Centre-of-mass effects in the nuclear shell-model

Abstract

An examination is made of the possible errors that may arise in nuclear shell-model calculations by failing to separate out centre-of-mass motions from the internal motions of the system; a central oscillator potential is used to make possible a simple analysis. The most important effect is the appearance of spurious states that do not refer to the internal motion at all; these must be considered whenever the state is described by two or more unclosed shells (in the sense of L-S coupling), as, for example, in the excited states of $^{16}$O.