Abstract

The dependence of atomic oscillator strengths (f values) on nuclear charge, which leads to systematic trends along isoelectronic sequences, is discussed with particular reference to beam foil spectroscopy. The theoretical background for the nuclear charge dependence is given first, and then several characteristic examples are reviewed in detail. The beam foil technique of measuring lifetimes is one of the most important sources of data for these studies, because it readily permits reliable experimental determinations of f values over several stages of ionization within isoelectronic sequences. It is shown that experimental data are most urgently needed when f values are affected by cancellation in the transition integral or configuration interaction effects, since in these cases most theoretical approaches run into great difficulties.

© 1968 Optical Society of America

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References

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  1. R. Hefferlin, L. Rascon, J. Opt. Soc. Amer. 57, 964 (1967).
    [CrossRef]
  2. W. L. Wiese, Proceedings of the Beam Foil Spectroscopy Conference (Gordon and Breach, New York, 1968); W. L. Wiese, A. W. Weiss, Phys. Rev.175(1968). (To be published.)
    [CrossRef]
  3. See, e.g., C. H. Wilcox, Ed., Perturbation Theory and Its Application in Quantum Mechanics (John Wiley & Sons, Inc., New York, 1966).
  4. E. Hylleraas, Z. Phys. 65, 209 (1930).
    [CrossRef]
  5. A. W. Weiss (to be published).
  6. A. W. Weiss, Astrophys. J. 138, 1262 (1963).
    [CrossRef]
  7. M. Cohen, A. Dalgarno, Proc. Roy. Soc. London Ser. A 275, 492 (1963).
    [CrossRef]
  8. K. Berkner, W. S. Cooper, S. N. Kaplan, R. V. Pyle, Phys. Lett. 16, 35 (1965).
    [CrossRef]
  9. D. R. Bates, A. Damgaard, Phil. Trans. Roy. Soc. London, A 242, 101 (1949).
    [CrossRef]
  10. P. S. Kelly, J. Quant. Spectrosc. Radiative Transfer 4, 117 (1964).
    [CrossRef]
  11. M. R. Lewis, T. Marshall, E. H. Carnevale, F. S. Zimnoch, G. W. Wares, Phys. Rev. 164, 94 (1967).
    [CrossRef]
  12. A. W. Weiss, Phys. Rev. 162, 71 (1967).
    [CrossRef]
  13. A. B. Bolotin, A. P. Yutsis, Zh. Ek p. Teor. Fiz. 24, 537 (1953).
  14. W. S. Bickel, Phys. Rev. 162, 7 (1967).
    [CrossRef]
  15. G. M. Lawrence, B. D. Savage, Phys. Rev. 141, 67 (1966).
    [CrossRef]
  16. A. B. Bolotin, I. B. Levinson, L. I. Levin, Sov. Phys.–JETP 2, 391 (1956).
  17. M. Cohen, A. Dalgarno, Proc. Roy. Soc. London Ser. A 280, 258 (1964).
    [CrossRef]
  18. G. Boldt, Z. Naturforsch. 18a, 1107 (1963).
  19. L. Heroux, AFCRL; private communication.
  20. E. Hinnov, J. Opt. Soc. Amer. 56, 1179 (1966).
    [CrossRef]
  21. A. N. Fillipov, Z. Phys. 69, 526 (1931).
    [CrossRef]
  22. V. K. Prokofev, Z. Phys. 58, 255 (1929).
    [CrossRef]
  23. J. C. Stewart, M. Rotenberg, Phys. Rev. 140, 1508A (1965).
    [CrossRef]
  24. A. W. Weiss (to be published).
  25. A. S. Douglas, R. H. Garstang, Proc. Cambridge Phil. Soc. 58, 377 (1962).
    [CrossRef]

1967 (4)

R. Hefferlin, L. Rascon, J. Opt. Soc. Amer. 57, 964 (1967).
[CrossRef]

M. R. Lewis, T. Marshall, E. H. Carnevale, F. S. Zimnoch, G. W. Wares, Phys. Rev. 164, 94 (1967).
[CrossRef]

A. W. Weiss, Phys. Rev. 162, 71 (1967).
[CrossRef]

W. S. Bickel, Phys. Rev. 162, 7 (1967).
[CrossRef]

1966 (2)

G. M. Lawrence, B. D. Savage, Phys. Rev. 141, 67 (1966).
[CrossRef]

E. Hinnov, J. Opt. Soc. Amer. 56, 1179 (1966).
[CrossRef]

1965 (2)

