrossRef]

Ravenhall, D. G.

G. E. Brown, D. G. Ravenhall, Proc. R. Soc. London Ser. A 208, 552 (1951).
[CrossRef]

Ridgeley, A.

B. C. Fawcett, A. Ridgeley, T. P. Hughes, Mon. Not. R. Astron. Soc. 188, 365 (1979).

G. E. Bromage, R. D. Cowan, B. C. Fawcett, A. Ridgeley, J. Opt. Soc. Am. 68, 48 (1978).
[CrossRef]

Safranova, U. I.

V. A. Boiko, S. A. Pikuz, U. I. Safranova, A. Ya. Faenov, J. Phys. B 10, 1253 (1977).
[CrossRef]

E. P. Ivanova, U. I. Safranova, J. Phys. B 8, 1591 (1975).
[CrossRef]

Safronova, U. I.

E. Ya. Kononov, U. I. Safronova, Opt. Spectrosc. (USSR) 43, 1 (1977).

Sampson, D. H.

D. H. Sampson, R. E. H. Clark, S. J. Goett, Phys. Rev. A 24, 2979 (1981);D. H. Sampson, S. J. Goett, R. E. H. Clark, At. Data Nucl. Data Tables 30, 125 (1984).
[CrossRef]

Sucher, J.

J. Sucher, Phys. Rev. A 22, 348 (1980).
[CrossRef]

Uehling, E. A.

E. A. Uehling, Phys. Rev. 48, 55 (1935).
[CrossRef]

Weiss, A. W.

A. W. Weiss, Adv. At. Mol. Phys. 9, 1 (1973).
[CrossRef]

A. W. Weiss, in Beam Foil Spectroscopy, I. A. Sellin, D. L. Pegg, eds. (Plenum, New York, 1976), Vol. 1, p. 51.
[CrossRef]

Zalubas, R.

W. C. Martin, R. Zalubas, A. Musgrove, J. Phys. Chem. Ref. Data 14, 751 (1985).
[CrossRef]

W. C. Martin, R. Zalubas, J. Phys. Chem. Ref. Data 9, 1 (Mg ix) (1980);J. Phys. Chem. Ref. Data 8, 817 (Al x) (1979);J. Phys. Chem. Ref. Data 12, 323 (Si xi) (1983).
[CrossRef]

Adv. At. Mol. Phys. (1)

A. W. Weiss, Adv. At. Mol. Phys. 9, 1 (1973).
[CrossRef]

Ann. Phys. (NY) (2)

P. J. Mohr, Ann. Phys. (NY) 88, 26, 52 (1974);Phys. Rev. A 26, 2388 (1982);At. Data Nucl. Data Tables 29, 453 (1983).
[CrossRef]

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

Astron. Astrophys. (1)

A. K. Bhatia, H. E. Mason, Astron. Astrophys. 103, 324 (1981).

At. Data Nucl. Data Tables (1)

B. C. Fawcett, At. Data Nucl. Data Tables 30, 1 (1984);At. Data Nucl. Data Tables 33, 479(E) (1985).
[CrossRef]

Comput. Phys. Commun. (1)

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

J. Opt. Soc. Am. (2)

J. Phys. B (6)

R. Glass, J. Phys. B 12, 1633 (1979).
[CrossRef]

A. Hibbert, J. Phys. B 12, L661 (1979).
[CrossRef]

O. Gorceix, P. Indelicato, J. P. Desclaux, J. Phys. B 20, 639 (1987).
[CrossRef]

V. A. Boiko, S. A. Pikuz, U. I. Safranova, A. Ya. Faenov, J. Phys. B 10, 1253 (1977).
[CrossRef]

E. P. Ivanova, U. I. Safranova, J. Phys. B 8, 1591 (1975).
[CrossRef]

K. T. Cheng, C. Froese Fischer, Y.-K. Kim, J. Phys. B 15, 181 (1982).
[CrossRef]

J. Phys. Chem. Ref. Data (2)

W. C. Martin, R. Zalubas, J. Phys. Chem. Ref. Data 9, 1 (Mg ix) (1980);J. Phys. Chem. Ref. Data 8, 817 (Al x) (1979);J. Phys. Chem. Ref. Data 12, 323 (Si xi) (1983).
[CrossRef]

