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Manuscript Title: A program for computing magnetic dipole and electric quadrupole hyperfine constants from MCHF wavefunctions.
Authors: P. Jonsson, C.-G. Wahlstrom, C.F. Fischer
Program title: MCHF_HFS
Catalogue identifier: ACLE_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 74(1993)399
Programming language: Fortran.
Computer: VAX 11/780.
Operating system: VMS, ULTRIX, Sun UNIX.
RAM: 210K words
Word size: 32
Peripherals: disc.
Keywords: Atomic physics, Structure, Hyperfine structure, A factor, B factor, Orbital term, Spin-dipole term, Fermi contact term, Electric quadrupole term, Mchf calculation, Ci calculation.
Classification: 2.1.

Subprograms used:
Cat Id Title Reference
ABZU_v1_0 MCHF_LIBRARIES CPC 64(1991)399
ABZV_v1_0 MCHF_GENCL CPC 64(1991)406
ABZW_v1_0 MCHF_NONH CPC 64(1991)417
ABZX_v1_0 MCHF_88 CPC 64(1991)431
ABZY_v1_0 MCHF_BREIT CPC 64(1991)455
ABZZ_v1_0 MCHF_CI CPC 64(1991)473
ACBA_v1_0 MCHF_MLTPOL CPC 64(1991)486
ACBB_v1_0 MCHF-LSTR AND MCHF_LSJTR CPC 64(1991)501

Nature of problem:
The atomic hyperfine splitting is determined by the hyperfine interaction constants AJ and BJ [1]. In strong external magnetic fields, where J is no longer a good quantum number, the splitting is also affected by the off-diagonal hyperfine constants AJ,J-1, BJ,J-1 and BJ,J-2 [2,3,4]. This program calculates the hyperfine constants using an electronic wavefunction generated with the MCHF or MCHF_CI programs of Froese Fischer [5].

Solution method:
The electronic wavefunction, Psi, for a state labelled gammaJ can be expanded in terms of configuration state functions, Psi = Sigmaj (cj Phi(gammaj *Lj *Sj *J). The hyperfine constants can then generally be calculated as Sigmaj,k (cj ck coef(j,k)(gammaj *Lj *Sj ||T**(K)|| gammak *Lk *Sk)) where T**(K) is a spherical tensor operator of rank Kappa. Evaluation of the reduced matrix element between arbitrarily LS coupled configurations is done by an extended version of the program TENSOR originally written by Robb [6,7,8].

Restrictions:
The orthogonality constraints are relaxed only within the restrictions described in [9], giving rise to at most two overlap integrals multiplying the one-electron active radial integral. Any number of s-, p-, or d-electrons are allowed in a configuration subshell, but no more than two electrons in a subshell with l>=3. If l>=4, the LS term for the subshell is restricted to those allowed for l=4. Only the subshells outside a set of closed subshells common to all configurations need to be specified. A maximum of 5 (five) subshells (in addition to common closed subshells) is allowed. This restriction may be removed by changing dimension statements and some format statements.

Unusual features:
The program allows for a limited degree of non-orthogonality between orbitals in the configuration state expansion.

Running time:
The CPU time required for the test cases is 0.1 seconds for the first and 0.19 seconds for the second on a SUN SPARC-station 330.

References:
[1] I.Lindgren and A. Rosen, Case Stud. At. Phys. 4(1974)93.
[2] G.K. Woodgate, Proc. Roy. Soc. London A293, (1966)17.
[3] J.S.M. Harvey, Proc. Roy. Soc. London A285, (1965)581.
[4] H. Orth, H. Ackermann and E.W. Otten, Z. Physik A 273 (1975)221.
[5] C.F. Fischer, Comp. Phys. Commun. 64(1991)431,473.
[6] W.D. Robb, Comp. Phys. Commun. 6(1973)132; 9(1985)181.
[7] R. Glass and A. Hibbert, Comp. Phys. Commun. 11(1976)125.
[8] C.F. Fischer, M.R. Godefroid and A. Hibbert, Comp. Phys. Commun. 64(1991)486.
[9] A. Hibbert, C.F. Fischer and M.R. Godefroid, Comp. Phys. Commun. 51(1988)285.