On variational trial functions in the extended Thomas-Fermi method

TL;DR

This paper examines how the smoothness of parametrized nucleon density distributions affects the accuracy of the extended Thomas-Fermi method in modeling nuclear matter, highlighting the importance of appropriate smoothness conditions.

Contribution

It clarifies the importance of smoothness conditions in variational trial functions for the extended Thomas-Fermi method, especially in complex structures like nuclear pasta.

Findings

Insufficient smoothness in parametrizations reduces accuracy.

Smoothness conditions are crucial for reliable results.

Application to nuclear pasta demonstrates the impact.

Abstract

Parametrized nucleon density distributions are widely employed for the calculation of the properties of atomic nuclei and dense inhomogeneous matter in compact stars within the Thomas-Fermi method and its extensions. We show that the use of insufficiently smooth parametrizations may deteriorate the accuracy of this method. We discuss and clarify the smoothness condition using the example of the so-called "nuclear pasta" in the neutron star mantle.