Abstract

The energies of the 37 observed levels of the 4ƒ<sup>3</sup> configuration of Pr III have been calculated with an rms deviation of ±29 cm<sup>-1</sup> by use of 13 adjustable parameters, including 5 parameters which account for nonlinear configuration-interaction effects. The physical significance of the nonlinear parameters is discussed in terms of the relative roles of various mechanisms of configuration interaction.

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  1. E. U. Condon and G. H. Shortley, The Theory of Atomic Spectra (Cambridge University Press, New York, 1935).
  2. G. Racah, Phys. Rev. 76, 1352 (1949).
  3. R. F. Bacher and S. Goudsmit, Phys. Rev. 46, 948 (1934).
  4. D. R. Layzer, dissertation, Harvard University, Cambridge, Massachusetts (1950).
  5. R. E. Trees, Phys. Rev. 83, 756 (1951); 84, 1089 (1951); 85, 382 (1952).
  6. G. Racah, Phys. Rev. 85, 381 (1952).
  7. G. Racah, Lunds Univ. Arsskr. AVD. 2 50, 31 (1954).
  8. R. E. Trees and C. K. Jørgensen, Phys. Rev. 123, 1278 (1961).
  9. K. Rajnak and B. G. Wybourne, Phys. Rev. 132, 280 (1963).
  10. R. E. Trees, Phys. Rev. 129, 1220 (1963).
  11. J. Sugar, J. Opt. Soc. Am. 53, 831 (1963).
  12. C. W. Nielson and George F. Koster, Spectroscopic Coefficients for the pn, dn and fn Configurations (Technology Press, Cambridge, Massachusetts, 1963).
  13. B. G. Wybourne, J. Chem. Phys. 40, 1457 (1964).
  14. K. Rajnak, J. Chem. Phys. 37, 2440 (1962).
  15. G. F. Koster and C. W. Nielson, a magnetic tape entitled "Energy Matrices for all Configurations of Equivalent ƒ Electrons," Massachusetts Institute of Technology, Cambridge, Massachusetts.
  16. William C. Davidon, "Variable Metric Method for Minimization," Argonne National Laboratory Report, ANL-5990 Rev. (1959). This general procedure has been adapted for spectroscopic problems by T. Clements of our Math and Computing group.
  17. R. E. Trees, J. Opt. Soc. Am. 54, 651 (1964).
  18. R. E. Trees, Phys. Rev. 84, 1089 (1951).
  19. G. Racah, Phys. Rev. 89, 381 (1952).
  20. The present notation for the linear parameters is that of I. The β used by Trees17 is related to the present γ, although they are not identical. Trees's γ is 1/12 of our β.
  21. B. R. Judd, Operator Techniques in Atomic Spectroscopy (McGraw—Hill Book Company, Inc., New York, 1963).
  22. B. R. Judd and I. Lindgren, Phys. Rev. 122, 1802 (1961).
  23. B. R. Judd, Proc. Roy. Soc. (London) A250, 562 (1959). These coefficients also appear in the tabulation of Nielson and Koster.12

Bacher, R. F.

R. F. Bacher and S. Goudsmit, Phys. Rev. 46, 948 (1934).

Condon, E. U.

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

Davidon, William C.

William C. Davidon, "Variable Metric Method for Minimization," Argonne National Laboratory Report, ANL-5990 Rev. (1959). This general procedure has been adapted for spectroscopic problems by T. Clements of our Math and Computing group.

Goudsmit, S.

R. F. Bacher and S. Goudsmit, Phys. Rev. 46, 948 (1934).

Jørgensen, C. K.

R. E. Trees and C. K. Jørgensen, Phys. Rev. 123, 1278 (1961).

Judd, B. R.

B. R. Judd and I. Lindgren, Phys. Rev. 122, 1802 (1961).

B. R. Judd, Proc. Roy. Soc. (London) A250, 562 (1959). These coefficients also appear in the tabulation of Nielson and Koster.12

B. R. Judd, Operator Techniques in Atomic Spectroscopy (McGraw—Hill Book Company, Inc., New York, 1963).

Koster, G. F.

G. F. Koster and C. W. Nielson, a magnetic tape entitled "Energy Matrices for all Configurations of Equivalent ƒ Electrons," Massachusetts Institute of Technology, Cambridge, Massachusetts.

Koster, George F.

