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Manuscript Title: A general program to calculate the matrix of the spin-orbit interaction.
Authors: W.-D. Klotz
Program title: SPINORBITWEIGHTS
Catalogue identifier: AAKL_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 9(1975)102
Programming language: Fortran.
Computer: CDC 6600.
Operating system: SCOPE 3.4.
RAM: 26K words
Word size: 60
Keywords: Atomic physics, Fine structure, Complex atoms, Spin-orbit coupling, Hyperfine structure, Configuration Interaction, Ls-coupling, Recoupling, Racah, Tensor operator, Nj-symbols, Wave function, Coefficients of Fractional parentage.
Classification: 2.7.

Subprograms used:
Cat Id Title Reference
ACQB_v1_0 CFPP CPC 1(1969)15
ACQC_v1_0 CFPD CPC 1(1969)16
AAGD_v1_0 NJSYM CPC 1(1970)241

Revision history:
Type Tit le Reference
correction 000A CORRECTION 18/07/75 See below
adaptation 0001 WKAPPAKQ See below

Nature of problem:
In atomic structure calculations with configuration interaction, one has to evaluate the matrix of the hamiltonian with respect to a basis set of configuration wave functions. For configurations with several open shells, the calculation of the matrix elements becomes cumbersome. A general program, which calculates the two-body part of the hamiltonian, already exists. We submit a program, which calculates the one-body spin-orbit interaction.

Solution method:
The coefficients of the spin-orbit radial integrals are obtained by integration over the coordinates of N-1 spectator electrons and the angular coordinates of the interacting electron of an N-electron atom. We used the scheme of Fano in analogy to a one-particle operator, using techniques of Racah and Briggs. We modified the program of Hibbert and used some of his subroutines. The coefficients are expressed as sums over cfp-coefficients, recoupling coefficients and reduced matrix e elements. The configurations are defined by thier occupied nl-shells and their numbers of electrons. The coupling schemes are defined by the S, L-values of the shells and their intermediate couplings.

Restrictions:
Only configurations with any number of electrons in s-, p- and d-shells are allowed, but no more than two electrons in any shell of higher orbital momentum. The submitted version allows up to 3 different configurations, 10 occupied shells and 60 coupling schemes in each configuration.

Unusual features:
A punch option is provided, but a punch subroutine has to be written by the user according to his individual problems.

Running time:
The running time of the test run is 8.2 s on a CDC 6600 during which 64 matrix elements are calculated.

CORRECTION SUMMARY
Manuscript Title: A general program to calculate the matrix of the spin-orbit interaction. (C.P.C. 9(1975)102).
Authors: W.-D. Klotz
Program title: 000A CORRECTION 18/07/75
Catalogue identifier: AAKL_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 10(1975)70
Classification: 2.7.

ADAPTATION SUMMARY
Manuscript Title: Reduced matrix elements of summations of one-particle tensor products.
Authors: W.-D. Klotz
Program title: 0001 WKAPPAKQ
Catalogue identifier: AAKL_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 10(1975)56
Programming language: Fortran.
Computer: CDC 6600.
Operating system: SCOPE 3.4.
RAM: 2K words
Word size: 60
Classification: 2.7.

Subprograms used:
Cat Id Title Reference
AAGD_v1_0 NJSYM CPC 1(1970)241
ACQB_v1_0 P SHELL C.F.P. CPC 1(1969)15
ACQC_v1_0 D SHELL C.F.P. CPC 1(1969)16

Nature of problem:
This adaptation is a generalization of the program SPINORBITWEIGHTS and calculates the reduced matrix elements of a general tensor operator which may be written as a sum of N one-particle tensor operators as defined exactly by Armstrong and Feneuille. The operator is a "spin x orbital" tensor product with rank 'k' in the spin-space and rank k in the orbital space. The matrix elements will be calculated to the same basis set of configuration wave functions as described in the early code. With the use of this program any one-particle interaction in an N-electron atom, like multipole radiation or hyperfine structure interactions, may be calculated in a very efficient way.

Restrictions:
The program is restricted to configurations with any number of s-, p- and d-electrons, but no more than two electrons in any shell of higher orbital angular momentum. The wave functions are restricted to pure LS- coupling.

Running time:
The execution time for the test run is 13.6 s. During that time 165 matrix elements are calculated.