Nuclear Structure Studies in Isotopes of Nickel and Iron

Abstract

The levels of ${\mathrm{Fe}}^{55}$, ${\mathrm{Fe}}^{58}$, ${\mathrm{Ni}}^{62}$, ${\mathrm{Ni}}^{63}$, and ${\mathrm{Ni}}^{65}$ are studied with ($d, p$) reactions; angular distributions and absolute cross sections are analyzed with the aid of distorted-wave Born-approximation calculations. Essentially all levels in the odd isotopes up to about 1-MeV binding energy are assigned to a shell-model state and their reduced widths are measured. From this, the "center of gravity" of each shell-model state is determined; the results for ${\mathrm{Fe}}^{55}$, which has one neutron above a closed shell, are ${p}_{\frac{3}{2}}\ensuremath{\gtrsim}0.1$ MeV, ${f}_{\frac{5}{2}}\ensuremath{-}1.4$ MeV, ${p}_{\frac{1}{2}}\ensuremath{\sim}3.2$ MeV, ${g}_{\frac{9}{2}}\ensuremath{-}3.8$ MeV, ${d}_{\frac{5}{2}}\ensuremath{\sim}6.7$ MeV, and ${s}_{\frac{1}{2}}\ensuremath{\sim}7.3$ MeV. The shell-model states in the Ni isotopes follow the same energy ordering except that the ${f}_{\frac{5}{2}}$ state decreases in energy to become the ground state of ${\mathrm{Ni}}^{65}$, but the energy range of the spectra is compressed for greater neutron excess. The ${p}_{\frac{3}{2}}$, ${f}_{\frac{5}{2}}$, and ${p}_{\frac{1}{2}}$ states increase in "fullness' with increasing neutron excess, while the other states remain completely empty. The widths of the energy distributions of levels belonging to single shell-model states agree well with the predictions of the giant resonance theory of Lane, Thomas, and Wigner.