Nuclear-Structure Studies of the Chromium Isotopes: TheCr50(p,p′)Cr50andCr50(d,p)Cr51Reactions

The ${\mathrm{Cr}}^{50}(p,p^{\prime }){\mathrm{Cr}}^{50}$ and ${\mathrm{Cr}}^{50}\mathrm{}(d,p)\mathrm{}{\mathrm{Cr}}^{51}$ reactions have been studied using 7.5-MeV protons and deuterons from the MIT-ONR electrostatic generator and the MIT multiple-gap spectrograph to analyze the reaction protons. Fifteen levels in ${\mathrm{Cr}}^{50}$ up to an excitation energy of 3.929 MeV and 156 levels in ${\mathrm{Cr}}^{51}$ up to an excitation energy of 7.931 MeV were observed. The ground-state $Q$ value for the ($d,p$) reaction was measured as 7.041±0.006 MeV. A zero-range, distorted-wave Born-approximation (DWBA) analysis was used to obtain values for the orbital angular momentum of the transferred neutrons and transition strengths for 52 levels. Three optical-model potentials for the deuteron were used in the DWBA analysis, each giving satisfactory fits to both elastic scattering and ($d,p$) data. The results are compared with shell-model, sum-rule limits, and with the level structure of other $N=27\mathrm{}$ nuclei (${\mathrm{Ca}}^{47}$ and ${\mathrm{Ti}}^{49}$).