Classification ofN13Levels by Partial Wave Analysis of Proton Scattering fromC12

Abstract

The nature of the excited levels in ${\mathrm{N}}^{13}$ between 2.24 and 5.64 Mev was investigated by analyzing the ${\mathrm{C}}^{12}\mathrm{}(p,p)\mathrm{}{\mathrm{C}}^{12}$ data of Goldhaber and Williamson. To carry out the analysis, the partial wave phase shifts were related to the level parameters by means of one level dispersion theory. Then by successive approximations of the level parameters, the partial wave expansion of the differential cross section for elastic scattering was fitted to the experimental curve. The analysis leads to the conclusion that the lower scattering anomaly is due to an $S_{\frac{1}{2}}$ level at 2.379 Mev above the ground state, and that the higher scattering anomaly results from a $P_{\frac{3}{2}}$ level at 3.501 Mev and a $D_{\frac{5}{2}}$ level at 3.549 Mev. Neither experiment nor analysis indicates any other levels in the range considered. It is shown that no other simple level assignment can account for the observed scattering cross section. The appearance of levels with $j=l+\frac{1}{2}$ instead of $j=l-\frac{1}{2}$ supports Mayer's hypothesis of level inversion in nuclei. The widths and energies of the levels obtained from the present analysis are in partial agreement with the values obtained from the ($p,\gamma$) reaction.