Detailed calculations for muon capture rates within the quasi-particle RPA

Abstract

Detailed calculations for bound muon capture in complex nuclei are performed by employing the quasi particle random phase approximation (QRPA). The required bound muon wavefunctions for the large and the small components of the Dirac muon wavefunctions are obtained by using the genetic algorithm approach. We ob- tained contributions for 2p muon orbit; that is to say wavefunctions for atomic ex- cited state of the muonic atoms in nucleus 28Si. As a byproduct the above method give the corresponding energies to these wavefunctions which are compared with those of other methods. Our goal is to use the method developed recently by Laganke, Zinner and Vogel and our advantageous numerical approach to obtain state by state calculations of the muon capture rates within the QRPA.