The giant resonance region of ${\mathrm{C}}^{12}$ and ${\mathrm{O}}^{16}$ is investigated using a continuum model, which is based on configuration mixing of negative-parity particle-hole states, with the particle in the continuum. Using this model $T=1\mathrm{}$, $J^{\pi }=1^{-}, \mathrm{and} 2^{-}$ electron-scattering spectra are calculated as well as the $0^{-}$, $1^{-}$, and $2^{-}$ nuclear-excitation spectra (or equivalently the neutrino spectra) in $\mu$ capture. The $\mathrm{SU}\left(4\right)\mathrm{}$ relationship ${M_P}^2={M_V}^2={M_A}^2$ is tested and found to be satisfied in both nuclei to better than 10%. In addition, the relationship $\left({M_V}^2\right)={\left({M_V}^2\right)}_{\mathrm{UD}}{\left|F_{\mathrm{el}}\right({{\nu }_{\mathrm{res}}}^2\left)\right|}^2$ is tested and found to hold to within 3%. Both of these results justify the previous work of Foldy and Walecka on calculations of total-muon-capture rates. The detailed behavior of the electron scattering spectra is examined as a function of momentum transfer with emphasis on the magnetic contribution to the $1^{-}$ transverse electric spectra and the giant magnetic quadrupole resonances. The momentum dependence of integrated form factors for certain regions of the excitation spectra is also investigated.

Close

PrevNext

View figure in article