Degenerate limit thermodynamics beyond leading order for models of dense matter

TL;DR

This paper derives analytical formulas for next-to-leading order temperature corrections in degenerate dense matter models, applicable across various nuclear physics and astrophysics scenarios, extending the validity of analytical approaches.

Contribution

It introduces a general formalism for calculating higher-order temperature effects in degenerate matter, applicable to both non-relativistic and relativistic models with arbitrary dimensionality.

Findings

Analytical formulas match well with exact numerical results.

Next-to-leading order effects significantly extend the validity range of analytical models.

The formalism applies to diverse models, including zero-range and finite-range interactions.

Abstract

Analytical formulas for next-to-leading order temperature corrections to the thermal state variables of interacting nucleons in bulk matter are derived in the degenerate limit. The formalism developed is applicable to a wide class of non-relativistic and relativistic models of hot and dense matter currently used in nuclear physics and astrophysics (supernovae, proto-neutron stars and neutron star mergers) as well as in condensed matter physics. We consider the general case of arbitrary dimensionality of momentum space and an arbitrary degree of relativity (for relativistic mean-field theoretical models). For non-relativistic zero-range interactions, knowledge of the Landau effective mass suffices to compute next-to-leading order effects, but in the case of finite-range interactions, momentum derivatives of the Landau effective mass function up to second order are required. Numerical computations are performed to compare results from our analytical formulas with the exact results for zero- and finite-range potential and relativistic mean-field theoretical models. In all cases, inclusion of next-to-leading order temperature effects substantially extends the ranges of partial degeneracy for which the analytical treatment remains valid.