Nature of physical problem
The atomic hyperfine structure splitting is characterized by the hyper- fine interaction constants A and B. Within the effective tensor operator formalism [1] these hyperfine interaction constants can be expressed as a linear combination of products between the relativistic one-electron hyperfine structure parameters a nl kskl and b nl kskl and corresponding angular coefficients alpha nl kskl and beta nl kskl, respectively [2]. The problem is to calculate the angular coefficients for the case of pure SL-coupling and, alternatively, the case of intermediate coupling for electronic configurations with up to four open electron shells. Method of solution
The program Chfs calculates the angular coefficients alpha nl kskl and beta nl kskl directly by evaluating explicit expressions for the matrix elements, which have been derived by the method of Racah algebra from effective Hamiltonians of hyperfine structure. The program Chfs allows two types of couplings to compute the matrix elements: |[(Psi1,Psi2)Psi12,(Psi3,Psi4)Psi34]Psi> as derived in [3] and |{[(Psi1,Psi2)Psi12,Psi3]Psi13],Psi4}Psi>, see ref. [4]. In the case of intermediate coupling the angular coefficients are obtained by summing up a set of matrix elements, with fine structure mixing coefficients as weighting factors. Restrictions on the complexity of the problem
A configuration may have up to maximal four open electron (sub)shells. Because of the limited availability of fractional parentage routines [5-7], the program Chfs is restriced to handle s-, p-, d- and f-shells and at most two particles in higher shells. Typical running time
some minutes on 486PC References
[1] P.G.H. Sandars and J. Beck, Proc. R. Soc. London, Ser. A 289(1965)97
[2] W.J. Childs, Case Stud. At. Phys. 3(1973)215
[3] H.-D. Kronfeldt, G. Klemz, S. Kroger and J.-F. Wyart, Phys. Rev. A 48(1993)4500
[4] H.-D. Kronfeldt, G. Klemz and S. Kroger, in preparation
[5] D.C.S. Allison, Comp. Phys. Comm. 1(1969)15
[6] A.T. Chivers, Comp. Phys. Comm. 6(1973)88
[7] D.C.S. Allison and J.E. McNulty, Comp. Phys. Comm. 8(1974)246
for LaTeX users @article{SKroger1997-103,
author = {S. Kr\"oger and M. Kr\"oger},
title = {A program to compute the angular coefficients of the relativistic one-electron hyperfine structure parameters (Erratum)},
journal = {Comput. Phys. Commun.},
volume = {103},
pages = {97-99},
year = {1997}
}
\bibitem{SKroger1997-103} S. Kr\"oger, M. Kr\"oger,
A program to compute the angular coefficients of the relativistic one-electron hyperfine structure parameters (Erratum),
Comput. Phys. Commun. {\bf 103} (1997) 97-99.SKroger1997-103
S. Kr\"oger, M. Kr\"oger
A program to compute the angular coefficients of the relativistic one-electron hyperfine structure parameters (Erratum)
Comput. Phys. Commun.,103,1997,97-99 |
mk@mat.ethz.ch
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