Year: 2021
Type: article
Abstract: Level density $\ensuremath{\rho}(E,A)$ is derived for a one-component nucleon system with a given energy $E$ and particle number $A$ within the mean-field semiclassical periodic-orbit theory beyond the saddle-point method of the Fermi gas model. We obtain $\ensuremath{\rho}\ensuremath{\propto}{I}_{\ensuremath{\nu}}(S)/{S}^{\ensuremath{\nu}}$, with ${I}_{\ensuremath{\nu}}(S)$ being the modified Bessel function of the entropy $S$. Within the micro-macro-canonical approximation (MMA), for a small thermal excitation energy $U$, with respect to rotational excitations ${E}_{\mathrm{rot}}$, one obtains $\ensuremath{\nu}=3/2$ for $\ensuremath{\rho}(E,A)$. In the case of excitation energy $U$ larger than ${E}_{\mathrm{rot}}$ but smaller than the neutron separation energy, one finds a larger value of $\ensuremath{\nu}=5/2$. A role of the fixed spin variables for rotating nuclei is discussed. The MMA level density $\ensuremath{\rho}$ reaches the well-known grand-canonical ensemble limit (Fermi gas asymptote) for large $S$ related to large excitation energies, and also reaches the finite micro-canonical limit for small combinatorial entropy $S$ at low excitation energies (the constant ``temperature'' model). Fitting the $\ensuremath{\rho}(E,A)$ of the MMA to the experimental data for low excitation energies, taking into account shell and, qualitatively, pairing effects, one obtains for the inverse level density parameter $K$ a value which differs essentially from that parameter derived from data on neutron resonances.
Source: Physical Review C
Institutions: Institute for Nuclear Research, Texas A&M University
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3144800751