Gravitational form factors of nuclei in the Skyrme model
Alberto García Martín-Caro, Miguel Huidobro, Yoshitaka Hatta
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 $D(0)\ensuremath{\propto}{B}^{\ensuremath{\beta}}$ with $\ensuremath{\beta}=1.7--1.8$. Other gravitational form factors can be calculated in the same framework, and we show the result for the $J(t)$ form factor associated with the angular momentum for the $B=3$ solution.