Matrix elements in the Ŝ²—adapted space

Abstract

Calculation of matrix elements in the spin eigenfunction basis has a long history (cf Pauncz 1979). The importance of this subject comes from the fact that for light molecules, where relativistic effects are negligible, the spin and the point group symmetries are the only symmetries of the system. Implementation of the abelian point group symmetry is rather trivial, being reduced to the choice of configurations of a proper symmetry. Non-abelian point group eigenfunctions on the other hand, are much harder to deal with than spin eigenfunctions, leaving the latter as the first non-trivial problem to attack. In recent years powerful group theoretical methods were applied to the problem of matrix element evaluation in Ŝ² —adapted spaces (cf Hinze 1981; Sutcliffe 1983 or McWeeny and Sutcliffe 1985). The same techniques are applicable also to eigenfunctions of isospin operator T̂ in nuclear shell-model calculations (cf Bohr and Mottelson 1969). Graphical approach that I will present here uses much simpler concepts than group theoretical approaches giving the same results.