Abstract

For an arbitrary electron configuration l1n1l2n2l3n3…, analytical expressions are derived for the energy-matrix coefficients of the electrostatic-interaction parameters Fk(li,lj) and Gk(li,lj) and of the spin-orbit parameters ξ (li). A computer program is described which calculates decimal values of these coefficients for any configuration with less than five open subshells, starting from only a table of the terms, parents, and coefficients of fractional parentage for each open subshell lini. Given also a set of values of the parameters, the program evaluates and diagonalizes the energy matrices to obtain the eigenvalues and eigenvectors of the states belonging to this configuration. If so specified, the program does the above for two configurations of opposite parity, differences eigenvalues to obtain wavelengths for dipole transitions, and from the eigenvectors computes line strengths and (given an absolute value for the reduced dipole matrix element) transition probabilities.

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  1. J. C. Slater, Phys. Rev. 34, 1293 (1929).
  2. E. U. Condon and G. H. Shortley, The Theory of Atomic Spectra (Cambridge Univ. Press, 1935).
  3. J. C. Slater, Quantum Theory of Atomic Structure (McGraw-Hill Book Co., New York, 1960), 2 Vols.
  4. Except where indicated to the contrary, in this paper lengths are measured in Bohr radii and energies in Rydbergs.
  5. G. Racah, (II) Phys. Rev. 62, 438 (1942); (III) Phys. Rev. 63, 367 (1943); (IV) Phys. Rev. 76, 1352 (1949).
  6. For a bibliography up to 1960 see Ref. 3, Ch. 24 and Appendix 21.
  7. F. R. Innes and C. W. Ufford, Phys. Rev. 111, 194 (1958); A. P. Yutsis, Ya. A. Vizbaraite, R. I. Karaziya, A. Yu. Savukinas, and A. A. Bandzaitis, Lietuvos Fisikos Rinkinys IV, 198 (1964); B. W. Shore, Phys. Rev. 139, A1042 (1965); U. Fano, Phys. Rev. 140, A67 (1965).
  8. C. W. Nielson and G. F. Koster, Spectroscopic Coefficients for the pn, dn, and fn Configurations (MIT Press, Cambridge, Mass., 1963). 9 R. D. Cowan and K. L. Andrew, J. Opt. Soc. Am. 55, 502 (1965).
  9. M. Rotenberg, R. Bivins, N. Metropolis, and J. Wooten, Jr., The 3-j and 6-j Symnbols (Technology Press, MIT, Cambridge, Mass., 1959).
  10. G. Racah, J. Opt. Soc. Am. 50, 408 (1960). The abbreviations LSLK, etc. used in the present paper are not unambiguous; they are intended only as suggestive abbreviated lists of the various intermediate quantum numbers, for reference purposes within this paper.
  11. 12 A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton Univ. Press, Princeton, New Jersey, 1957).
  12. F. R. Innes, Phys. Rev. 91, 31 (1953), Eq. (13).
  13. Reference 3, Sec. 14-2.
  14. F. Rohrlich, Astrophys. J. 129, 441, 449 (1959).
  15. B. G. Wybourne, Spectroscopic Properties of the Rare Earths (John Wiley & Sons, Inc., New York, 1965).
  16. Reference 10, Eqs. (3.1) and (2.7).
  17. The author is indebted to J. D. Louck for pointing out this relation to him.
  18. Reference 2, Eqs. 54(8) and 94(14), and Ref. 9, Eqs. (23)-(24).
  19. F. Rohrlich, Phys. Rev. 74, 1372 (1948).
  20. J. Sugar (private communication).
  21. R. D. Cowan and N. J. Peacock, Astrophys. J. 142, 390 (1965); 143, 283 (1966). N. J. Peacock, R. D. Cowan, and G. A. Sawyer, in Proc. of the Seventh International Conference on Phenomena in Ionized Gases (Beograd, 1966), Vol. II, p. 599; B. C. Fawcett, N. J. Peacock, and R. D. Cowan, Proc. Phys. Soc. (London) 1B, 295 (1968).
  22. R. D. Cowan, Astrophys. J. 147, 377 (1967).
  23. C. J. Humphreys, E. Paul, Jr., R. D. Cowan, and K. L. Andrew, J. Opt. Soc. Am. 57, 855 (1967).
  24. L. Å Svensson and J. O. Ekberg, Arkiv Fysik 37, 65 (1968).

Andrew, K. L.

C. J. Humphreys, E. Paul, Jr., R. D. Cowan, and K. L. Andrew, J. Opt. Soc. Am. 57, 855 (1967).

Bivins, R.

