Spectra of ${\mathrm{Ti}}^{51}$, ${\mathrm{Cr}}^{53}$, and ${\mathrm{Fe}}^{55}$ and the Unified Model

The spectrum and level properties of ${\mathrm{Ti}}^{51}$ have been investigated by the reaction ${\mathrm{Ti}}^{50}(d, p){\mathrm{Ti}}^{51}$ using a high-resolution magnetic analysis system. The four nuclei ${\mathrm{Ca}}^{49}$, ${\mathrm{Ti}}^{51}$, ${\mathrm{Cr}}^{53}$, and ${\mathrm{Fe}}^{55}$ have an odd neutron outside a closed $f_{\frac{7}{2}}$ neutron shell. The spectrum of ${\mathrm{Ca}}^{49}$ as observed in a ($d, p$) reaction on ${\mathrm{Ca}}^{48}$ is single-particle-like. In the other nuclei, the neutron single-particle states are fragmented to varying degrees. An attempt has been made to study the information available for ${\mathrm{Ti}}^{51}$, ${\mathrm{Cr}}^{53}$, and ${\mathrm{Fe}}^{55}$ on the basis of the unified model by coupling the $p_{\frac{3}{2}}$, $p_{\frac{1}{2}}$, and $f_{\frac{5}{2}}$ shell model states to a quadrupole vibrational core. Core states of up to three phonons have been included in the calculation. Reasonable agreement has been obtained with the excitations and transition strengths of the low-lying levels of the three nuclei as observed in ($d, p$) reactions on the corresponding even-even nuclei. In the case of ${\mathrm{Cr}}^{53}$ which is stable, additional experimental information is available, viz., the ground state magnetic moment, the static quadrupole moment and the lifetime of the 2.32-MeV level. Using the model wavefunctions obtained for ${\mathrm{Cr}}^{53}$, these quantities have been computed and found to be in poor agreement with the experimentally observed values.