Shell Model Calculations of the Hyperfine Effect inμ-Meson Capture

Numerical values for the difference in $\mu$-meson capture rates from the two hyperfine states of a mesonic atom are obtained for ${\mathrm{F}}^{19}$, ${\mathrm{Al}}^{27}$, and ${\mathrm{P}}^{31}$, employing the simple Mayer-Jensen version of the shell model for ${\mathrm{Al}}^{27}$ and ${\mathrm{P}}^{31}$, and an intermediate coupling version for ${\mathrm{F}}^{19}$. In all these cases, we get considerably larger values than those found in previous estimates, thus rendering experiments more feasible. In view of the consequences of atomic conversion on the observation of the capture-rate differences, conversion effects in the rate and asymmetry of $\mu$-meson decay electrons are discussed also.