Energy density functional on a microscopic basis

TL;DR

This paper examines the challenges and potential of constructing nuclear energy density functionals from a microscopic basis, comparing their accuracy and connection to fundamental interactions with phenomenological models.

Contribution

It analyzes the feasibility and limitations of deriving nuclear energy density functionals from microscopic nucleon-nucleon interactions using a density matrix expansion.

Findings

Microscopic functionals face challenges in matching phenomenological accuracy.

Connection to nuclear matter Equation of State is complex.

Finite size effects are significant in functional development.

Abstract

In recent years impressive progress has been made in the development of highly accurate energy density functionals, which allow to treat medium-heavy nuclei. In this approach one tries to describe not only the ground state but also the first relevant excited states. In general, higher accuracy requires a larger set of parameters, which must be carefully chosen to avoid redundancy. Following this line of development, it is unavoidable that the connection of the functional with the bare nucleon-nucleon interaction becomes more and more elusive. In principle, the construction of a density functional from a density matrix expansion based on the effective nucleon-nucleon interaction is possible, and indeed the approach has been followed by few authors. However, to what extent a density functional based on such a microscopic approach can reach the accuracy of the fully phenomenological ones remains an open question. A related question is to establish which part of a functional can be actually derived by a microscopic approach and which part, on the contrary, must be left as purely phenomenological. In this paper we discuss the main problems that are encountered when the microscopic approach is followed. To this purpose we will use the method we have recently introduced to illustrate the different aspects of these problems. In particular we will discuss the possible connection of the density functional with the nuclear matter Equation of State and the distinct features of finite size effects proper of nuclei.