J. C. Stewart, M. Rotenberg, Phys. Rev. 140, 1508A (1965).
[CrossRef]

K. Berkner, W. S. Cooper, S. N. Kaplan, R. V. Pyle, Phys. Lett. 16, 35 (1965).
[CrossRef]

1964 (2)

M. Cohen, A. Dalgarno, Proc. Roy. Soc. London Ser. A 280, 258 (1964).
[CrossRef]

P. S. Kelly, J. Quant. Spectrosc. Radiative Transfer 4, 117 (1964).
[CrossRef]

1963 (3)

G. Boldt, Z. Naturforsch. 18a, 1107 (1963).

A. W. Weiss, Astrophys. J. 138, 1262 (1963).
[CrossRef]

M. Cohen, A. Dalgarno, Proc. Roy. Soc. London Ser. A 275, 492 (1963).
[CrossRef]

1962 (1)

A. S. Douglas, R. H. Garstang, Proc. Cambridge Phil. Soc. 58, 377 (1962).
[CrossRef]

1956 (1)

A. B. Bolotin, I. B. Levinson, L. I. Levin, Sov. Phys.–JETP 2, 391 (1956).

1953 (1)

A. B. Bolotin, A. P. Yutsis, Zh. Ek p. Teor. Fiz. 24, 537 (1953).

1949 (1)

D. R. Bates, A. Damgaard, Phil. Trans. Roy. Soc. London, A 242, 101 (1949).
[CrossRef]

1931 (1)

A. N. Fillipov, Z. Phys. 69, 526 (1931).
[CrossRef]

1930 (1)

E. Hylleraas, Z. Phys. 65, 209 (1930).
[CrossRef]

1929 (1)

V. K. Prokofev, Z. Phys. 58, 255 (1929).
[CrossRef]

Bates, D. R.

D. R. Bates, A. Damgaard, Phil. Trans. Roy. Soc. London, A 242, 101 (1949).
[CrossRef]

Berkner, K.

K. Berkner, W. S. Cooper, S. N. Kaplan, R. V. Pyle, Phys. Lett. 16, 35 (1965).
[CrossRef]

Bickel, W. S.

W. S. Bickel, Phys. Rev. 162, 7 (1967).
[CrossRef]

Boldt, G.

G. Boldt, Z. Naturforsch. 18a, 1107 (1963).

Bolotin, A. B.

A. B. Bolotin, I. B. Levinson, L. I. Levin, Sov. Phys.–JETP 2, 391 (1956).

A. B. Bolotin, A. P. Yutsis, Zh. Ek p. Teor. Fiz. 24, 537 (1953).

Carnevale, E. H.

M. R. Lewis, T. Marshall, E. H. Carnevale, F. S. Zimnoch, G. W. Wares, Phys. Rev. 164, 94 (1967).
[CrossRef]

Cohen, M.

M. Cohen, A. Dalgarno, Proc. Roy. Soc. London Ser. A 280, 258 (1964).
[CrossRef]

M. Cohen, A. Dalgarno, Proc. Roy. Soc. London Ser. A 275, 492 (1963).
[CrossRef]

Cooper, W. S.

K. Berkner, W. S. Cooper, S. N. Kaplan, R. V. Pyle, Phys. Lett. 16, 35 (1965).
[CrossRef]

Dalgarno, A.

M. Cohen, A. Dalgarno, Proc. Roy. Soc. London Ser. A 280, 258 (1964).
[CrossRef]

M. Cohen, A. Dalgarno, Proc. Roy. Soc. London Ser. A 275, 492 (1963).
[CrossRef]

Damgaard, A.

D. R. Bates, A. Damgaard, Phil. Trans. Roy. Soc. London, A 242, 101 (1949).
[CrossRef]

Douglas, A. S.

A. S. Douglas, R. H. Garstang, Proc. Cambridge Phil. Soc. 58, 377 (1962).
[CrossRef]

Fillipov, A. N.

A. N. Fillipov, Z. Phys. 69, 526 (1931).
[CrossRef]

Garstang, R. H.

A. S. Douglas, R. H. Garstang, Proc. Cambridge Phil. Soc. 58, 377 (1962).
[CrossRef]

Hefferlin, R.

R. Hefferlin, L. Rascon, J. Opt. Soc. Amer. 57, 964 (1967).
[CrossRef]

Heroux, L.

L. Heroux, AFCRL; private communication.

Hinnov, E.

E. Hinnov, J. Opt. Soc. Amer. 56, 1179 (1966).
[CrossRef]

Hylleraas, E.

