Fermi-momentum dependence of relativistic effective mass below saturation from superscaling of quasielastic electron scattering

TL;DR

This study uses a novel superscaling analysis of quasielastic electron scattering data across various nuclei to extract the Fermi momentum dependence of the relativistic effective mass below saturation density, revealing universal scaling behavior.

Contribution

It introduces a new superscaling method to determine the relativistic effective mass and Fermi momentum from experimental data below nuclear saturation density.

Findings

Approximately one-third of the data scales universally with a constrained uncertainty band.

The analysis provides a functional relationship between the effective mass and Fermi momentum.

Universal superscaling behavior is observed across a wide range of nuclei from deuterium to uranium.

Abstract

The relativistic effective mass $M^*$, and Fermi momentum, $k_F$, are important ingredients in the determination of the nuclear equation of state, but they have rarely been extracted from experimental data below saturation density where translationally invariant nuclear matter becomes unstable against clusterization into the existing atomic nuclei. Using a novel kind of superscaling analysis of the quasielastic cross section electron scattering data involving a suitable selection criterion and $^{12}$C as a reference nucleus, the global scaling properties of the resulting set of data for 21 nuclei ranging from $^2$H to $^{238}$U are then analyzed. We find that a subset of a third of the about $20000$ data approximately scales to an universal superscaling function with a more constrained uncertainty band than just the reference $^{12}$C case and provides $M^*$ as a function of $k_F$.