M. Rotenberg, R. Bivins, N. Metropolis, and J. Wooten, Jr., The 3-j and 6-j Symnbols (Technology Press, MIT, Cambridge, Mass., 1959).

Condon, E. U.

E. U. Condon and G. H. Shortley, The Theory of Atomic Spectra (Cambridge Univ. Press, 1935).

Cowan, R. D.

C. J. Humphreys, E. Paul, Jr., R. D. Cowan, and K. L. Andrew, J. Opt. Soc. Am. 57, 855 (1967).

R. D. Cowan and N. J. Peacock, Astrophys. J. 142, 390 (1965); 143, 283 (1966). N. J. Peacock, R. D. Cowan, and G. A. Sawyer, in Proc. of the Seventh International Conference on Phenomena in Ionized Gases (Beograd, 1966), Vol. II, p. 599; B. C. Fawcett, N. J. Peacock, and R. D. Cowan, Proc. Phys. Soc. (London) 1B, 295 (1968).

R. D. Cowan, Astrophys. J. 147, 377 (1967).

Edmonds, A. R.

12 A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton Univ. Press, Princeton, New Jersey, 1957).

Ekberg, J. O.

L. Å Svensson and J. O. Ekberg, Arkiv Fysik 37, 65 (1968).

Humphreys, C. J.

C. J. Humphreys, E. Paul, Jr., R. D. Cowan, and K. L. Andrew, J. Opt. Soc. Am. 57, 855 (1967).

Innes, F. R.

F. R. Innes, Phys. Rev. 91, 31 (1953), Eq. (13).

F. R. Innes and C. W. Ufford, Phys. Rev. 111, 194 (1958); A. P. Yutsis, Ya. A. Vizbaraite, R. I. Karaziya, A. Yu. Savukinas, and A. A. Bandzaitis, Lietuvos Fisikos Rinkinys IV, 198 (1964); B. W. Shore, Phys. Rev. 139, A1042 (1965); U. Fano, Phys. Rev. 140, A67 (1965).

Koster, G. F.

C. W. Nielson and G. F. Koster, Spectroscopic Coefficients for the pn, dn, and fn Configurations (MIT Press, Cambridge, Mass., 1963). 9 R. D. Cowan and K. L. Andrew, J. Opt. Soc. Am. 55, 502 (1965).

Metropolis, N.

M. Rotenberg, R. Bivins, N. Metropolis, and J. Wooten, Jr., The 3-j and 6-j Symnbols (Technology Press, MIT, Cambridge, Mass., 1959).

Nielson, C. W.

C. W. Nielson and G. F. Koster, Spectroscopic Coefficients for the pn, dn, and fn Configurations (MIT Press, Cambridge, Mass., 1963). 9 R. D. Cowan and K. L. Andrew, J. Opt. Soc. Am. 55, 502 (1965).

Paul, Jr., E.

C. J. Humphreys, E. Paul, Jr., R. D. Cowan, and K. L. Andrew, J. Opt. Soc. Am. 57, 855 (1967).

Peacock, N. J.

R. D. Cowan and N. J. Peacock, Astrophys. J. 142, 390 (1965); 143, 283 (1966). N. J. Peacock, R. D. Cowan, and G. A. Sawyer, in Proc. of the Seventh International Conference on Phenomena in Ionized Gases (Beograd, 1966), Vol. II, p. 599; B. C. Fawcett, N. J. Peacock, and R. D. Cowan, Proc. Phys. Soc. (London) 1B, 295 (1968).

Racah, G.

G. Racah, J. Opt. Soc. Am. 50, 408 (1960). The abbreviations LSLK, etc. used in the present paper are not unambiguous; they are intended only as suggestive abbreviated lists of the various intermediate quantum numbers, for reference purposes within this paper.

G. Racah, (II) Phys. Rev. 62, 438 (1942); (III) Phys. Rev. 63, 367 (1943); (IV) Phys. Rev. 76, 1352 (1949).

Rohrlich, F.

F. Rohrlich, Astrophys. J. 129, 441, 449 (1959).

F. Rohrlich, Phys. Rev. 74, 1372 (1948).

Rotenberg, M.

M. Rotenberg, R. Bivins, N. Metropolis, and J. Wooten, Jr., The 3-j and 6-j Symnbols (Technology Press, MIT, Cambridge, Mass., 1959).

Shortley, G. H.

E. U. Condon and G. H. Shortley, The Theory of Atomic Spectra (Cambridge Univ. Press, 1935).

Slater, J. C.

