The ($\alpha , d$) reactions on targets of ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$, and ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ were studied using $\alpha$-particle beams of 40.1, 46.0, 45.4, and 44.5 MeV, respectively. Angular distributions were obtained. States where the captured protonneutron pair is in the ${{\left(1\mathrm{}{d}_{\frac{5}{2}}\right)}_{5+,0}}^2$ configuration coupled to an unperturbed target core are located and possible spin assignments are suggested. These states are ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$, 13.03 MeV ($\frac{11}{2}-$), 11.95 MeV ($\frac{9}{2}-$); ${}_{}{}^{16}{}_{}{}^{}\mathrm{N}$, 5.75 MeV (5+); ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$, 7.74 MeV ($\frac{11}{2}-$), 9.14 MeV ($\frac{9}{2}-$); ${}_{}{}^{22}{}_{}{}^{}\mathrm{Na}$, 1.528 MeV (5+). Separated isotopes ${}_{}{}^{52}{}_{}{}^{}\mathrm{Cr}$, ${}_{}{}^{54,56}{}_{}{}^{}\mathrm{Fe}$, ${}_{}{}^{58,60,62}{}_{}{}^{}\mathrm{Ni}$, and ${}_{}{}^{64,66,68}{}_{}{}^{}\mathrm{Zn}$ were used as targets to study the ($\alpha , d$) reaction with a 50-MeV $\alpha$-particle beam. States with a probable configuration of ${{\left(1\mathrm{}{g}_{\frac{9}{2}}\right)}_{9+,0}}^2$ were located. These states are ${}_{}{}^{54}{}_{}{}^{}\mathrm{Mn}$, 9.47 MeV; ${}_{}{}^{56}{}_{}{}^{}\mathrm{Co}$, 8.92 MeV; ${}_{}{}^{58}{}_{}{}^{}\mathrm{Co}$, 6.79 MeV; ${}_{}{}^{60}{}_{}{}^{}\mathrm{Cu}$, 5.99 MeV; ${}_{}{}^{62}{}_{}{}^{}\mathrm{Cu}$, 4.75 MeV; ${}_{}{}^{64}{}_{}{}^{}\mathrm{Cu}$, 4.57 MeV; ${}_{}{}^{66}{}_{}{}^{}\mathrm{Ga}$, 2.99 MeV; ${}_{}{}^{68}{}_{}{}^{}\mathrm{Ga}$, 2.88 MeV; ${}_{}{}^{70}{}_{}{}^{}\mathrm{Ga}$, 2.88 MeV. The residual-interaction energies between the proton and neutron in the configurations ${{\left(1\mathrm{}{d}_{\frac{5}{2}}\right)}_{5+,0}}^2$, ${{\left(1\mathrm{}{f}_{\frac{7}{2}}\right)}_{7+,0}}^2$, and ${{\left(1\mathrm{}{g}_{\frac{9}{2}}\right)}_{9+,0}}^2$ were derived from the excitation energies determined in the present work and previous work on ${{\left(1\mathrm{}{d}_{\frac{5}{2}}\right)}_{5+,0}}^2$ and ${{\left(1\mathrm{}{f}_{\frac{7}{2}}\right)}_{7+,0}}^2$ states. For $T_z\ne 0$ nuclides, an "interactionmodel" method was proposed to extract the residual-interaction energy. The mean values of the residualinteraction energies are about -3.9, -3.0, and -2.2 MeV, respectively, for the three mentioned configurations. There is a slight decrease of residual-interaction energy with increasing $A$. These results are reproduced satisfactorily by conventional shell-model calculations. Both the interaction-model method and Talmi's shell-model calculation method were used to calculate the excitation energies of states with the ${{\left(1\mathrm{}{d}_{\frac{5}{2}}\right)}_{5+,0}}^2$ configuration. In general, the former method gives better agreement with the experimental results.

• Received 19 May 1969

DOI:https://doi.org/10.1103/PhysRev.186.1086