Semiclassical shell-structure micro-macroscopic approach for the level density

Abstract

Level density $\rho (E,A)$ 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 $\rho \propto I_{\nu }(S)/S^{\nu }$, with $I_{\nu }(S)$ 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 $\nu =3/2$ for $\rho (E,A)$. 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 $\nu =5/2$. A role of the fixed spin variables for rotating nuclei is discussed. The MMA level density $\rho$ reaches the well-known grand-canonical ensemble limit (Fermi gas asymptotic) 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 $\rho (E,A)$ 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.

arXiv comment21 pages, 4 figures, 1 Table

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Cited by in corpus (3)

• Entropy and Temperature in finite isolated quantum systems
• Level density within a micro-macroscopic approach
• Shell-structure and asymmetry effects in level densities