Capture Rates of Highly Degenerate Neutrons

TL;DR

This study investigates how neutron degeneracy in neutron star crusts significantly enhances neutron capture rates on neutron-rich nuclei, with implications for astrophysical nucleosynthesis modeling.

Contribution

It introduces a statistical Hauser-Feshbach model incorporating neutron degeneracy effects, providing tabulated rates and analytical fits for a wide range of nuclei.

Findings

Neutron degeneracy can increase capture rates by several orders of magnitude.

Uncertainties in reaction rates grow away from stability but are mitigated near the neutron drip line.

New parametrization improves the accuracy of rate calculations with Lorentzian terms.

Abstract

At the low temperature and high density conditions of a neutron star crust neutrons are degenerate. In this work, we study the effect of this degeneracy on the capture rates of neutrons on neutron rich nuclei in accreted crusts. We use a statistical Hauser-Feshbach model to calculate neutron capture rates and find that neutron degeneracy can increase rates significantly. Changes increase from a factor of a few to many orders of magnitude near the neutron drip line. We also quantify uncertainties due to model inputs for masses, $\gamma$-strength functions, and level densities. We find that uncertainties increase dramatically away from stability and that degeneracy tends to increase these uncertainties further, except for cases near the neutron drip line where degeneracy leads to more robustness. As in the case of capture of classically distributed neutrons, variations in the mass model have the strongest impact. Corresponding variations in the reaction rates can be as high as 3 to 4 orders of magnitude, and be more than 5 times larger than under classical conditions. To ease the incorporation of neutron degeneracy in nucleosynthesis networks, we provide tabulated results of capture rates as well as analytical expressions as function of temperature and neutron chemical potential, for proton numbers between $3 \le Z \le 85$, derived from fits to our numerical results. Fits are based on a new parametrization that complements previously employed power law approximations with additional Lorentzian terms that account for low energy resonances, significantly improving accuracy.