ANGULAR INTEGRATION USING SYMBOLIC STATE EXPANSIONS
C. Froese Fischer^a and D. Ellis^b
aDepartment of Computer Science, Box 1679B, Vanderbilt University, Nashville, TN 37235, USA
E-mail: Charlotte.F.Fischer@Vanderbilt.Edu
^bDepartment of Physics and Astronomy, University of Toledo, Toledo, OH 43606, USA
Received 23 April 2004

Dedicated to the 100th anniversary of Professor A. Jucys

Angular integrations are not concerned with the principal quantum numbers of orbitals, only their angular momentum coupling, although antisymmetry and normalization need to be considered. We show that by expressing wave function expansions in terms of certain symbolic states, the angular data needed for a calculation becomes largely independent of problem size under the assumption that one- and two-electron operators for matrix elements between two-electron states can be evaluated when needed. Furthermore, for the Coulomb interaction, all many-electron matrix elements between symbolic states arising from single and double excitations from a multireference set can be expressed in terms of a sum of contributions, each of which is a product of three factors: a constant, a two-electron matrix element, and a factor depending on the orbital quantum numbers of the interacting orbitals. The 1s²2s^{2 1}S beryllium ground state is considered in detail.

KAMPINIS INTEGRAVIMAS PANAUDOJANT SIMBOLINIUS BŪSENŲ SKLEIDINIUS
C. Froese Fischer^a, D. Ellis^b
aVanderbilto universitetas, Nešvilis, JAV
^bToledo universitetas, Toledas, JAV

Pateiktas bendras algoritmas atomo banginės funkcijos skleidiniui gauti ir įvairių atominių dydžių operatorių matriciniams elementams skaičiuoti. Elektrostatinės sąveikos operatoriaus matricinis elementas yra išreiškiamas kaip trijų daugiklių – konstantos, dvielektronio matricinio elemento ir daugiklio, priklausančio nuo sąveikaujančių elektronų orbitinių kvantinių skaičių, – sandauga. Išsamiai aprašyta berilio 1s²2s^{2 1}S pagrindinė būsena.