(d, t) and (d,He3) Reactions on the Calcium Isotopes

The ${\mathrm{Ca}}^{42}(d, t){\mathrm{Ca}}^{41}$, ${\mathrm{Ca}}^{43}(d, t){\mathrm{Ca}}^{42}$, ${\mathrm{Ca}}^{44}(d, t){\mathrm{Ca}}^{43}$, ${\mathrm{Ca}}^{46}(d, t){\mathrm{Ca}}^{45}$, ${\mathrm{Ca}}^{48}(d, t){\mathrm{Ca}}^{47}$, ${\mathrm{Ca}}^{42}(d,{\mathrm{He}}^3){\mathrm{K}}^{41}$, ${\mathrm{Ca}}^{43}(d, {\mathrm{He}}^3){\mathrm{K}}^{42}$, and ${\mathrm{Ca}}^{44}(d, {\mathrm{He}}^3){\mathrm{K}}^{43}$, reactions have been investigated at an incident deuteron energy of 22 MeV. The angular distributions have been compared with distorted-wave calculations and the spectroscopic strength has been extracted. The larger fraction of the $d_{\frac{3}{2}}$ strength was found in the ${\frac{3}{2}}^{+}$ states at 2.02, 0.99, 1.89, and 2.60 MeV in ${\mathrm{Ca}}^{41}$, ${\mathrm{Ca}}^{43}$, ${\mathrm{Ca}}^{45}$, and ${\mathrm{Ca}}^{47}$, respectively. Strong $s$-wave transitions were observed to levels at 1.96, 2.40, and 2.60 MeV in ${\mathrm{Ca}}^{43}$, ${\mathrm{Ca}}^{45}$, and ${\mathrm{Ca}}^{47}$, respectively. The ${\mathrm{½}}^{+}$ hole state at 2.67 MeV in ${\mathrm{Ca}}^{41}$ was found to be less pure than the other strong $s$- and $d$-hole states. Similarly, a pronounced fractionation of the $s$-hole configuration among the levels at 0.982, 1.273, 1.595, and 2.73 MeV was found in ${\mathrm{K}}^{41}$—in contrast with the other even-parity hole states in ${\mathrm{K}}^{41}$ and ${\mathrm{K}}^{43}$ (including the ${\mathrm{½}}^{+}$ level at 0.56 MeV), which are rather pure. This splitting is attributed in part to the interaction of another ${\mathrm{½}}^{+}$ state with the $s$-proton hole state. Some $2p_{\frac{3}{2}}$ admixture was observed in each of the neutron pickup reactions and a $2p_{\frac{1}{2}}$ admixture was seen in ${\mathrm{Ca}}^{48}$. Comparison between the relative intensities of the transitions to the ${\frac{3}{2}}^{-}$ levels in ${\mathrm{Ca}}^{41}$ and ${\mathrm{Ca}}^{43}$ and those of the ($d, p$) reactions to those levels suggest the admixture of core-excited configurations in the ground state of ${\mathrm{Ca}}^{42}$ and ${\mathrm{Ca}}^{44}$. The upper limit for the $f_{\frac{7}{2}}$-proton admixture in the ground state of ${\mathrm{Ca}}^{42}$ was found to be $C^{2}S\le 0.4$. The second $0^{+}$ state in ${\mathrm{Ca}}^{42}$ is excited with about 10% of the strength of the first $0^{+}$ state. The strength of the transitions to the $0^{+}$ and $2^{+}$ states together with those of the $4^{+}$ and $6^{+}$ states is significantly smaller than expected from simple shell-model considerations and suggests that other levels with ${\left(f_{\frac{7}{2}}\right)}^2$ configurations exist in ${\mathrm{Ca}}^{42}$ at higher energies. The $l=0\mathrm{}$ transitions to states in ${\mathrm{Ca}}^{42}$ rarely mix with the $l=2\mathrm{}$ transitions. There is a fairly good correspondence between the $s$-hole states and the $3^{-}$ states. Application of the sum rule and comparison with the other reactions suggest that the total spectroscopic factor for $s_{\frac{1}{2}}$, $T=1\mathrm{}$ pickup is considerably smaller than would be expected from a closed $2s$ shell. The four lowest levels in ${\mathrm{K}}^{42}$ have $l=2\mathrm{}$ transitions and the strengths are in agreement with a $2^{-}$, $3^{-}$, $4^{-}$, $5^{-}$ sequence. In addition, $s$-proton hole states in ${\mathrm{K}}^{42}$ were observed at 1.2, 2.01, and 2.13 MeV. A possible $d_{\frac{5}{2}}$-hole state was found in ${\mathrm{K}}^{41}$ at an excitation energy of 3.566 MeV.