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

Abstract

Various nuclear models and methods of calculation for total muon capture rates by complex nuclei are compared. The statistical model is worked out with improved accuracy for N = Z nuclei. Calculations with a simple shell model are made with and without the use of the closure approximation for wave functions calculated with the following potential wells: harmonic oscillator well, infinite potential well, finite potential well. Various corrections are considered, e.g., the influence of the velocity dependent terms. Numerical results are given for 16O and 40Ca. The various models are in reasonable mutual agreement and the closure approximation turns out to be rather reasonable. The coupling constants derived from the experimental capture rates for 16O and 40Ca agree with each other within 10%, but are about 50% lower than the value required according to a universal Fermi interaction. The deviation from this value may arise from the use of wave functions in our models which are not yet sufficiently realistic.