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

A general program to calculate the matrix of the spin-orbit interaction
of 1
All materials on our website are shared by users. If you have any questions about copyright issues, please report us to resolve them. We are always happy to assist you.
Related Documents
  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.

Jalan terjal

May 18, 2018

Oda al sistema

May 18, 2018
Similar documents
View more...
Related Search
We Need Your Support
Thank you for visiting our website and your interest in our free products and services. We are nonprofit website to share and download documents. To the running of this website, we need your help to support us.

Thanks to everyone for your continued support.

No, Thanks