We study the weak proton-induced muon production reaction using the impulse approximation. The process is studied below threshold for real pion production assuming a ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ target. The theoretical predictions for muon angular distributions are given for the ground state, low-lying excited states, and the energetically available nuclear continuum. The process is a very rare event using presently available beam intensities. We argue that corrections to the impulse approximation are expected to be important and indicate how to use partial conservation of axial vector current and experimental ($p$,$\pi$) results to obtain more reliable estimates. The reaction can be a rich additional source of information regarding the relationship between the many-body pion source current and the space and time components of the nuclear axial current. Even with the conjectured substantial increase over the impulse approximation, the subthreshold counting rate seems too low for detailed experimental investigation at this time. A simple exploratory experiment starting above pion threshold and working downward in energy is suggested.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$($p$,${\mu }^{+}\nu$)${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$, $E_p\simeq 148$ MeV, calculated $\sigma \left(\theta \right)$ and ${\sigma }_T$ impulse approximation, PCAC extensions.

• Received 24 August 1981

DOI:https://doi.org/10.1103/PhysRevC.25.991