Shell-structure and asymmetry effects in level densities

Abstract

Level density $\rho (E,N,Z)$ is derived for a nuclear system with a given energy $E$, neutron $N$, and proton $Z$ particle numbers, within the semiclassical extended Thomas-Fermi and periodic-orbit theory beyond the Fermi-gas saddle-point method. We obtain $\rho \propto I_{\nu }(S)/S^{\nu }$,~~ where $I_{\nu }(S)$ is the modified Bessel function of the entropy $S$, and $\nu$ is related to the number of integrals of motion, except for the energy $E$. For small shell structure contribution one obtains within the micro-macroscopic approximation (MMA) the value of $\nu =2$ for $\rho (E,N,Z)$. In the opposite case of much larger shell structure contributions one finds a larger value of $\nu =3$. The MMA level density $\rho$ reaches the well-known Fermi gas asymptote for large excitation energies, and the finite micro-canonical limit for low excitation energies. Fitting the MMA $\rho (E,N,Z)$ to experimental data on a long isotope chain for low excitation energies, due mainly to the shell effects, one obtains results for the inverse level density parameter $K$, which differs significantly from that of neutron resonances.

arXiv comment26 pages, 3 figures, 1 table. arXiv admin note: text overlap with arXiv:2103.16480

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Cited by in corpus (1)

• Level density within a micro-macroscopic approach