Statistical Analysis of Reactions Induced with 21-63 MeVLi6Ions onFe54: Effects of Angular Momentum and Closed Shells on Nuclear Level Densities

Abstract

Two sets of statistical theory calculations have been compared with experimental excitation functions for the production of ${\mathrm{Ni}}^{56}$, ${\mathrm{Ni}}^{57}$, ${\mathrm{Co}}^{56}$, ${\mathrm{Co}}^{57}$, ${\mathrm{Mn}}^{54}$, and ${\mathrm{Fe}}^{52}$ at excitation energies up to 70 MeV. The reactions were induced with ${\mathrm{Li}}^{6}$ ions on ${\mathrm{Fe}}^{54}$. The first set of calculations was based on the assumption that $\ensuremath{\rho}(E,J)=C(2J+1)\ensuremath{\rho}(E)$, where $\ensuremath{\rho}(E)={C}^{\ensuremath{'}}{E}^{\ensuremath{-}2}\mathrm{exp}2{(\mathrm{aE})}^{\frac{1}{2}}$. The excitation energy $E$ was corrected for pairing, $a$ was taken equal to 7.0 Me${\mathrm{V}}^{\ensuremath{-}1}$ as determined from ($p,\ensuremath{\alpha}$) and ($\ensuremath{\alpha},{\ensuremath{\alpha}}^{\ensuremath{'}}$) spectra, and optical-model nonelastic cross sections were used for inverse reaction cross sections. All permutations of $n$, $p$, $d$, $t$, ${\mathrm{He}}^{3}$, and $\ensuremath{\alpha}$ emission were calculated for the first two particles out, followed by all permutations of $n$, $p$, and $\ensuremath{\alpha}$ emission for further evaporation. The excitation functions so calculated were narrower, and peaked at lower excitation energies than the experimental excitation functions. A second set of calculations was made assuming $\ensuremath{\rho}(E,J)={C}^{\ensuremath{'}}(2J+1)\ensuremath{\rho}(E\ensuremath{-}{\overline{E}}_{\mathrm{rotational}})$, where the average rotational energy, assumed to remain constant throughout the series of intermediate nuclei involved in a particle emission cascade, was calculated with the use of optical-model transmission coefficients for ${\mathrm{Li}}^{6}$ ions incident on ${\mathrm{Fe}}^{54}$. Excitation functions calculated with the latter assumption are in excellent agreement with experimental values with respect to width and excitation energy of maxima. Neither set of calculations is in good agreement with experimental values with respect to magnitude of maxima. It is suggested that these discrepancies may partially be explained as due to the influence of the 28-neutron and 28-proton shells on nuclear level densities.