Gravitational form factors of nuclei in the Skyrme model

TL;DR

This paper calculates the gravitational form factors of nuclei using the Skyrme model, revealing how these form factors depend on baryon number and demonstrating the use of group theory for non-spherical configurations.

Contribution

It provides numerical calculations of gravitational form factors for various nuclei within the generalized Skyrme model, including non-spherical configurations for larger baryon numbers.

Findings

The $D(0)$ form factor scales with baryon number as $B^{1.7-1.8}$.

Numerical results are presented for nuclei with baryon numbers up to 108.

The framework allows calculation of other gravitational form factors like $J(t)$ for specific nuclei.

Abstract

We compute the gravitational form factor $D(t)$ of various nuclei in the generalized Skyrme model where nuclei are described as solitonic field configurations each with a definite baryon number $B$. We separately discuss the cases $B=1$ (nucleons), $B=2$ (deuteron), $B=3$ (helium-3 and tritium) and extrapolate to larger $B$-values. Configurations with $B>1$ are in general not spherically symmetric, and we demonstrate how group theory helps to extract the form factor. Numerical results are presented for the configurations with $B=1,2,3,4,5,6,7,8,32,108$. We find that the $B$-dependence is consistent with a power-law $D(0)\propto B^{\beta}$ with $\beta=1.7\sim 1.8$. Other gravitational form factors can be calculated in the same framework, and we show the result for the $J(t)$ form factor associated with angular momentum for the $B=3$ solution.