E. Hylleraas, Z. Phys. 65, 209 (1930).
[CrossRef]

Kaplan, S. N.

K. Berkner, W. S. Cooper, S. N. Kaplan, R. V. Pyle, Phys. Lett. 16, 35 (1965).
[CrossRef]

Kelly, P. S.

P. S. Kelly, J. Quant. Spectrosc. Radiative Transfer 4, 117 (1964).
[CrossRef]

Lawrence, G. M.

G. M. Lawrence, B. D. Savage, Phys. Rev. 141, 67 (1966).
[CrossRef]

Levin, L. I.

A. B. Bolotin, I. B. Levinson, L. I. Levin, Sov. Phys.–JETP 2, 391 (1956).

Levinson, I. B.

A. B. Bolotin, I. B. Levinson, L. I. Levin, Sov. Phys.–JETP 2, 391 (1956).

Lewis, M. R.

M. R. Lewis, T. Marshall, E. H. Carnevale, F. S. Zimnoch, G. W. Wares, Phys. Rev. 164, 94 (1967).
[CrossRef]

Marshall, T.

M. R. Lewis, T. Marshall, E. H. Carnevale, F. S. Zimnoch, G. W. Wares, Phys. Rev. 164, 94 (1967).
[CrossRef]

Prokofev, V. K.

V. K. Prokofev, Z. Phys. 58, 255 (1929).
[CrossRef]

Pyle, R. V.

K. Berkner, W. S. Cooper, S. N. Kaplan, R. V. Pyle, Phys. Lett. 16, 35 (1965).
[CrossRef]

Rascon, L.

R. Hefferlin, L. Rascon, J. Opt. Soc. Amer. 57, 964 (1967).
[CrossRef]

Rotenberg, M.

J. C. Stewart, M. Rotenberg, Phys. Rev. 140, 1508A (1965).
[CrossRef]

Savage, B. D.

G. M. Lawrence, B. D. Savage, Phys. Rev. 141, 67 (1966).
[CrossRef]

Stewart, J. C.

J. C. Stewart, M. Rotenberg, Phys. Rev. 140, 1508A (1965).
[CrossRef]

Wares, G. W.

M. R. Lewis, T. Marshall, E. H. Carnevale, F. S. Zimnoch, G. W. Wares, Phys. Rev. 164, 94 (1967).
[CrossRef]

Weiss, A. W.

A. W. Weiss, Phys. Rev. 162, 71 (1967).
[CrossRef]

A. W. Weiss, Astrophys. J. 138, 1262 (1963).
[CrossRef]

A. W. Weiss (to be published).

A. W. Weiss (to be published).

Wiese, W. L.

W. L. Wiese, Proceedings of the Beam Foil Spectroscopy Conference (Gordon and Breach, New York, 1968); W. L. Wiese, A. W. Weiss, Phys. Rev.175(1968). (To be published.)
[CrossRef]

Yutsis, A. P.

A. B. Bolotin, A. P. Yutsis, Zh. Ek p. Teor. Fiz. 24, 537 (1953).

Zimnoch, F. S.

M. R. Lewis, T. Marshall, E. H. Carnevale, F. S. Zimnoch, G. W. Wares, Phys. Rev. 164, 94 (1967).
[CrossRef]

Astrophys. J. (1)

A. W. Weiss, Astrophys. J. 138, 1262 (1963).
[CrossRef]

J. Opt. Soc. Amer. (2)

R. Hefferlin, L. Rascon, J. Opt. Soc. Amer. 57, 964 (1967).
[CrossRef]

E. Hinnov, J. Opt. Soc. Amer. 56, 1179 (1966).
[CrossRef]

J. Quant. Spectrosc. Radiative Transfer (1)

P. S. Kelly, J. Quant. Spectrosc. Radiative Transfer 4, 117 (1964).
[CrossRef]

Phil. Trans. Roy. Soc. London, A (1)

D. R. Bates, A. Damgaard, Phil. Trans. Roy. Soc. London, A 242, 101 (1949).
[CrossRef]

Phys. Lett. (1)

K. Berkner, W. S. Cooper, S. N. Kaplan, R. V. Pyle, Phys. Lett. 16, 35 (1965).
[CrossRef]

Phys. Rev. (5)

