A theoretical estimate of the influence of the character of the four-fermion interaction on the muon capture rate

Abstract

The four fermion interaction for muon capture may contain the Fermi interaction as well as the Gamow-Teller interaction, similar to the situation for the beta radioactivity. Theoretical calculations of the muon capture rate were made for both types of interaction for the nuclei from Ca to Ni, assuming nuclear shell structure. It follows that an experimental determination of the ratio of Fermi to Gamow-Teller interaction should be feasible by measuring the ratio of muon capture rates in suitably chosen nuclei (preferably the separated isotopes, although the use of the natural isotope mixtures is not quite excluded). The ratio of the capture rates for two nuclei differs often up to 50% for Fermi and Gamow-Teller interaction. As several simplifying assumptions were made, the results of the calculations may have more qualitative than quantitative significance; however, the results obtained seem to justify further theoretical and experimental work on the subject. The published experimental data do not allow to draw any conclusions with certainty, but may contain an indication for preponderant Gamow-Teller interaction.