New formulae for the $(-2)$ moment of the photo-absorption cross section, $\sigma_{_{-2}}$

TL;DR

This paper introduces two new formulae for calculating the $(-2)$ moment of the photo-absorption cross section, improving understanding of nuclear polarization and aligning with theoretical models.

Contribution

The paper presents novel formulae for $\sigma_{-2}$ based on experimental data and a mass-dependent symmetry energy coefficient, enhancing nuclear physics models.

Findings

Power-law $\sigma_{-2}=2.4 A^{5/3} \\mu$b/MeV fits data for $A\gtrsim50$ with 6\\% RMS deviation.

The formula aligns with Migdal's hydrodynamic model and sum rule calculations.

Inclusion of $a_{sym}(A)$ offers deeper insight into nuclear polarization for $A\geqq10$.

Abstract

Two new formulae for the $(-2)$ moment of the photo-absorption cross section, $\sigma_{_{-2}}$, have been determined, respectively, from the 1988 compilation of Dietrich and Berman and a mass-dependent symmetry energy coefficient, $a_{sym}(A)$. The data for $A\gtrsim50$ follow, with a {\small $RMS$} deviation of 6\%, the power-law $\sigma_{_{-2}}=2.4 A^{5/3}$$\mu$b/MeV, which is in agreement with Migdal's calculation of $\sigma_{_{-2}}=2.25A^{5/3}$$\mu$b/MeV based on the hydrodynamic model and the $\sigma_{_{-2}}$ sum rule. The additional inclusion of $a_{sym}(A)$ provides a deeper insight to the nuclear polarization of $A\geqq10$ nuclei.