Partial and Total Capture Probabilities of Negative Muons byC12

Abstract

The capture probability of negative muons by the ${\mathrm{C}}^{12}$ nucleus is calculated as a sum of partial transition rates to the individual levels of ${\mathrm{B}}^{12}$. The calculation is based on an extreme single-particle shell model. The calculation is an application of the general formalism developed by Morita and Fujii for predicting the transition rate between two definite nuclear states, following muon capture. Regarding bound-state captures, the agreement between theory and experiment is good. An exception is the prediction concerning the 1.67-MeV level of ${\mathrm{B}}^{12}$, the calculated transition rate being too large by a factor whose lower limit is about 2. This casts some doubt on the spin and parity assignments currently accepted for this level. The total capture probability is too small by a factor of 2, as is the ratio of unbound-to-bound captures. The discrepancy is accounted for in part by the existence of little-known, highly excited virtual states of ${\mathrm{B}}^{12}$. These conclusions are of limited scope because of the use of the single-particle shell model.