Level structure ofMn57from aMn55(t, p)Mn57reaction study and a mixed-configuration shell model calculation

Twenty-seven levels below 2.7 MeV excitation in ${}_{}{}^{57}{}_{}{}^{}\mathrm{Mn}$ have been identified using the ${}_{}{}^{55}{}_{}{}^{}\mathrm{Mn}(t, p){}_{}{}^{57}{}_{}{}^{}\mathrm{Mn}$ reaction. Of these levels 18 were not reported in an earlier ${}_{}{}^{54}{}_{}{}^{}\mathrm{Cr}(\alpha , p){}_{}{}^{57}{}_{}{}^{}\mathrm{Mn}$ and ${}_{}{}^{54}{}_{}{}^{}\mathrm{Cr}(\alpha , p\gamma ){}_{}{}^{57}{}_{}{}^{}\mathrm{Mn}$ work. From a distorted-wave Born approximation analysis of the angular distributions for states up to 2.1 MeV, the $J=\frac{5}{2}$ ground state spin was confirmed and $J=\frac{5}{2} \mathrm{and} \left(\frac{11}{2}\right)$ spin assignments were made to levels at 1837 and 1916 keV, respectively. Further, the $L$ values extracted from the ${}_{}{}^{55}{}_{}{}^{}\mathrm{Mn}(t, p){}_{}{}^{57}{}_{}{}^{}\mathrm{Mn}$ angular distributions were consistent with all of the tentative spin assignments given in the ${}_{}{}^{54}{}_{}{}^{}\mathrm{Cr}(\alpha , p\gamma ){}_{}{}^{57}{}_{}{}^{}\mathrm{Mn}$ study. The ground state $Q$ value is 7438.2 ± 3.6 keV. A shell model calculation for ${}_{}{}^{57}{}_{}{}^{}\mathrm{Mn}$ was also attempted. A ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$ core was assumed with the valence protons restricted to the $f_{\frac{7}{2}}$ subshell and the valence neutrons allowed to occupy the $2p_{\frac{3}{2}}$, $1f_{\frac{5}{2}}$, and $2p_{\frac{1}{2}}$ subshells. The agreement between the experimental and predicted level schemes is extremely good to 2 MeV. Above 2 MeV where core and valence particle excitations are expected, the model begins to break down since these configurations were not included in the model's configuration space. The shell model wave functions were also used to calculate spectroscopic amplitudes for two nucleon transfer reactions. The quantitative agreement between the predicted strengths and the strengths extracted from the experiment for the ${}_{}{}^{55}{}_{}{}^{}\mathrm{Mn}(t, p){}_{}{}^{57}{}_{}{}^{}\mathrm{Mn}$ reaction is satisfactory.