A formalism for inelastic nucleon scattering from nuclei is developed which takes into account explicitly the effect of giant multipole resonance states. The transition amplitudes derived from this formalism, when energy averaged, separate into two primary components. The first is the slowly energy varying direct reaction amplitude that is mediated by an effective interaction while the second is the energy varying semidirect reaction amplitude associated with doorway state excitations of giant resonances. The determination of quantum numbers and associated properties of giant resonances follow from analyses of inelastic nucleon scattering to low lying nuclear states. Specifically, from the application to the inelastic scattering of 23 to 45 MeV protons from ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ leading to the $1^{+}$ (12.71 MeV $T=0\mathrm{} \mathrm{and} 15.1$ MeV $T=1\mathrm{}$) states, the strength distributions of the giant isovector $E1\mathrm{}$ and isoscalar $E2\mathrm{}$ and $E3\mathrm{}$ resonances are determined.

NUCLEAR REACTION ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(p, p^{\prime })$, $E=22.5-45\mathrm{}$ MeV; measured $\sigma \left(\theta \right)$; DWBA analysis; included resonance effects; deduced ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ giant dipole, giant quadrupole strength distribution.

• Received 24 July 1975

DOI:https://doi.org/10.1103/PhysRevC.12.1697