Estimating the nuclear level density with the Monte Carlo shell model

A method for making realistic estimates of the density of levels in even-even nuclei is presented making use of the Monte Carlo shell model (MCSM). The procedure follows three basic steps: (1) computation of the thermal energy with the MCSM, (2) evaluation of the partition function by integrating the thermal energy, and (3) evaluating the level density by performing the inverse Laplace transform of the partition function using Maximum Entropy reconstruction techniques. It is found that results obtained with schematic interactions, which do not have a sign problem in the MCSM, compare well with realistic shell-model interactions provided an important isospin dependence is accounted for. PACS number(s): 21.10.Ma, 21.60.-n,21.60.Cs, 21.60.Ka Typeset using REVTEX 1 The density of levels in nuclei plays an important role in understanding compound nuclear reactions. Two particularly important examples are the decay of the giant-dipole resonance (GDR) in hot nuclei [1], and the radiative capture of light nuclei, i.e., protons, neutrons, and alphas, in nucleosynthesis [2]. In the first case, properties of the GDR, in particular the damping width, have been studied in several nuclei for excitation energies ranging from 50 to 200 MeV, and it has been shown that the analysis of experimental data is very sensitive to the the dependence of the level density on excitation energy [3]. In contrast to the GDR studies, the particle capture probability, which determines the rate at which nucleosynthesis reactions occur, is sensitive to the level density near the particle-decay threshold: i.e., ∼ 5− 15 MeV. In most applications where the level density is required, the Fermi-gas model estimate [4] is employed ρ(E) = √ π 12a1/4E5/4 exp(2 √ aE), (1) where E is the excitation energy, and a is the level-density parameter, which is determined by the number of single-particle states at the Fermi energy. The principal shortcoming of the Fermi gas estimate is that interactions between nucleons are ignored. Effects due to shell corrections and pairing correlations are approximated in Eq.(1) by replacing the excitation energy E by backshifted quantity E−∆ [5]. Emprically, both a and ∆ exhibit a dependence on E and the number of nucleons, A, that cannot simply be estimated within the context of the Fermi-gas model; a typical value for a at low excitation energies is a ∼ A/8. An alternative model that explicitly includes both oneand two-body correlations is the shell model. State-of-the-art shell-model Hamiltonians, such as the universal sd-shell (USD) Hamiltonian of Wildenthal [6] have been very successful at describing both excitation energies and transition amplitudes for states in a wide range of nuclei (18 ≤ A ≤ 48) up to excitation energies of the order 5-10 MeV. Although the shell model might appear to be the obvious method for estimating the level density at low excitation energies, direct diagonalization of the Hamiltonian faces severe computational limitations due to the fact that the number of basis states scales as the exponential of the number of valence particles. Indeed,