Abstract

The nuclear-charge-expansion method is used in conjunction with a modified screening approximation to predict oscillator strengths, correct through first order in the perturbation, for the 3d–4p and 4p–4d transitions in the sodium isoelectronic sequence. The results are compared with the values recommended by Smith and Wiese.

© 1973 Optical Society of America

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References

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  1. M. W. Smith and W. L. Wiese, Astrophys. J. Suppl. Ser. 23(196), 103 (1971).
    [Crossref]
  2. D. Layzer, Z. Horak, M. N. Lewis, and D. P. Thompson, Ann. Phys. (N.Y.) 29, 101 (1964).
    [Crossref]
  3. M. Cohen and A. Dalgarno, Proc. R. Soc. A 293, 359 (1966).
    [Crossref]
  4. A. Dalgarno and A. L. Stewart, Proc. R. Soc. A 257, 534 (1960).
    [Crossref]
  5. R. P. McEachran, C. E. Tull, and M. Cohen, Can. J. Phys. 47, 835 (1969).
    [Crossref]
  6. S. Hameed, A. Herzenberg, and M. G. James, J. Phys. B 1, 822 (1968); J. C. Weisheit and A. Dalgarno, Chem. Phys. Lett. 9, 517 (1971); J. H. Black, J. C. Weisheit, and E. Laviana, Astrophys. J. 177, 567 (1972).
    [Crossref]
  7. A. Dalgarno and E. M. Parkinson, Proc. R. Soc. A 301, 253 (1967).
    [Crossref]

1971 (1)

M. W. Smith and W. L. Wiese, Astrophys. J. Suppl. Ser. 23(196), 103 (1971).
[Crossref]

1969 (1)

R. P. McEachran, C. E. Tull, and M. Cohen, Can. J. Phys. 47, 835 (1969).
[Crossref]

1968 (1)

S. Hameed, A. Herzenberg, and M. G. James, J. Phys. B 1, 822 (1968); J. C. Weisheit and A. Dalgarno, Chem. Phys. Lett. 9, 517 (1971); J. H. Black, J. C. Weisheit, and E. Laviana, Astrophys. J. 177, 567 (1972).
[Crossref]

1967 (1)

A. Dalgarno and E. M. Parkinson, Proc. R. Soc. A 301, 253 (1967).
[Crossref]

1966 (1)

M. Cohen and A. Dalgarno, Proc. R. Soc. A 293, 359 (1966).
[Crossref]

1964 (1)

D. Layzer, Z. Horak, M. N. Lewis, and D. P. Thompson, Ann. Phys. (N.Y.) 29, 101 (1964).
[Crossref]

1960 (1)

A. Dalgarno and A. L. Stewart, Proc. R. Soc. A 257, 534 (1960).
[Crossref]

Cohen, M.

R. P. McEachran, C. E. Tull, and M. Cohen, Can. J. Phys. 47, 835 (1969).
[Crossref]

M. Cohen and A. Dalgarno, Proc. R. Soc. A 293, 359 (1966).
[Crossref]

Dalgarno, A.

A. Dalgarno and E. M. Parkinson, Proc. R. Soc. A 301, 253 (1967).
[Crossref]

M. Cohen and A. Dalgarno, Proc. R. Soc. A 293, 359 (1966).
[Crossref]

A. Dalgarno and A. L. Stewart, Proc. R. Soc. A 257, 534 (1960).
[Crossref]

Hameed, S.

S. Hameed, A. Herzenberg, and M. G. James, J. Phys. B 1, 822 (1968); J. C. Weisheit and A. Dalgarno, Chem. Phys. Lett. 9, 517 (1971); J. H. Black, J. C. Weisheit, and E. Laviana, Astrophys. J. 177, 567 (1972).
[Crossref]

Herzenberg, A.

S. Hameed, A. Herzenberg, and M. G. James, J. Phys. B 1, 822 (1968); J. C. Weisheit and A. Dalgarno, Chem. Phys. Lett. 9, 517 (1971); J. H. Black, J. C. Weisheit, and E. Laviana, Astrophys. J. 177, 567 (1972).
[Crossref]

Horak, Z.

D. Layzer, Z. Horak, M. N. Lewis, and D. P. Thompson, Ann. Phys. (N.Y.) 29, 101 (1964).
[Crossref]

James, M. G.

S. Hameed, A. Herzenberg, and M. G. James, J. Phys. B 1, 822 (1968); J. C. Weisheit and A. Dalgarno, Chem. Phys. Lett. 9, 517 (1971); J. H. Black, J. C. Weisheit, and E. Laviana, Astrophys. J. 177, 567 (1972).
[Crossref]

Layzer, D.

