Level widths and level densities of nuclei in the32<~A<~60mass region inferred from fluctuation analysis of total neutron cross sections

Abstract

Level widths and level densities of nuclei in the $32l~Al~60$ mass region are inferred from the fluctuation analysis of total neutron cross sections. The experimentally determined level densities are compared to phenomenological and microscopic predictions. The total neutron cross sections were measured in the $0.75l~{E}_{n}l~11.3 \mathrm{MeV}$ range for ${}^{31}\mathrm{P},$ ${}^{32}\mathrm{S},$ ${}^{39}\mathrm{K},$ ${}^{51}\mathrm{V},$ ${}^{56}\mathrm{Fe},$ and ${}^{59}\mathrm{Co}$ using a white neutron source and standard time-of-flight techniques. Measured cross sections agree well in magnitude and structure with earlier measurements. Nuclear level widths and cross section variances were determined for the compound nuclei ${}^{32}\mathrm{P},$ ${}^{33}\mathrm{S},$ ${}^{40}\mathrm{K},$ ${}^{52}\mathrm{V},$ ${}^{57}\mathrm{Fe},$ and ${}^{60}\mathrm{Co}$ by means of Fourier analysis of the fluctuating excitation functions and subsequent least squares fit to the resulting $\mathrm{ln}{S}_{k}$ spectra. Nuclear level densities for the above compound nuclei were extracted by relating them to the variance (variance method) of the total neutron cross sections via Ericson theory of fluctuating cross sections. Furthermore, level density values were derived by relating level densities to average level widths (gamma method) via compound nuclear theory. The present study shows good agreement between the two methods for ${}^{32}\mathrm{P}$ and ${}^{33}\mathrm{S},$ with an uncertainty of 30--40 %. Inclusion of a finite energy resolution correction and use of local instead of global optical model parameters improve agreement, but do not resolve the discrepancy between the two methods completely, especially for $Ag40.$ Nuclear level densities were compared with microscopic calculations utilizing a BCS pairing Hamiltonian and specific sets of realistic sets of single-particle energies. A further comparison was made with results obtained from phenomenological models based on the Fermi gas formalism. For ${}^{32}\mathrm{P},$ ${}^{33}\mathrm{S},$ and ${}^{40}\mathrm{K},$ experimental values and phenomenological predictions agree well, but diverge with increasing A. From least squares fits to the present level density data, level density parameters $(a$ and $\ensuremath{\Delta})$ were extracted for ${}^{32}\mathrm{P},$ ${}^{33}\mathrm{S},$ and ${}^{40}\mathrm{K}.$ Results for the level density parameter are consistent with $a=A/9.$