Polarizability of screened Coulomb potential

Abstract

We have obtained the co-ordinate space wavefunction by the inverse Fourier transform of the momentum space wavefunction for the screened Coulomb potential, $$ V\left( r \right)\; = \; - {\text{e}}^{{{ - }\mu {\text{r}}}} /{\text{r}} $$ , problem. The dipole polarizability αd is evaluated in the closure approximation. In this approximation $$ \alpha_{\text{d}} \; = \;\frac{2}{3}\frac{{\langle r^{2} \rangle }}{\Updelta } $$ , where ∆ is the mean excitation energy which is related to the information entropy via Bethe theory for the stopping cross-section for a moving point charge interacting with a bound quantum mechanical system. We find that αd increases with μ. Near the Coulomb limit, we find $$ \alpha_{\text{d}} \left( \mu \right)\; = \,\alpha_{\text{H}} \left( {1\; + \;2.9245 \mu^{2} } \right), $$ where α H is the polarizability of hydrogen atom. Results have been compared with the recent theoretical works.