Temperature-dependent combinatorial level densities with the D1M Gogny force

Abstract

The combinatorial model of nuclear level densities has now reached a level of accuracy comparable to that of the best global analytical expressions without suffering from the limits imposed by the statistical hypothesis on which the latter expressions rely. In particular, it provides naturally, non-Gaussian spin distribution as well as nonequipartition of parities which are known to have a significant impact on cross section predictions at low energies. Our previous global model [S. Goriely, S. Hilaire, and A. J. Koning, Phys. Rev. C 78, 064307 (2008)] suffered from deficiencies, in particular in the way the collective effects-both vibrational and rotational-were treated. We have recently improved the level density calculations using simultaneously the single-particle levels and collective properties predicted by a newly derived Gogny interaction [S. Goriely, S. Hilaire, M. Girod, and S. Péru, Phys. Rev. Lett. 102, 242501 (2009)], therefore enabling a microscopic description of energy-dependent shell, pairing, and deformation effects. In addition, for deformed nuclei, the transition to sphericity is coherently taken into account on the basis of a temperature-dependent Hartree-Fock calculation which provides at each temperature the structure properties needed to build the level densities. This new method is described and shown to give reasonable results with respect to available experimental data.

Nuclear level density: Shell-model approach

“…As the collective phenomena of these types correspond typically to the slow self-consistent motion of many particles, it is natural to expect that such coherent combinations of single-particle excitations partly compensate the deficit of levels at low energy due to the pairing gaps and give rise to the so-called collective enhancement of the level density [22,47] in comparison to the single-particle combinatorics of independent particles and holes. Modern refined approaches of this class account in various forms for the pairing phenomenon that changes the excitation spectrum, especially in even-even nuclei [23][24][25].…”

“…The influential review of earlier approaches of this type was given by Ericson [17], the later derivations can be found in [18][19][20][21], see also [22]. The recent achievements in this direction [23][24][25] include the pairing correlations considered as a part of the self-consistent mean field in the framework of the BCS theory or Hartree-FockBogoliubov variational ansatz. The shell-model MonteCarlo methods [26][27][28], being very demanding computationally, work relatively well at least with some parts of the full shell-model interaction but require the projection to the correct values of spin and parity.…”

Description of induced nuclear fission with Skyrme energy functionals. II. Finite temperature effects

“…There have been many applications of the finitetemperature formalism in nuclear structure, including early studies of fission barriers using the Thomas-Fermi approximation [15][16][17][18][19][20], the Hartree-Fock (FT-HF) approximation [21,22], and more recently at the HartreeFock-Bogoliubov (FT-HFB) approximation [23][24][25], or applications in the calculation of Giant Dipole Resonances and level densities [26][27][28][29]. Until now, however, there has been no systematic study of the validity and applicability of finite-temperature DFT in the description of induced fission.…”

Proton capture cross section ofGe72and astrophysical implications

“…Approaches like the Fermi gas model [28], the constant temperature model [29], the back-shifted Fermi gas model [30], and the generalized superfluid model [31,32] constitute the phenomenological expressions. For microscopic calculations, Hartree-Fock [33], Skyrme-Hartree-FockBogolyubov framework [34], and temperature-dependent Hartree-Fock-Bogolyubov methods [35] are used. More details can be found in Ref.…”