On the theory of muon capture by complex nuclei (II)

Abstract

Results of shell model calculations on total muon capture rates are presented for a number of nuclei. Previous calculations on 16O and 40Ca are extended. It is studied in particular in which way the total capture rates depend on the depth of the finite potential well used for calculating the shell model wave functions. It is found that variations of the well depth, which cause a large variation of the fraction of final neutrons in bound or continuum states, cause only rather small variations in the total capture rates. A study is made of total capture rates in even nuclei with Z = 20 or N = 28 , such as 40Ca, 44Ca, 50Ti, 52Cr, 54Fe. It is argued that the variation of the total square of the nuclear matrix elements for muon capture will be linear with Z and N in a reasonable approximation. The nuclear matrix elements and capture rates are calculated using shell model wave functions, comparing results for infinite and finite potential wells for deriving the wave functions. The results for these nuclei depend on the V or A character of the interaction, but also on details of the nuclear model used, in such a way that it seems difficult to determine a reliable value for the ratio of the V and A coupling constants from such data.