Deuteron Stripping Studies in the Light Isotopes of Nickel

Measurements of protons from ($d,p$) reactions on ${\mathrm{Ni}}^{58}$ and ${\mathrm{Ni}}^{60}$ were made with the Aldermaston tandem Van de Graaff and multigap spectrograph. A large number of states of the final nuclei (well over a hundred in each case) were observed and assigned to single-particle states. For the states in the $28<N\le 50$ shell, the results for both energies and degree of filling are compared with pairing theory; the agreement is good. A sufficiently large fraction of the $l=2\mathrm{}$ states are observed to locate the $d_{\frac{5}{2}}$ and $d_{\frac{3}{2}}$ single-particle states at 6.0 and 9.3 MeV, respectively, in ${\mathrm{Ni}}^{59}$, and at 5.0 and 8.4 MeV, respectively, in ${\mathrm{Ni}}^{61}$. A relation between neutron-reduced width ${{\Gamma }_n}^0$ (from neutron experiments) and the stripping spectroscopic factor $S$ is derived and checked experimentally with two levels observed in both experiments; the agreement is satisfactory. Plots of neutron strength function versus energy are obtained containing both neutron and stripping data, and subjected to the requirements of $\Sigma S=1\mathrm{}$ and $\mathrm{width}=2W$ (where $W$ is the depth of the imaginary potential in optical model). The results give the location of the $3s_{\frac{1}{2}}$ states as 7.3 MeV in ${\mathrm{Ni}}^{59}$ and 6.0 MeV in ${\mathrm{Ni}}^{61}$. The distribution of states belonging to each single-particle state is found to have approximately the expected width $2W$ except for the $g_{\frac{9}{2}}$ state in ${\mathrm{Ni}}^{61}$ which is concentrated in a single nuclear level. It is shown that the latter behavior is expected since there are no other positive-parity states expected even nearly within a distance $W$ of the single-particle state. In ${\mathrm{Ni}}^{59}$, the situation is similar except that states are expected and found at a distance $\approx 1.5W$, and these are mixed in weakly.