Nuclear structure ofK46: Studies withCa48(d,αγ)K46and deuteron-transfer reactions

The reactions ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}(d,\alpha ){}_{}{}^{46}{}_{}{}^{}\mathrm{K}$ and ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}(d,\alpha \gamma )$ were studied at $E_d=17\mathrm{} \mathrm{and} 7$ MeV, respectively. Angular distributions for the ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}(d,\alpha )$ reaction were obtained in 5° steps from ${\theta }_{\mathrm{lab}}=10\mathrm{}°$ to ${\theta }_{\mathrm{lab}}=145\mathrm{}°$. Data for $\theta \le 60°$ were taken with a split-pole spectrograph with resolutions of 13-25 keV. Only the levels at 0, 0.587, 0.691, 0.886, 1.370, 1.738, and 1.941 MeV were seen significantly above background. Excitation functions for $16\le E_d\le 17$ MeV at $\theta =90\mathrm{} \mathrm{and} 100°$ showed energy dependent cross section variations of ≲ ± 15% for the ground state and 0.587 MeV level, larger ones for the 1.738 MeV state and negligible variations for the 0.691, 0.886, and 1.941 MeV levels. The level energies listed were also deduced from the fast $\alpha -\gamma$ coincidence spectra which also served to set independent spin limits. A simultaneous microscopic distorted wave Born approximation analysis for the ($d,\alpha$) data and the ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}(p,{}_{}{}^3{}_{}{}^{}\mathrm{He})$ and ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}\mathrm{}(p,t)\mathrm{}{}_{}{}^{46}{}_{}{}^{}\mathrm{Ca}$ ($T=4\mathrm{}$) cross sections previously studied at $E_p=42\mathrm{}$ MeV was performed. Under the assumption that ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$ is doubly magic theoretical and empirical wave functions for the six low-lying negative parity states of ${}_{}{}^{46}{}_{}{}^{}\mathrm{K}$ were deduced and used to derive empirical ${\left(s_{\frac{1}{2}}{f}_{\frac{7}{2}}\right)}^2$, ${\left(d_{\frac{3}{2}}{f}_{\frac{7}{2}}\right)}^2$, and ($s_{\frac{1}{2}}{f}_{\frac{7}{2}},d_{\frac{3}{2}}{f}_{\frac{7}{2}}$) residual $n-p$ interaction matrix elements. The ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}(d,\alpha )$ reaction at 17 MeV, as well as the ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}(p,{}_{}{}^3{}_{}{}^{}\mathrm{He})$ and the ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}\mathrm{}(p,t)\mathrm{}$ transitions at $E_p=42\mathrm{}$ MeV show some features that cannot be explained by one-step direct two-nucleon transfer. The excitation of unnatural parity states in ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}\mathrm{}(p,t)\mathrm{}{}_{}{}^{46}{}_{}{}^{}\mathrm{Ca}$ ($T=24\mathrm{}$) and the importance of $L>j-1\mathrm{}$ transitions for the corresponding states in ${}_{}{}^{46}{}_{}{}^{}\mathrm{K}$ point to significant two-step contributions. Similarly, the triplet ($\Delta S=1\mathrm{}$), ($\Delta T=0\mathrm{}$) transfers in ($p,{}_{}{}^3{}_{}{}^{}\mathrm{He}$) are underpredicted with respect to singlet transfers.