Adependence of the enhancement factor in energy-weighted sums for isovector giant resonances

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We consider the energy weighted sums (EWS) for isovector giant dipole resonances (IVGDR) in finite nuclei within Landau kinetic theory. The dependence of both IVGDR energy, ${E}_{\mathrm{IVGDR}}$, and the EWS enhancement factor, $\ensuremath{\kappa}(A)$, on the mass number $A$ occurs because of the boundary condition on the moving nuclear surface. The values of ${E}_{\mathrm{IVGDR}}{A}^{1/3}$ and $\ensuremath{\kappa}(A)$ increase with $A$. The obtained value of the enhancement factor is about $10%$ for light nuclei and reaches approximately $20%$ for heavy nuclei. A fit of the enhancement factor to the proper experimental data provides a value for the isovector Landau amplitude of ${F}_{1}^{'}\ensuremath{\simeq}1.1$.