D. Layzer, Z. Horak, M. N. Lewis, and D. P. Thompson, Ann. Phys. (N.Y.) 29, 101 (1964).
[Crossref]

Lewis, M. N.

D. Layzer, Z. Horak, M. N. Lewis, and D. P. Thompson, Ann. Phys. (N.Y.) 29, 101 (1964).
[Crossref]

McEachran, R. P.

R. P. McEachran, C. E. Tull, and M. Cohen, Can. J. Phys. 47, 835 (1969).
[Crossref]

Parkinson, E. M.

A. Dalgarno and E. M. Parkinson, Proc. R. Soc. A 301, 253 (1967).
[Crossref]

Smith, M. W.

M. W. Smith and W. L. Wiese, Astrophys. J. Suppl. Ser. 23(196), 103 (1971).
[Crossref]

Stewart, A. L.

A. Dalgarno and A. L. Stewart, Proc. R. Soc. A 257, 534 (1960).
[Crossref]

Thompson, D. P.

D. Layzer, Z. Horak, M. N. Lewis, and D. P. Thompson, Ann. Phys. (N.Y.) 29, 101 (1964).
[Crossref]

Tull, C. E.

R. P. McEachran, C. E. Tull, and M. Cohen, Can. J. Phys. 47, 835 (1969).
[Crossref]

Wiese, W. L.

M. W. Smith and W. L. Wiese, Astrophys. J. Suppl. Ser. 23(196), 103 (1971).
[Crossref]

Ann. Phys. (N.Y.) (1)

D. Layzer, Z. Horak, M. N. Lewis, and D. P. Thompson, Ann. Phys. (N.Y.) 29, 101 (1964).
[Crossref]

Astrophys. J. Suppl. Ser. (1)

M. W. Smith and W. L. Wiese, Astrophys. J. Suppl. Ser. 23(196), 103 (1971).
[Crossref]

Can. J. Phys. (1)

R. P. McEachran, C. E. Tull, and M. Cohen, Can. J. Phys. 47, 835 (1969).
[Crossref]

J. Phys. B (1)

S. Hameed, A. Herzenberg, and M. G. James, J. Phys. B 1, 822 (1968); J. C. Weisheit and A. Dalgarno, Chem. Phys. Lett. 9, 517 (1971); J. H. Black, J. C. Weisheit, and E. Laviana, Astrophys. J. 177, 567 (1972).
[Crossref]

Proc. R. Soc. A (3)

A. Dalgarno and E. M. Parkinson, Proc. R. Soc. A 301, 253 (1967).
[Crossref]

M. Cohen and A. Dalgarno, Proc. R. Soc. A 293, 359 (1966).
[Crossref]

A. Dalgarno and A. L. Stewart, Proc. R. Soc. A 257, 534 (1960).
[Crossref]

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Figures (2)

Fig. 1
Fig. 1

Na-sequence 3d 2D−4p 2P° oscillator strengths as a function of 1/Z. Smith and Wiese (Ref. 1), recommended curve, ——. First-order Z expansions: Hartree–Fock, – – – ; exact, — —. Recommended Hartree–Fock curve, ···.

Fig. 2
Fig. 2

Na-sequence 4p 2P°–4d 2D oscillator strengths as a function of 1/Z. Smith and Wiese (Ref. 1), recommended curve, ——. First-order Z expansions: Hartree–Fock, – – –; exact, — —.

Tables (1)

Tables Icon

Table I Values of I0, I1, I1HF, f0, f1, f1HF, and σ for the 3 d 4 p and 4 p 4 d transitions in sodium-like ions [see Eqs. (1), (3), (7), and (8)].

Equations (8)

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I ( n l , n l ) = I 0 Z + I 1 Z 2 + I 2 Z 3 + ,
E n l E n l = Δ E 0 Z 2 + Δ E 1 Z + Δ E 2 + ,
f = f 0 + f 1 Z 1 + f 2 Z 2 + ,
f 0 = 2 I 0 2 Δ E 0 / 3 ( 2 l + 1 ) ,
f 1 = 2 I 0 [ I 0 Δ E 1 + 2 I 1 Δ E 0 ] / 3 ( 2 l + 1 ) .
I ( n l , n l ) = I 0 Z s , s = I 1 / I 0
I ( n l , n l ) = I 0 Z σ + I 1 σ I 0 ( Z σ ) 2 ,
I HF ( n l , n l ) = I 0 Z σ + I 1 HF σ I 0 ( Z σ ) 2