Nuclear-Structure Studies in the Nickel Isotopes with (d, t) Reactions

Nuclear levels of the nickel isotopes were investigated with ($d, t$) reactions at 15-MeV deuteron energy. Absolute differential cross sections were obtained from isotopically enriched ${\mathrm{Ni}}^{58}$, ${\mathrm{Ni}}^{60}$, ${\mathrm{Ni}}^{61}$, ${\mathrm{Ni}}^{62}$, and ${\mathrm{Ni}}^{64}$ targets with $\Delta E-\times -E$ counter telescope and two-parameter multichannel analysis. Two sets of distorted-wave Born approximation (DWBA) calculations were made for all $Q$ values and $l$ values of interest, and spectroscopic factors and $l$ values were extracted from the comparison of data and theory. In addition, a number of $j$ values, for the final states, were assigned on the basis of empirical rules. A $j$ dependence was observed for all $l=1\mathrm{}$ and $l=3\mathrm{}$ transitions where resolution and statistics were good enough to allow analysis of the data for angles larger than about 45°. For all but the very weakly excited levels, correct $j$ values could also be obtained from a comparison of ($d, p$) and ($d, t$) spectroscopic factors leading to the same final state. It was noted that a number of $l=3\mathrm{}$ transitions previously observed by Cohen, Fulmer, and McCarthy in $\mathrm{Ni}(d, p)$ reactions led to final states that we find to be $f_{\frac{7}{2}}$. This indicates that in the light Ni isotopes the $f_{\frac{7}{2}}$ shell is not completely filled. The spectroscopic factors reported are discussed in terms of the shell-model pairing theory by Kisslinger and Sorensen, Our results for the energies and fullness of single-quasiparticle levels are in agreement with results from ($d, p$) work provided the correct $j$ assignments are used. It was found that all DWBA predictions without 1·s interaction failed to give good quantitative agreement with the observed ($d, t$) angular distributions for angles beyond the stripping peak. DWBA calculations were made for a conventional neutron form factor which is determined by the neutron separation energy, and also for a recently suggested form factor which is determined by a constant binding energy for all neutrons with a given $j$, regardless of differences in separation energy. The two form factors lead to almost identical predictions for the angular distributions; however, systematic differences are found in the spectroscopic factors. In terms of shell-model expectations, the conventional approximation for the neutron form factor leads to more consistent results.