Semileptonic weak and electromagnetic interactions in nuclei: Recoil polarization in muon capture

Abstract

An analysis of the polarization of the recoiling nucleus following the capture of polarized muons by nuclei is performed. New general expressions for abitrary nuclear spin are obtained in terms of the same reduced matrix elements which govern inelastic electron scattering and β -decay. As an application we consider the A = 12 system and study uncertainties in the nuclear structure by using different sets of one-body density matrices. With the canonical values of the weak form factors (i.e. absence of second-class currents) we achieve a fairly good agreement with the experimental data including the inelastic form factor at high momentum transfers and the recently measured average 12B polarization. Implications Of the new corrected value of the average polarization on weak form factors and nuclear structure are discussed.