Exact solutions to the center of mass problem in a model theory

Abstract

A model theory, standard time-independent perturbation theory in a harmonic oscillator shell model basis, is used to investigate various aspects of the center of mass problem. In this model it is shown that the center of mass problem can be solved by projection techniques, but that the way in which one projects is crucial. The apropriate projection functions are found to be $\mathrm{const}\ifmmode\times\else\texttimes\fi{}{R}^{\ensuremath{-}\frac{3}{2}}$ for wave function projection and 1 for density projection. The former illustrates, among other things, that the center of mass problem cannot be solved by simply eliminating the spurious components of the wave function. The latter agrees with the Gartenhaus-Schwartz prescription. Also, explicit center of mass corrections are calculated.NUCLEAR STRUCTURE Methods for treating center of mass effects tested in a model theory.