Comparisons of BCS Nuclear Wave Functions with Exact Solutions. II. Particle-Number-Conserving Method

Abstract

We investigate whether, in the nuclear pairing theory of the BCS type, a sudden transition from configuration mixing to nonconfiguration mixing state at a critical force strength $G_c$ is a physical phenomenon. The variational method taking the components of the BCS wave function with correct particle number shows that such a transition is an artificial feature of the theory arising mainly from the number fluctuation in the wave function. The effect of a 4-quasiparticle component in the number-conserving method is to improve higher order amplitudes of the wave function, to necessitate a reduction of $\Delta$, and to modify the roles of the $u$ and $v$ parameters. The absence of a sudden transition is expected to have some bearing on the question of whether a discontinuous "Mottelson-Valatin effect" in the nuclear rotational spectra does exist in nature.