C. W. Nielson and George F. Koster, Spectroscopic Coefficients for the pn, dn and fn Configurations (Technology Press, Cambridge, Massachusetts, 1963).

Layzer, D. R.

D. R. Layzer, dissertation, Harvard University, Cambridge, Massachusetts (1950).

Lindgren, I.

B. R. Judd and I. Lindgren, Phys. Rev. 122, 1802 (1961).

Nielson, C. W.

G. F. Koster and C. W. Nielson, a magnetic tape entitled "Energy Matrices for all Configurations of Equivalent ƒ Electrons," Massachusetts Institute of Technology, Cambridge, Massachusetts.

C. W. Nielson and George F. Koster, Spectroscopic Coefficients for the pn, dn and fn Configurations (Technology Press, Cambridge, Massachusetts, 1963).

Racah, G.

G. Racah, Phys. Rev. 89, 381 (1952).

G. Racah, Lunds Univ. Arsskr. AVD. 2 50, 31 (1954).

G. Racah, Phys. Rev. 85, 381 (1952).

G. Racah, Phys. Rev. 76, 1352 (1949).

Rajnak, K.

K. Rajnak, J. Chem. Phys. 37, 2440 (1962).

K. Rajnak and B. G. Wybourne, Phys. Rev. 132, 280 (1963).

Shortley, G. H.

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

Sugar, J.

J. Sugar, J. Opt. Soc. Am. 53, 831 (1963).

Trees, R. E.

R. E. Trees, Phys. Rev. 84, 1089 (1951).

R. E. Trees, Phys. Rev. 83, 756 (1951); 84, 1089 (1951); 85, 382 (1952).

R. E. Trees and C. K. Jørgensen, Phys. Rev. 123, 1278 (1961).

R. E. Trees, Phys. Rev. 129, 1220 (1963).

R. E. Trees, J. Opt. Soc. Am. 54, 651 (1964).

Wybourne, B. G.

B. G. Wybourne, J. Chem. Phys. 40, 1457 (1964).

K. Rajnak and B. G. Wybourne, Phys. Rev. 132, 280 (1963).

Other (23)

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

G. Racah, Phys. Rev. 76, 1352 (1949).

R. F. Bacher and S. Goudsmit, Phys. Rev. 46, 948 (1934).

D. R. Layzer, dissertation, Harvard University, Cambridge, Massachusetts (1950).

R. E. Trees, Phys. Rev. 83, 756 (1951); 84, 1089 (1951); 85, 382 (1952).

G. Racah, Phys. Rev. 85, 381 (1952).

G. Racah, Lunds Univ. Arsskr. AVD. 2 50, 31 (1954).

R. E. Trees and C. K. Jørgensen, Phys. Rev. 123, 1278 (1961).

K. Rajnak and B. G. Wybourne, Phys. Rev. 132, 280 (1963).

R. E. Trees, Phys. Rev. 129, 1220 (1963).

J. Sugar, J. Opt. Soc. Am. 53, 831 (1963).

C. W. Nielson and George F. Koster, Spectroscopic Coefficients for the pn, dn and fn Configurations (Technology Press, Cambridge, Massachusetts, 1963).

B. G. Wybourne, J. Chem. Phys. 40, 1457 (1964).

K. Rajnak, J. Chem. Phys. 37, 2440 (1962).

G. F. Koster and C. W. Nielson, a magnetic tape entitled "Energy Matrices for all Configurations of Equivalent ƒ Electrons," Massachusetts Institute of Technology, Cambridge, Massachusetts.

William C. Davidon, "Variable Metric Method for Minimization," Argonne National Laboratory Report, ANL-5990 Rev. (1959). This general procedure has been adapted for spectroscopic problems by T. Clements of our Math and Computing group.

R. E. Trees, J. Opt. Soc. Am. 54, 651 (1964).

R. E. Trees, Phys. Rev. 84, 1089 (1951).

G. Racah, Phys. Rev. 89, 381 (1952).

The present notation for the linear parameters is that of I. The β used by Trees17 is related to the present γ, although they are not identical. Trees's γ is 1/12 of our β.

B. R. Judd, Operator Techniques in Atomic Spectroscopy (McGraw—Hill Book Company, Inc., New York, 1963).

B. R. Judd and I. Lindgren, Phys. Rev. 122, 1802 (1961).

B. R. Judd, Proc. Roy. Soc. (London) A250, 562 (1959). These coefficients also appear in the tabulation of Nielson and Koster.12

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