W. C. Martin, R. Zalubas, A. Musgrove, J. Phys. Chem. Ref. Data 14, 751 (1985).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (1)

V. A. Boiko, A. Y. Faenov, S. A. Pikuz, J. Quant. Spectrosc. Radiat. Transfer 19, 11 (1978).
[CrossRef]

Mon. Not. R. Astron. Soc. (1)

B. C. Fawcett, A. Ridgeley, T. P. Hughes, Mon. Not. R. Astron. Soc. 188, 365 (1979).

Opt. Spectrosc. (USSR) (1)

E. Ya. Kononov, U. I. Safronova, Opt. Spectrosc. (USSR) 43, 1 (1977).

Phys. Rev. (2)

P. O. Lowdin, Phys. Rev. 97, 1509 (1955).
[CrossRef]

E. A. Uehling, Phys. Rev. 48, 55 (1935).
[CrossRef]

Phys. Rev. A (4)

G. Hose, U. Kaldor, Phys. Rev. A 30, 2932 (1984).
[CrossRef]

D. H. Sampson, R. E. H. Clark, S. J. Goett, Phys. Rev. A 24, 2979 (1981);D. H. Sampson, S. J. Goett, R. E. H. Clark, At. Data Nucl. Data Tables 30, 125 (1984).
[CrossRef]

D. G. Ellis, Phys. Rev. A 28, 1223 (1983).
[CrossRef]

J. Sucher, Phys. Rev. A 22, 348 (1980).
[CrossRef]

Phys. Scr. (2)

C. F. Bunge, Phys. Scr. 21, 328 (1980).
[CrossRef]

B. C. Fawcett, R. W. Hayes, Phys. Scr. 8, 244 (1973).
[CrossRef]

Proc. R. Soc. London Ser. A (1)

G. E. Brown, D. G. Ravenhall, Proc. R. Soc. London Ser. A 208, 552 (1951).
[CrossRef]

Selected Tables of Atomic Spectra (1)

C. E. Moore, Selected Tables of Atomic Spectra, Natl. Stand. Ref. Data Ser. Natl. Bur. Stand. 3, Sec. 3 (C iii) (1970);Selected Tables of Atomic Spectra Sec. 4 (N iv) (1971);Selected Tables of Atomic Spectra Sec. 9 (O v) (1980).

Other (2)

A. W. Weiss, in Beam Foil Spectroscopy, I. A. Sellin, D. L. Pegg, eds. (Plenum, New York, 1976), Vol. 1, p. 51.
[CrossRef]

B. Edlén, in Handbuch der Physik, S. Flügge, ed. (Springer-Verlag, Berlin, 1964), Vol. 27, p. 165.

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Figures (3)

Fig. 1
Fig. 1

Differences between calculated and experimental wave numbers for the 2s2 1S0–2s3p 1P1 lines (C2+–O4+ and Mg8+–P11+). Note that filled circles and filled squares represent differences with and without the calculated residual correlation energies, respectively. The data for Z = 6–8 are from Table 1, and for Z = 12–15, experimental wave numbers σ(exp) corresponding to wavelengths in Table 3 were subtracted from calculated energies in Table 2. The error bars represent estimated experimental uncertainties. The errors of the σ(exp) values for Z = 6, 7, 8 are negligible on the scale of this graph.

Fig. 2
Fig. 2

Wavelengths of the 2s2 1S0–2s3p (J = 1) lines in spectra of the berylliumlike ions Mg8+–Kr32+. The quantities involved in the wavelength differences represented by the two curves are the calculated wavelengths of the transitions from the upper 2s3p level (λu) and from the lower 2s3p level (λl) and the average of these two wavelengths (λave)for each ion. Experimental wavelengths were also subtracted from the average of the two calculated values. The resulting differences are represented by open circles and filled circles for transitions from the upper and lower J = 1 levels, respectively. The dashed lines connecting the upper and lower curves indicate an interchange of the 3P1 and 1P1 designations predicted to occur between Sc17+ (Z = 21) and Ti18+ (Z = 22).

