Symmetrieverletzende Modellzustände und kollektive Bewegungen

Abstract

A variational procedure is investigated which leads to solutions that can describe collective modes connected with symmetries of the Hamiltonian in a non-phenomenological way. Starting from a given set of trial ware functions {Φ} all superpositions of the symmetry-transforms of anyΦ are permitted in addition. The trial wave functionsΦ and the weight functions of the superposition are varied simultaneously. The solutions are shown to be eigenfunctions of the symmetry operators. The weight functions are partly determined by group properties. In the case of one-dimensional representations, i.e. especially for Abelian symmetry groups, the superposition degenerates to become a projection.

In the limit of a strongly symmetry-violating solutionΦ the energy spectrum is also determined by group properties and the weight function may be interpreted as the wave function of a collective motion. The equations of motion will then describe the interaction between collective and intrinsic modes.

The non-axial rotator is considered as an example.