The role of the continuum and the spurious 1⁻ transitions in incoherent μ⁻ - e⁻ conversion rate calculations

Abstract

By using the Continuum RPA (CRPA) method, the incoherent transition strength of the exotic μ⁻ - e⁻ conversion in nuclei is investigated. The question whether excited nuclear states lying high in the continuum give an important contribution to the incoherent rate is addressed. Results for ⁴⁰Ca are compared with those obtained previously for ²⁰⁸Pb. For both nuclei we then investigate in detail the admixture of spurious components in the rate coming from 1⁻ excitations, within the self-consistent CRPA with Skyrme interactions as well as within a less consistent version. We employ and compare two methods for removing the spurious strength: the use of effective operators, as done in a previous work for ²⁰⁸Pb, or simply the exclusion of the spurious state appearing close to zero energy. In all cases, the correction achieved is quite large.