Nuclear Level Densities with Microscopic Statistical Method Using a Consistent Residual Interaction

Abstract

Nuclear level density (NLD) evaluated under the framework of the microscopic statistical method is examined. We calculate single-particle levels by the Skyrme-Hartree-Fock (SHF) + Bardeen-CooperSchrieffer (BCS) method, and the grand partition function is calculated with the same two-body interaction as used in the SHF+BCS method. The results are compared with preceding theoretical calculations using different residual interactions. Cumulative numbers and s-wave neutron resonance spacings are reproduced fairly well. The effect of a renormalization term neglected in conventional microscopic statistical methods is also investigated. In order to test a practical application, we calculate neutron capture cross section and compare it with experimental results.

New results on proton-induced reactions on Vanadium for $^{47}$Sc production and the impact of level densities on theoretical cross sections

“…Stacked-foils targets, composed by a set of thin metallic nat V foils (purity > 99.8%, thickness=20 µm) interchanged with monitor foils and nat Al energy degraders, were used in the experiments [7]. The nat Ni(p,x) 57 Ni and the 27 Al(p,x) 24 Na cross sections, recommended by the IAEA [31], were considered as monitor reactions respectively for energies lower and higher than 40 MeV. nat Ni (purity > 99.95%, thickness=10 µm) or nat Al (purity > 99.0%, thickness=10 µm) foils were thus added in the stacked-structure after each nat V target foil (see Fig.…”

“…The results will allow to accurately estimate the production yields of 47 Sc and contaminants and to design an irradiation experiment for the production of 47 Sc with the highest isotopic and radionuclidic purities. A preliminary assessment of the optimal conditions was presented in [12] in which the energy interval [19][20][21][22][23][24][25][26][27][28][29][30] MeV was identified as the most promising by performing a parametric extrapolation at low energy of the available data: in this analysis we follow a different approach by considering a microscopic theoretical model and, by introducing the tuning of the level densities, we get an excellent reproduction of the data in the region (mass and energy) of interest. Thus, without any parametric-fit extrapolation of data at low energies, we obtain an optimized theoretical prediction of the yields, as well as of the contamination by stable isotopes, such as 45 Sc, which typically are not measurable by γ-spectroscopy.…”

Microscopic model for the collective enhancement of nuclear level densities

“…A number of microscopic approaches to modelling NLD have been reported, such as the Shell-Model Monte Carlo method [5,6], the moments method derived from random matrix theory and statistic spectroscopy [7,8], the stochastic estimation method [9], the Lanczos method using realistic nuclear Hamiltonians [10], and the self-consistent mean-field approach based on the extended Thomas-Fermi approximation with Skyrme forces [11]. Microscopic methods based on the selfconsistent Hartree-Fock (HF) plus BCS model [12][13][14] and Hartree-Fock-Bogoliubov (HFB) model [15][16][17] have also been developed to describe NLD. In this framework the partition function is determined using the same twobody interaction as in the HF plus BCS or HFB meanfield models [13] and, therefore, shell, pairing, and deformation effects are included self-consistently.…”

“…Microscopic methods based on the selfconsistent Hartree-Fock (HF) plus BCS model [12][13][14] and Hartree-Fock-Bogoliubov (HFB) model [15][16][17] have also been developed to describe NLD. In this framework the partition function is determined using the same twobody interaction as in the HF plus BCS or HFB meanfield models [13] and, therefore, shell, pairing, and deformation effects are included self-consistently. The intrinsic level density is obtained by an inverse Laplace transform of the partition function with the saddle-point approximation [18].…”