A new and effective means of calculating matrix elements relevant to direct interactions is introduced and applied to a distorted-wave $t$ matrix approximation analysis of the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}\mathrm{}(p,2p)\mathrm{}{}_{}{}^{11}{}_{}{}^{}\mathrm{B}$ and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}\mathrm{}(p,2p)\mathrm{}{}_{}{}^{15}{}_{}{}^{}\mathrm{N}$ reactions at 45-50 MeV incident energy. A realistic separable two-body $t$ matrix has been employed and core polarization, whereby the final state is generated after excitation of giant resonance target states, has been included. The integrals involved in the matrix elements were calculated analytically by making a parametrization of the distorted scattering wave functions, the nucleon-nucleon interaction, and the bound state wave function, the parameters being chosen in accordance with elastic ($p,p$) and inelastic ($p,p^{\prime }$) data and realistic shell model wave functions. The results indicate the inadequacy of a distorted-wave $t$-matrix approximation analysis at these energies.

[NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}\mathrm{}(p,2p)\mathrm{}$, $E=50\mathrm{}$ MeV; ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}\mathrm{}(p,2p)\mathrm{}$, $E=45\mathrm{}$ MeV; DWTA analysis, including resonance effects.]

• Received 28 February 1977

DOI:https://doi.org/10.1103/PhysRevC.17.473