Observable Hyperfine Effects in Muon Capture by Complex Nuclei

Abstract

The capture rates, $\ensuremath{\Lambda}_{\ifmmode\pm\else\textpm\fi{}}^{}{}_{}{}^{\mathrm{cap}}$, of the two hyperfine states ${F}_{\ifmmode\pm\else\textpm\fi{}}$ of the ($p\ensuremath{\mu}$) atom are, in general, expected to be different (spin dependence of muon capture). This difference depends quantitatively on the details of the interaction Hamiltonian, being maximum for an F-GT (i.e., $V\ensuremath{-}A$ type) interaction. An experimental comparison for the ($p\ensuremath{\mu}$) system appears at present difficult, but related spin-dependence effects will be exhibited by bound protons, i.e., complex nuclei. Observable hyperfine (hf) effects of this kind form the object of this paper; their theory is summarized in Sec. II. The character of such effects is dominated by the rate $R$ at which the upper hf state can be converted into the true ground state (through an $M1$ Auger process). Section III contains a detailed calculation of $R$ for all cases of practical interest, while a variety of possible experiments are discussed in Sec. IV. The considerations of this section show that ${\mathrm{F}}^{19}$ constitutes the ideal target, leading to the largest and most readily analyzable effects. We performed three experiments with this target, viz., measured (1) the time distribution of the neutral capture products, (2) the asymmetry of the decay electrons, and (3) the time distribution of the latter; these measurements are described and analyzed in Secs. V through VII. We conclude (Sec. VIII) on the basis of measurements (1) and (3) that the interaction is definitely of the F-GT (as opposed to F+GT) type, assuming that both F and GT interactions are present. Invoking independent observations on muon capture by complex nuclei, this assumption becomes redundant, and we may conclude that the universal Fermi interaction ("$V\ensuremath{-}xA$") is implied by our results. This conclusion is in agreement with recent results on muon capture in liquid hydrogen. The conversion rate observed in experiments (1) and (3) (6.1\ifmmode\pm\else\textpm\fi{}0.7 \ensuremath{\mu}${\mathrm{sec}}^{\ensuremath{-}1}$) agrees with our prediction ($R=5.8$ \ensuremath{\mu}${\mathrm{sec}}^{\ensuremath{-}1}$), which is qualitatively confirmed by experiment (2).