Fig. 3
Fig. 3

Oscillator strengths for the 2s2 1S0–(2s3p + 2p3s) J = 1 lines for selected ions in the beryllium sequence. The three spectra for O4+, Ar14+, and Ge28+ illustrate the changes in the strengths of the two 2s3p transitions that are due to the change from LS to jj coupling. The Pd42+ and Sn46+ spectra show the crossing of the upper 2s3p level by the 2p3s interloper with its concomitant theft of oscillator strength. At Pd42+ (Z = 46), the interloper is the short-wavelength line; at Sn46+ (Z = 50), it is the middle line. For Yb66+ (Z = 70), the interloper has died out and the spectrum has returned to normal. Note that wavelength separations are plotted to the same scale for all ions except O4+.

Tables (4)

Tables Icon

Table 1 Excitation Energies (in cm−1) for the 2s2–2s3p Transitions of Berylliumlike Ions

Tables Icon

Table 2 Theoretical Energies, 2s2 1S0 and 2s3p J = 1 Levels (in cm−1)a

Tables Icon

Table 3 Eigenvector Percentages for 2s3p (J = 1) Levels, Wavelengths (λ), and Oscillator Strengths (f) for 2s2–2s3p Transitions in the Berylliumlike Ions

Tables Icon

Table 4 Eigenvector Percentages for the Three Lowest J = 1 Levels of (2s3p + 2p3s), Wavelengths (λ), and Oscillator Strengths (f) for 2s2−(2s3p + 2p3s) Transitions in Berylliumlike Ions

Equations (16)

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Ψ = a 0 1 s 2 2 s 2 + b 0 1 s 2 2 p 2 + i j a 1 s 2 s i j 1 s 2 s ϕ i ϕ j + i j b 1 s 2 s i j 1 s 2 p ϕ i ϕ j + i j a 1 s 1 s i j 2 s 2 ϕ i ϕ j + i j b 1 s 1 s i j 2 p 2 ϕ i ϕ j
Ψ = a 0 1 s 2 2 s 3 p + b 0 1 s 2 2 p 3 s + c 0 1 s 2 2 p 3 d + i j a 1 s 2 s i j 1 s 3 p ϕ i ϕ j + i j b 1 s 2 p i j 1 s 3 s ϕ i ϕ j + i j c 1 s 2 p i j 1 s 3 d ϕ i ϕ j + i j a 1 s 3 p i j 1 s 2 s ϕ i ϕ j + i j b 1 s 3 s i j 1 s 2 p ϕ i ϕ j + i j a 1 s 1 s i j 2 s 3 p ϕ i ϕ j + i j b 1 s 1 s i j 2 p 3 s ϕ i ϕ j
χ p = N p ζ r p 1 exp ( ζ p r ) .
H p = ( α 2 / 8 ) p 4 + ( α 2 Z / 2 ) δ ( r ) ( α 2 / 8 ) [ ξ ( r ) ] l · s ,
H D = μ h D ( μ ) + μ > ν 1 / r μ ν ,
h D = α · p c + β c 2 Z / r
Ψ ( J = 0 ) = a 2 s 1 / 2 2 + b 2 p 1 / 2 2 + c 2 p 3 / 2 2 ,
Ψ ( J = 1 ) = a 2 s 1 / 2 3 p 1 / 2 + b 2 s 1 / 2 3 p 3 / 2 + c 2 p 1 / 2 3 s 1 / 2 + d 2 p 3 / 2 3 s 1 / 2 + e 2 p 1 / 2 3 d 3 / 2 + f 2 p 3 / 2 3 d 3 / 2 + g 2 p 3 / 2 3 d 5 / 2 ,
σ i = a Z 2 + b i Z + c i Z 4 ,
δ λ = δ σ i / σ i 2
E = Z 2 n 2 α 2 Z 4 n 4 ( n j + 1 / 2 3 4 ) .
E ( 2 s ) = Z 2 2 2 α 2 Z 4 2 4 5 4 ,
E ( 3 p ) = Z 2 3 2 α 2 Z 4 3 4 ( 3 j + 1 / 2 3 4 ) .
σ ( 3 p ) E ( 3 p ) E ( 2 s ) = 5 Z 2 36 + O ( α 2 Z 4 ) ,
δ σ σ ( 3 p 3 / 2 ) σ ( 3 p 1 / 2 ) = α 2 Z 4 54 .
δ λ = δ σ / σ 2 = ( 24 / 25 ) α 2 R 1 = 0.0466 Å ,

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