M. R. Lewis, T. Marshall, E. H. Carnevale, F. S. Zimnoch, G. W. Wares, Phys. Rev. 164, 94 (1967).
[CrossRef]

A. W. Weiss, Phys. Rev. 162, 71 (1967).
[CrossRef]

W. S. Bickel, Phys. Rev. 162, 7 (1967).
[CrossRef]

G. M. Lawrence, B. D. Savage, Phys. Rev. 141, 67 (1966).
[CrossRef]

J. C. Stewart, M. Rotenberg, Phys. Rev. 140, 1508A (1965).
[CrossRef]

Proc. Cambridge Phil. Soc. (1)

A. S. Douglas, R. H. Garstang, Proc. Cambridge Phil. Soc. 58, 377 (1962).
[CrossRef]

Proc. Roy. Soc. London Ser. A (2)

M. Cohen, A. Dalgarno, Proc. Roy. Soc. London Ser. A 280, 258 (1964).
[CrossRef]

M. Cohen, A. Dalgarno, Proc. Roy. Soc. London Ser. A 275, 492 (1963).
[CrossRef]

Sov. Phys.–JETP (1)

A. B. Bolotin, I. B. Levinson, L. I. Levin, Sov. Phys.–JETP 2, 391 (1956).

Z. Naturforsch. (1)

G. Boldt, Z. Naturforsch. 18a, 1107 (1963).

Z. Phys. (3)

E. Hylleraas, Z. Phys. 65, 209 (1930).
[CrossRef]

A. N. Fillipov, Z. Phys. 69, 526 (1931).
[CrossRef]

V. K. Prokofev, Z. Phys. 58, 255 (1929).
[CrossRef]

Zh. Ek p. Teor. Fiz. (1)

A. B. Bolotin, A. P. Yutsis, Zh. Ek p. Teor. Fiz. 24, 537 (1953).

Other (5)

L. Heroux, AFCRL; private communication.

A. W. Weiss (to be published).

W. L. Wiese, Proceedings of the Beam Foil Spectroscopy Conference (Gordon and Breach, New York, 1968); W. L. Wiese, A. W. Weiss, Phys. Rev.175(1968). (To be published.)
[CrossRef]

See, e.g., C. H. Wilcox, Ed., Perturbation Theory and Its Application in Quantum Mechanics (John Wiley & Sons, Inc., New York, 1966).

A. W. Weiss (to be published).

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Figures (6)

Fig. 1
Fig. 1

Dependence of f value on nuclear charge for the 2s2S–2p2Po transitions of the lithium isoelectronic sequence. The complete references to the authors are given in the text.

Fig. 2
Fig. 2

f value vs 1/Z for the multiplets 3s3S–3p3Po of the beryllium sequence. The broken line represents simply the best estimated fit through the data points.

Fig. 3
Fig. 3

f value vs 1/Z for the 2s22p2Po–2s2p2 2D transitions of the boron sequence. The authors are referenced in the text.

Fig. 4
Fig. 4

f value vs 1/Z for the multiplets 2s22p2 3P–2s2p3 3Po of the carbon sequence. Complete references to the authors are given in the text.

Fig. 5
Fig. 5

f value vs 1/Z for the 2s–3p transitions of the lithium sequence.

Fig. 6
Fig. 6

f value vs 1/Z for the 3s–4p transitions of the sodium sequence.

Equations (16)

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S ( i , k ) = ψ i * D ψ k d V 2 < i p r p k > 2 ,
f i k = 2 3 ( E k - E i ) 1 g i S ( i , k ) = 2 3 ( E k - E i ) 1 g i < i p r p k > 2 ,
H = p [ 1 2 p 2 + Z r p ] + p < q 1 r p q ,
p < q 1 r p q
H = H 0 + H 1 ,
H 1 = p < q 1 r p q
H = - p ( 1 2 p 2 + 1 ρ ) + 1 Z p < q 1 ρ p q ,
H = H 0 + ( 1 / Z ) H 1 ,
( H 0 + Z - 1 H 1 ) ψ = ψ ,
ψ = n = 0 Z - n φ n = φ 0 + φ 1 / Z + φ 2 / Z 2 + ,
= n = 0 Z - n n = 0 + 1 / Z + 2 / Z 2 + ,
E = Z 2 n = 0 Z - n n = 0 Z 2 + 1 Z + 2 + .
( H 0 - 0 ) φ 0 = 0 ,
S = m = 0 s m Z - m - 2 = s 0 / Z 2 + s 2 / Z 3 + s 1 / Z 4 + ,
Z 2 S = m = 0 s m Z - m = s 0 + s 1 / Z + s 2 / Z 2 + ,
f = m = 0 a m Z - m = a 0 + a 1 / Z + a 2 / Z 2 + .

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