Decay of Collective Nuclear States Excited in Muon Capture

Excitation of giant-dipole and related collective states has been found to give predominant contributions to muon capture. The present work obtains polarizations of the neutrons emitted in the subsequent decay of these states, for capture in some $0^{+}$ closed-shell nuclei (their angular distributions are shown to be isotropic). The polarization of the neutrons is due to the polarization of the captured muon, and is obtained both according to type (longitudinal and transverse) and according to magnitude (it depends on the configuration mixing of the dipole states). The generalized Goldhaber-Teller model is used for the calculation of the excitation, and Boeker's form of the Wigner $R$-matrix theory for the decay, together with standard Racah methods. In an Appendix, the longitudinal polarization of the directly emitted neutrons of highest energy following muon capture in nuclei, and its dependence on the weak coupling constants, are discussed briefly.