Microscopic calculations of nuclear level densities with the Lanczos method

A new method for computing the density of states in nuclei using an extrapolated form for the tri-diagonal matrix obtained from the Lanczos method is presented. This can be applied to configuration-interaction calculations with fully realistic nuclear Hamiltonians that are known to provide an excellent description of the low-lying structure of nuclei. This extrapolated Lanczos matrix (ELM) approach provides an accurate computation of the density of states up to the neutron separation energy for states that lie within the configuration space. Comparisons between theory and experiment for the average level density for p-wave resonances for iron isotopes using the 1p−0f-shell model space and realistic nuclear Hamiltonians are shown. Also we show results for J-dependence of the level density and the total level density for negative-parity states. The density of states is a fundamental property of nuclear structure that plays an important role in nuclear reactions. Of particular importance is the radiative capture of neutrons on short-lived nuclei, which through the r-process [1] in supernovae and neutron-star mergers [2], are thought to be responsible for the synthesis of the elements heavier than iron. Ideally, these reactions can be measured or constrained by experiment. Unfortunately, in most cases, the target nuclei are so short lived that direct measurement is infeasible, and the only alternatives are to rely on theoretical calculations or on indirect measurements, such as surrogates [3], which themselves reliant on theoretical input. Theoretical modeling requires an in-depth, and accurate description of the reaction processes, and in particular the density of states at or near the neutron decay threshold. We report on a new microscopic framework to provide an accurate estimate of the level density for a variety of nuclei using an extension of the configuration-interaction approach with fully realistic nuclear Hamiltonians that are known to provide an excellent description of the low-lying structure of nuclei. We will exploit a universal property of the Lanczos algorithm, which will allow us to extrapolate the tri-diagonal Lanczos matrix elements beyond what is computationally viable, to accurately estimate the density of states within the shell-model configuration space. We demonstrate that the information needed to perform the extrapolation can be extracted from just the lowest 100 Lanczos iterations, thus, leading to a computationally efficient way to compute the density of states.