New formulas for the $\left(-2\right)$ moment of the photoabsorption cross section, ${\sigma }_{-2}$

Two new formulas for the $\left(-2\right)$ moment of the photoabsorption cross section, ${\sigma }_{-2}$, have been determined, respectively, from the 1988 photoneutron evaluation of Dietrich and Berman and a mass-dependent symmetry energy coefficient, $a_{\mathrm{sym}}\left(A\right)$. The data for $A\gtrsim 50$ follow, with a RMS deviation of 6%, the power law ${\sigma }_{-2}=2.4A^{5/3}\mu \mathrm{b}/\mathrm{MeV}$, which is in agreement with Migdal's calculation of ${\sigma }_{-2}=2.25A^{5/3}\mu \mathrm{b}/\mathrm{MeV}$ based on the hydrodynamic model and the ${\sigma }_{-2}$ sum rule. The additional inclusion of $a_{\mathrm{sym}}\left(A\right)$ provides a deeper insight into the nuclear polarization of $A\geqq 10$ nuclei.

Figure 1

The $\left(-2\right)$ moment of the total photoabsorption cross section ${\sigma }_{-2}$ vs $A$ on a log-log scale. The experimental values from the 1988 compilation [11] are given by circles. These data follow a power-law relationship ${\sigma }_{-2}=2.4A^{5/3}\mu \mathrm{b}/\mathrm{MeV}$. The dashed line represents Levinger's fit to the available data (squares) in 1957, ${\sigma }_{-2}=3.5A^{5/3}\mu \mathrm{b}/\mathrm{MeV}$ [2]. In both cases, $\kappa =1$ is assumed.

Figure 2

The polarizability parameter $\kappa$ given by $\frac{{\sigma }_{-2}}{2.4A^{5/3}}$ using the ${\sigma }_{-2}$ data in the Dietrich and Berman compilation (circles) [11]. The horizontal solid line corresponds to $\kappa =1$. Large deviations from the hydrodynamic model prediction $\left(\kappa =1\right)$ are observed for $A\lesssim 50$.

Figure 3

Symmetry energy coefficient, $a_{\mathrm{sym}}\left(A\right)$, of finite nuclei as a function of mass number $A$ using Eq. (10) [32].

Figure 4

The $\left(-2\right)$ moment of the total photoabsorption cross section ${\sigma }_{-2}$ vs $A$ on a log-log scale using Eq. (12) (solid line). For comparison purposes, Eq. (9) (dashed line) and the data from the 1988 compilation [11] are also plotted.