Reactions Induced in ${\mathrm{Ni}}^{58}$ with 0-24 MeV Deuterons: Statistical Model Analysis

Excitation functions for ${\mathrm{Ni}}^{58}(d, \alpha )$, ($d, \alpha p$), ($d, \alpha n$), ($d, 2pn$), ($d, 2np$), and ${\mathrm{Ni}}^{60}(d, 2\alpha )$ reactions have been measured radiochemically for deuteron energies up to 24 MeV. The decrease in the ($d, \alpha$) excitation curve above the threshold of competing reactions such as ($d, \alpha p$) and ($d, \alpha n$) is consistent with the qualitative behavior of compound-nucleus reactions. The experimental results have been compared with statistical-model calculations that assume nuclear level densities of the form $\rho \mathrm{}\left(E\right)\mathrm{}\propto \mathrm{}(2J+1)\mathrm{}{E}^{-2\mathrm{}}\exp \left[2\mathrm{}{\mathrm{}\left(\mathrm{aE}\right)\mathrm{}}^{\frac{1}{2}}\right]$, where the excitation energy $E$ was corrected for pairing. The value of the parameter $a$ was set equal to the experimental value determined by Brady and Sherr (from alpha-particle energy spectra produced by bombarding ${\mathrm{Ni}}^{58}$ with 15.6- and 19.4-MeV protons). Cross sections were calculated for all permutations of $n$, $p$, $d$, $t$, ${\mathrm{He}}^3$, and $\alpha$ emission for two successive evaporations, followed by a calculation of a third evaporation of a neutron, proton, or alpha particle where it was energetically possible. In these calculations the inverse cross sections of particles with energy $\epsilon$, ${\sigma }_{\mathrm{inv}}\left(\epsilon \right)$, were assumed to be of the following forms: for neutrons, ${\sigma }_{\mathrm{inv}}\left(\epsilon \right)={\sigma }_1\left(\frac{1+{\epsilon }_n}{\epsilon }\right)$; for charged particles, ${\sigma }_{\mathrm{inv}}\left(\epsilon \right)={\sigma }_2(1-\frac{{\epsilon }_c}{\epsilon })$ when $\epsilon >{\epsilon }_c$, and ${\sigma }_{\mathrm{inv}}\left(\epsilon \right)=0\mathrm{}$ when $\epsilon <{\epsilon }_c$. The parameters ${\sigma }_1$, ${\epsilon }_n$, ${\sigma }_2$, and ${\epsilon }_c$ were chosen so that values of ${\sigma }_{\mathrm{inv}}\left(\epsilon \right)$ would approximate optical-model calculations of the capture cross sections. Two sets of compound-nucleus excitation functions were calculated. In the first set the alpha-particle and the proton inverse cross sections, ${\sigma }_{\mathrm{inv}}\left(\epsilon \right)$, were chosen to correspond to optical-model reaction cross sections calculated with parameters deduced from experimental elastic scattering. In the second set of compound-nucleus excitation function calculations the inverse cross sections, ${\sigma }_{\mathrm{inv}}\left(\epsilon \right)$, were chosen to correspond to nuclear radii 10% smaller than those used in the first set of calculations. The experimental excitation functions nearly all fall between the two sets of calculated functions.