Bounds to binding energies from the concavity of thermodynamical functions

TL;DR

This paper explores how the concavity of thermodynamical functions can be used to estimate and bound nuclear binding energies, enabling more accurate extrapolations towards drip lines.

Contribution

It introduces a method to use the concavity of thermodynamical functions for bounding and extrapolating nuclear binding energies, improving predictions near drip lines.

Findings

Concavity of thermodynamical functions allows bounds on binding energies.

Extrapolation schemes based on concavity provide reliable estimates.

Numerical estimates for nuclei near drip lines are obtained.

Abstract

Sequences of experimental ground-state energies 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, can be used to 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, when present in such functions, allows trivial interpolations and extrapolations providing upper and lower bounds, respectively, to binding energies. Such bounds define an error bar for the prediction of binding energies. An extrapolation scheme for such concave functions is tested. We conclude with numerical estimates of the binding energies of a few nuclei closer to drip lines.