The ($d$, ${\mathrm{He}}^3$) reaction on ${\mathrm{Ca}}^{40}$ and isotopically enriched targets of ${\mathrm{Ti}}^{46}$, ${\mathrm{Ti}}^{47}$, ${\mathrm{Ti}}^{48}$, ${\mathrm{Ti}}^{49}$, and ${\mathrm{Ti}}^{50}$ has been investigated. Absolute differential cross sections for a number of transitions were obtained over an angular range from 11 to 33°. The angular distributions are compared with distorted-wave calculations which use the optical-model-potential parameters derived from the elastic scattering of 21-MeV deuterons on the same target materials. The data for the elastic scattering are given together with the optical-model fits. The ${\mathrm{Ca}}^{40}(d, {\mathrm{He}}^3){\mathrm{K}}^{39}$ reaction was used to obtain the normalization coefficients necessary to extract spectroscopic factors from the comparison of the measured and calculated differential cross sections. The results show that the excitation energies of the $d_{\frac{3}{2}}$ and $s_{\frac{1}{2}}$ proton-hole states are surprisingly low and increase with the number of $f_{\frac{7}{2}}$ neutrons in the nucleus. In the case of ${\mathrm{Sc}}^{45}$, the $d_{\frac{3}{2}}$ hole state which contains the full $d_{\frac{3}{2}}$ strength is found at an excitation energy of less than 50 keV. The excitation energy of the $d_{\frac{3}{2}}$ hole state increases to 800 keV for ${\mathrm{Sc}}^{47}$ and to about 2.4 MeV in ${\mathrm{Sc}}^{49}$. The excitation energy of the $s_{\frac{1}{2}}$ hole state increases from 0.92 MeV in ${\mathrm{Sc}}^{45}$ to 2.1 MeV in ${\mathrm{Sc}}^{48}$.

• Received 31 January 1964

DOI:https://doi.org/10.1103/PhysRev.134.B976