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

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 $A\gtrsim 50$ follow, with a {\small $RMS$} deviation of 6\%, the power-law ${\sigma }_{{}_{-2}}=2.4A^{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 $A\geqq 10$ nuclei.

Comments: 4 pages, 4 figures