Concavity for nuclear binding energies, thermodynamical functions and density functionals

TL;DR

This paper explores the concavity properties of nuclear binding energies and thermodynamical functions, enabling improved extrapolations and bounds for nuclear masses near drip lines, and discusses their relation to nuclear density functional theory.

Contribution

It introduces a method to map experimental energies onto concave patterns, facilitating reliable extrapolations and bounds for nuclear masses and connects these properties to density functional theory.

Findings

Concavity allows for bounds on nuclear binding energies.

Thermodynamical functions exhibit concavity, aiding interpolation.

Method improves predictions near nuclear drip lines.

Abstract

Sequences of experimental ground-state energies for both odd and even $A$ are mapped onto concave patterns cured from convexities due to pairing and/or shell effects. The same patterns, completed by a list of excitation energies, give numerical estimates of the grand potential $\Omega(\beta,\mu)$ for a mixture of nuclei at low or moderate temperatures $T=\beta^{-1}$ and at many chemical potentials $\mu.$ The average nucleon number $<{\bf A} >(\beta,\mu)$ then becomes a continuous variable, allowing extrapolations towards nuclear masses closer to drip lines. We study the possible concavity of several thermodynamical functions, such as the free energy and the average energy, as functions of $<{\bf A} >.$ Concavity, which always occur for the free energy and is usually present for the average energy, allows easy interpolations and extrapolations providing upper and lower bounds, respectively, to binding energies. Such bounds define an error bar for the prediction of binding energies. Finally we show how concavity and universality are related in the theory of the nuclear density functional.