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A general program to calculate the matrix of the spin-orbit interaction

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Computer Physics Communications 9 1975) 102-116 © North-Holland Publishing Company C-295
A GENERAL PROGRAM TO CALCULATE THE MATRIX OF THE SPIN ORBIT INTERACTION
W.-D. KLOTZ
Technische Universitaet Berlhl Institut fiir Strahlungs und Kernphysik 1000 Berlin 37 Rondellstrasse 5 Germany
Received 4 June 1974 P~.OGRAM
SUMMARY
Title of program:
SPINORBIT WEIGHTS
Catalogue number:
AAKL
Computer:
CDC 6600;
Installation:
Technical Univ. Berlin, Germany
Operating system or monitor under which the program is executed:
Scope 3.4
Programming language used:
Fortran
High speed storage required:
26278 words
No. of bits in a word:
60
Overlay structure:
None
No. of magnetic tapes required:
None
Other peripherals used:
Card reader, line printer
No. of cards hi combbaed program and test deck:
1549
CPC Library subprograms used: Catal. no. : Title: Ref. in CPC:
ACQB CFPP 1 1969) 15 ACQC CFPD 1 1969) 16 AAGD NJSYM 1 1970) 241
Keywords:
Atomic, structure, fine structure, hyper-fine struc- ture, configuration interaction, complex atoms, wave func- tion, spin-orbit coupling, LS-coupling, recoupling, Racah, tensor operator, N/-symbols, coefficients of fractional paren- tage.
Nature of physical problem
In atomic structure calculations with configuration interac- tion, one has to evaluate the matrix of the hamiltonian with respect to a basis set of configuration wave functions. For con- figurations with several open shells, the calculation of the ma- trix elements becomes cumbersome. A general program, which calculates the two-body part of the hamiltonian, exists al- ready [ 1 ]. We present a program which calculates the one- body spin-orbit interaction.
Method of solution
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 [2] in analogy to a one-particle operator, using techniques of Racah [3] and Briggs [4]. We modified the program of Hibbert [1] and used some of his subroutines. The coefficients are expressed as sums over cfp-coefficients [ 51, recoupling coefficients [ 6 ] and reduced matrix elements [7, 8]. The configurations are de- fined by their occupied n/-shells and their numbers of elec- trons. The coupling schemes are defined by the S,L-values of the shells and their intermediate couplings.
Restrictions on the complexity of the problem
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 al- lows up to 3 different configurations, 10 occupied shells and 60 coupling schemes in each configuration.
Typical rumthlg time
The running time of the test run is 8.2 sec on a CDC 6600 during which 64 matrix elements are calculated.
Unusual features
A punch option is provided, but a punch subroutine has to be written by the user according to his individual problems.
References
[1] A. Hibbert, Computer Phys. Commun. 1 1969) 359 and 2 1971) 180. [2] U. Fano, Phys. Rev. 140, 1A 1965) A67. [3] G. Racah, Phys. Rev. 63 1943) 367. [4] J.S. Briggs, J. Math. Phys. 11, 4 1970) 1198. [5l D.C.S. Allison, Computer. Phys. Commun. 1 1969) 15. [6] P.G. Burke, Computer. Phys. Commun. 1 1970) 241. [7] A.R. Edmonds, Angular Momentum in Quantum Me- chanics Princeton Univ. Press, 1960). [8] S. Feneuille, J. Phys. Radium 28 1967) 61.

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