Muon Capture in C12 and Nuclear Structure

TLDR: In this article, the effect of the finite size of the nucleus on the muon wave functions is easily taken into account, and an excellent fit to the ex-perimental data for the capture rate as well as for the ft value has been obtained with the B12 wave function proposed by Kurath to explain the magnetic moment of B12 and a C 12 wave function introduced by Cohen and Kurath.

Abstract: general p-shell wave functions which were obtained by considering the dynamical properties in the A = 12 system. Our theoretical formula for the capture rate is of such a form that the effect of the finite size of the nucleus on the muon wave functions is easily taken into account. The experimentalft value of B12, which in all previous theories is used to normalize the muon capture rate, has not been adopted in our analysis. An excellent fit to the ex­ perimental data for the capture rate as well as for the ft value has been obtained with the B12 wave function proposed by Kurath to explain the magnetic moment of B12 and a C12 wave function introduced by us. These wave functions have slightly different values of configuration mixing parameters from those originally given by Cohen and Kurath. The value for the oscillator strength parameter which we use is b= 1.64 f; this is in conformity with the elastic and most of the inelastic electron scattering data. On the other hand, should b be taken as 1.90 f, the value derived from the analysis of the inelastic electron scattering data associated with the 15.1 MeV level in 0 2, it is relatively difficult to have a simultaneous fit to the data for the capture rate and the ft value. Our results are based on the assumptions of 1) uni­ versality of the V-A interaction in muon capture and beta decay, 2) the validity of the con­ served vector current theory, and 3) the induced pseudoscalar coupling constant estimated by Goldberger and Treiman.