The (α${,}^2$He) reaction has been investigated at bombarding energies around 56 MeV on targets of ${}_{}{}^{40,42,44,48}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{50,52,54}{}_{}{}^{}\mathrm{Cr}$, ${}_{}{}^{54,56,58}{}_{}{}^{}\mathrm{Fe}$, ${}_{}{}^{58,60,62,64}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{64,66}{}_{}{}^{}\mathrm{Zn}$, and ${}_{}{}^{70,72}{}_{}{}^{}\mathrm{Ge}$. The angular distributions of prominent two-neutron states were analyzed with the distorted-wave Born approximation. Preferential population of states with dominant (${\mathit{f}}_{5/2}$,${\mathit{g}}_{9/2}$${)}_7^{\mathrm{-}}$, (${\mathit{g}}_{9/2}$${)}_8^{+2\mathrm{}}$, and (${\mathit{g}}_{9/2}$,${\mathit{d}}_{5/2}$${)}_6^{+}$ configurations was observed for all nuclei with a closed ${\mathit{f}}_{7/2}$ neutron shell. The binding energies of the $7^{\mathrm{-}}$, $8^{+}$, and $6^{+}$ states are linearly dependent on the mass number and the isospin and well described by the weak-coupling model. The extracted parameters agree with the averaged values of a similar analysis for ${\mathit{f}}_{5/2}$, ${\mathit{g}}_{9/2}$, and ${\mathit{d}}_{5/2}$ single-particle states in the corresponding odd-even nuclei. The excitation energies of the high-spin states could be well reproduced by a simplified shell model where only pure configurations are considered and the residual interaction energy is neglected. The simple structure of the experimentally observed states is further tested by large-scale shell-model calculations. Two-body matrix elements are extracted from the data for the (${\mathit{f}}_{5/2}$,${\mathit{g}}_{9/2}$${)}_7^{\mathrm{-}}$ and (${\mathit{g}}_{9/2}$${)}_8^{+2\mathrm{}}$ configurations.

• Received 22 June 1990

DOI:https://doi.org/10.1103/PhysRevC.42.2375