Shell model study of ${}^{40}$Ca muon capture and the $(0^{+},0)$$\to$$(0^{-},2626)$ axial charge transition

Abstract

We report results from shell model studies of muon capture on ${}^{40}$Ca to low-lying levels of ${}^{40}$K. We discuss the comparison between calculated capture rates, measured capture rates and analogous transitions in ($e$,$e^{\prime }$) scattering in terms of the particle-hole structure of the ${}^{40}$Ca-${}^{40}$K nuclei. We highlight the ${}^{40}$Ca$(0^{+},0)$$\to$${}^{40}$K$(0^{-},2626)$ axial charge transition and its sensitivity to the induced pseudoscalar coupling $g_p$ of the proton's weak interaction. In addition, we address the hindrance of unique first-forbidden transitions due to particle-hole interactions and the emergence of allowed Gamow-Teller transitions due to ground state correlations. Lastly, we examine the longitudinal alignment of ${}^{40}$K recoils following muon capture, and discuss this possibility for independently determining the induced coupling $g_p$.

Comments: 29 pages, 4 figures, submitted to Phys. Rev. C