Muon Capture and Inelastic Electron Scattering inC12andO16

The dipole (first-forbidden) contribution to the muon-capture matrix elements $M_V$, $M_A$, and $M_P$, is calculated using wave functions computed in the particle-hole theory. It is found that ${\left(M_{V^2}\right)}_D={\left(M_{A^2}\right)}_D={\left(M_{P^2}\right)}_D$ to within 13%. The assumption that the dipole part of the nuclear matrix element may be expressed as the unretarded dipole matrix element multiplied by the elastic form factor is found to hold to about 1%. Calculations of inelastic electron scattering from the $2^{-}$, $T=1\mathrm{}$ states in these nuclei predict large cross sections for some of the states at about 100 MeV/c momentum transfer. These "giant-magnetic-quadrupole states" are identified with observed levels found in recent 180° electron-scattering experiments.