Shell energy and the level-density parameter of hot nuclei

Macroscopic-microscopic calculations have been performed with the Yukawa folded mean field for 134 spherical even-even nuclei and 6 deformed ones at temperatures $0⩽T⩽5$ MeV and elongations ranging from oblate shapes to the scission configuration of fissioning nuclei. The Strutinsky type free-energy shell corrections for this sample of nuclei and their temperature and deformation dependence are found by a folding procedure in particle-number space. The average dependence of the single-particle level-density parameter on mass number $A$ and isospin $I$ is determined and compared with previous estimates obtained using the relativistic mean-field theory, the Hartree-Fock approximation with the Skyrme effective interaction, and the phenomenological Thomas-Fermi approach adjusted to experimental data. The estimates for the level-density parameter obtained for different deformations are fitted by a liquid-drop type expression.

Figure 1

Free shell-correction energy for protons (upper part) and neutrons (lower part) for a sample of 134 nearly spherical nuclei evaluated at various temperatures $T$ with the Yukawa-folded potential as function of mass number $a$.

Figure 2

Differences between the averaged total free energies at $T=0$ and $T=1$, 2, 3, 4 MeV for spherical even-even nuclei as function of the mass number $a$ (upper part) obtained within the Yukawa-folded approach. The corresponding factor $n=A/a$ of Eq. (28) is also shown (lower part). The frequently used heuristic value $n=10$ is given as a dashed line.

Figure 3

Level-density parameter obtained with the Yukawa-folded mean-field approach (YF) and their liquid-drop type fit, Eq. (32), [YF4($A,Z$)] to spherical and deformed nuclei as compared to the self-consistent results of RMFT [25], Skyrme Hartree-Fock [11] calculations, and Thomas Fermi estimates (TF) [26] for spherical even-even isotopes (upper left), isotones (upper right), and β-stable nuclei (lower left). The corresponding factor $n=A/a$ is also shown (lower right).

Figure 4

Deformation dependence of the total (neutron + proton) shell correction energy as function of the Funny-Hills$\hspace{1em}$ elongation parameter $c$ (see text) for different temperatures $T$.

Figure 5

Temperature dependence of the total shell-correction energy for different values of $c$ as obtained with the approximation of Eq. (25).

Figure 6

Same as Fig. 5 but with the temperature dependence obtained by a folding procedure in $\mathcal{N}$ space (see text).

Figure 7

Level-density parameter as function of $c$ obtained by folding in $\mathcal{N}$ space (YF, solid lines) as compared to the four-parameter fit, Eq. (32) (YF4, dashed lines).