Level Densities from Excitation Functions of Isolated Levels

Abstract

Thick-target excitation functions were measured for the reactions ${\mathrm{Co}}^{59}(p,{\ensuremath{\alpha}}_{0}){\mathrm{Fe}}^{56}$, ${\mathrm{Co}}^{59}(p,{\ensuremath{\alpha}}_{1}){\mathrm{Fe}}^{56}$, ${\mathrm{Co}}^{59}(p,{\ensuremath{\alpha}}_{2}){\mathrm{Fe}}^{56}$, ${\mathrm{Mn}}^{55}(p,{\ensuremath{\alpha}}_{0}){\mathrm{Cr}}^{52}$, ${\mathrm{Mn}}^{55}(p,{\ensuremath{\alpha}}_{1}){\mathrm{Cr}}^{52}$, and ${\mathrm{Ni}}^{62}(p,{\ensuremath{\alpha}}_{0}){\mathrm{Co}}^{59}$ at two or more angles for proton bombarding energies 6-13.5 MeV. The ${\mathrm{Fe}}^{56}(\ensuremath{\alpha},{p}_{0}){\mathrm{Co}}^{59}$ reaction was studied at $\ensuremath{\alpha}$-particle bombarding energies of 12-18.5 MeV. These measurements were used to determine the parameters in three different level-density formulas which were thought to be reasonable candidates to describe the level densities of the residual nuclei. In addition, the experimental values of the cross sections to isolated levels were used in conjunction with available values of the level width $\ensuremath{\Gamma}$ from cross-section fluctuation measurements to determine level densities of compound nuclei at about 20-MeV excitation energy. The absolute values and energy dependence of the nuclear level density in the excitation energy range 0-20 MeV investigated for several nuclei agree with a back-shifted Fermi gas model. The constant-temperature model gives a reasonable fit to the level density in the energy range 0-10 MeV but fails at higher excitation energies. The conventional shifted Fermi gas model does not reproduce the energy dependence and absolute values of the various experimental level densities for any value of the level-density parameter $a$.