Level Densities from 0-30 MeV

TL;DR

This paper calculates and analyzes level densities from 0 to 30 MeV in 17 nuclei, incorporating photon strength and resonance contributions, and compares results with various nuclear models to identify universal parameters.

Contribution

It introduces a combined approach using the modified Brink-Axel formulation and the CT-JPI model to determine level densities across a wide energy range for multiple nuclei.

Findings

Level densities increase exponentially at low energies.

A peak in level density occurs near the GDR energy.

Good agreement with FGLD and BDFG models, but not HFB.

Abstract

Photon strength, $f(E_{\gamma})$, measured in photonuclear reactions, is the product of the average level density per MeV, $\rho(E_x)$, and the average reduced level width, $\Gamma_{\gamma}/E_{\gamma}^3$ for levels populated primarily by E1 transitions at an excitation energy $E_x=E_{\gamma}$. It can be calculated with the Brink-Axel (BA) formulation modified to include contributions from the Giant Dipole Resonance (GDR) and higher lying resonances. Level densities and reduced widths have been calculated for 17 nuclei with atomic numbers between Z=14-92. Level densities below the GDR energy were calculated with the CT-JPI model and combined with the BA photon strength to determine the associated reduced widths. The reduced widths varied exponentially with level energy and could be extrapolated up to higher energies. The extrapolated widths were then combined with the BA photon strength to determine the level densities at higher energies. The level densities are found to increase exponentially at low energies, peak near the GDR energy due to the appearance of new states at the $2\hbar\omega$ shell closure, and continue to increase less rapidly up to at least 30 MeV. The average level densities have been compared with the Fermi Gas Level Density (FGLD), Back-Shifted Fermi Gas (BSFG), and Hartree-Fock-Bogoliubov (HFB) models. Good agreement is found with the nearly identical FGLD and BDFG models, while the HFB models gives substantially lower level densities. A universal set of FGLD model parameters were determined as a function of mass and temperature that are applicable to all nuclei.