Muon capture in nuclei

Abstract

Theoretical calculations of the total capture rate for muons in certain light nuclei (40Ca,16O,12C,4He) have been carried out with cognizance taken of the important role played by giant dipole resonances in the capture process. The calculation involves the following steps: 1) Relating the dipole contribution of the vector interaction to its unretarded value by the use of the ground-state elastic form factor. 2) Relating the unretarded dipole part of the vector interaction to an integral over the photo-disintegration cross-section (by the use of isotopic-spin invariance) and using empirical photo-disintegration data to evaluate this contribution. 3) Using the Wigner supermultiplet theory to relate the matrix elements of the axial vector and induced pseudoscalar interaction to those of the vector interaction. 4) Using the shell model (with and without the closure approximation) to evaluate other multipolar contributions and recoil correction terms. The assumptions implicit in the above steps have been examined in as much detail as present knowledge permits. In particular, arguments are given on the basis of several models to justify step 1). The basic assumption involved in the supermultiplet theory used in step 3) is that of weak spin-dependence of the forces. This theory predicts that the giant electric dipole resonance is one of a family (vector supermultiplet) of giant resonances involving spins and isospins. Evidence for the existence of at least one other such resonance is shown to exist in inelastic electron scattering data on16O. The effect of spin-dependence of the forces in splitting this giant resonance supermultiplet is investigated by examining the 0−, 1−, and 2− particle-hole states calculated by Lewis for16O: its effect in our calculations is relatively small. Agreement between theory and experiment is within the uncertainties of both (but with the possibility of a real discrepancy in1He) thus exhibiting general consistency of muon capture with the universality of weak interactions. Inelastic electron scattering data can be a rich source of information to serve as the basis for better calculations and for exploring the giant resonance supermultiplet.