Determination of the Forward Scattering Amplitude from the Optical-Model Potential in the High-Energy Limit

A relation between the two-particle forward scattering amplitude, $f_k\mathrm{}\left(0\right)\mathrm{}$, and the volume integral over the optical potential, $V_k\left(\mathrm{x}\right)$, is given in the high-energy limit, which is valid at least to second order in the two-body interactions, neglecting correlation and exchange terms. The relation is $\int V_k\left(\mathrm{x}\right)d\mathrm{x}=-\left(\frac{2\pi {\hslash }^2}{m}\right)A{f}_k\mathrm{}\left(0\right),$ Where $A$ is the number of nucleons in the target, and $m$ is the reduced mass of the two-particle system. The connection between the shape of the optical-model potential and the density distribution of the target nucleus is discussed.