Shell-Model Calculations forN=30Nuclei

The results of shell-model calculations on $N=30\mathrm{}$ nuclei with $20\le Z\le 27$ are reported. An inert ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$ core is assumed, protons are restricted to the $1f_{\frac{7}{2}}$ shell, and the two active neutrons can occupy the $2p_{\frac{3}{2}}$, $2p_{\frac{1}{2}}$, and $1f_{\frac{5}{2}}$ orbits. A Hamiltonian is used which leads to a good fit to selected experimental data in this same mass region. For all nuclei treated here except ${}_{}{}^{57}{}_{}{}^{}\mathrm{Co}$, the agreement of the calculated spectra with experimental spectra for states below an excitation energy of about 2.5 MeV is satisfactory. The shell-model wave functions are used to calculate spectroscopic factors for one- and two-nucleon transfer reactions which involve ${}_{}{}^{54}{}_{}{}^{}\mathrm{Cr}$, ${}_{}{}^{55}{}_{}{}^{}\mathrm{Mn}$, and ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}$. The qualitative results for the one-nucleon transfer reactions are in satisfactory agreement with the factors extracted from experimental data. The predicted relative strengths for strong transitions in these reactions are not in good agreement with the extracted numbers. The quantitative agreement between the predicted strengths and the strengths extracted from experiment for the ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}(t, p){}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}$ reaction is good.