J. C. Slater, Quantum Theory of Atomic Structure (McGraw-Hill Book Co., New York, 1960), 2 Vols.

J. C. Slater, Phys. Rev. 34, 1293 (1929).

Svensson, L. Å

L. Å Svensson and J. O. Ekberg, Arkiv Fysik 37, 65 (1968).

Ufford, C. W.

F. R. Innes and C. W. Ufford, Phys. Rev. 111, 194 (1958); A. P. Yutsis, Ya. A. Vizbaraite, R. I. Karaziya, A. Yu. Savukinas, and A. A. Bandzaitis, Lietuvos Fisikos Rinkinys IV, 198 (1964); B. W. Shore, Phys. Rev. 139, A1042 (1965); U. Fano, Phys. Rev. 140, A67 (1965).

Wooten, Jr., J.

M. Rotenberg, R. Bivins, N. Metropolis, and J. Wooten, Jr., The 3-j and 6-j Symnbols (Technology Press, MIT, Cambridge, Mass., 1959).

Wybourne, B. G.

B. G. Wybourne, Spectroscopic Properties of the Rare Earths (John Wiley & Sons, Inc., New York, 1965).

Other

J. C. Slater, Phys. Rev. 34, 1293 (1929).

E. U. Condon and G. H. Shortley, The Theory of Atomic Spectra (Cambridge Univ. Press, 1935).

J. C. Slater, Quantum Theory of Atomic Structure (McGraw-Hill Book Co., New York, 1960), 2 Vols.

Except where indicated to the contrary, in this paper lengths are measured in Bohr radii and energies in Rydbergs.

G. Racah, (II) Phys. Rev. 62, 438 (1942); (III) Phys. Rev. 63, 367 (1943); (IV) Phys. Rev. 76, 1352 (1949).

For a bibliography up to 1960 see Ref. 3, Ch. 24 and Appendix 21.

F. R. Innes and C. W. Ufford, Phys. Rev. 111, 194 (1958); A. P. Yutsis, Ya. A. Vizbaraite, R. I. Karaziya, A. Yu. Savukinas, and A. A. Bandzaitis, Lietuvos Fisikos Rinkinys IV, 198 (1964); B. W. Shore, Phys. Rev. 139, A1042 (1965); U. Fano, Phys. Rev. 140, A67 (1965).

C. W. Nielson and G. F. Koster, Spectroscopic Coefficients for the pn, dn, and fn Configurations (MIT Press, Cambridge, Mass., 1963). 9 R. D. Cowan and K. L. Andrew, J. Opt. Soc. Am. 55, 502 (1965).

M. Rotenberg, R. Bivins, N. Metropolis, and J. Wooten, Jr., The 3-j and 6-j Symnbols (Technology Press, MIT, Cambridge, Mass., 1959).

G. Racah, J. Opt. Soc. Am. 50, 408 (1960). The abbreviations LSLK, etc. used in the present paper are not unambiguous; they are intended only as suggestive abbreviated lists of the various intermediate quantum numbers, for reference purposes within this paper.

12 A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton Univ. Press, Princeton, New Jersey, 1957).

F. R. Innes, Phys. Rev. 91, 31 (1953), Eq. (13).

Reference 3, Sec. 14-2.

F. Rohrlich, Astrophys. J. 129, 441, 449 (1959).

B. G. Wybourne, Spectroscopic Properties of the Rare Earths (John Wiley & Sons, Inc., New York, 1965).

Reference 10, Eqs. (3.1) and (2.7).

The author is indebted to J. D. Louck for pointing out this relation to him.

Reference 2, Eqs. 54(8) and 94(14), and Ref. 9, Eqs. (23)-(24).

F. Rohrlich, Phys. Rev. 74, 1372 (1948).

J. Sugar (private communication).

R. D. Cowan and N. J. Peacock, Astrophys. J. 142, 390 (1965); 143, 283 (1966). N. J. Peacock, R. D. Cowan, and G. A. Sawyer, in Proc. of the Seventh International Conference on Phenomena in Ionized Gases (Beograd, 1966), Vol. II, p. 599; B. C. Fawcett, N. J. Peacock, and R. D. Cowan, Proc. Phys. Soc. (London) 1B, 295 (1968).

R. D. Cowan, Astrophys. J. 147, 377 (1967).

C. J. Humphreys, E. Paul, Jr., R. D. Cowan, and K. L. Andrew, J. Opt. Soc. Am. 57, 855 (1967).

L. Å Svensson and J. O. Ekberg, Arkiv Fysik 37, 65 (1968).

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