The energy correction due to a finite size nucleus of the hydrogen atom confined in a penetrable spherical cavity

Abstract

We computed accurate values for the ground state energy of a hydrogen atom by a finite spherical barrier of height V₀ as a function of the confinement radius . We consider the nucleus as a sphere with a uniform charge distribution instead of as a point particle. The contribution to the ground state energy due to the finite nuclear size is computed as a function of the confinement radius,  and the height of the barrier, V₀, using time-independent perturbation theory. For an impenetrable cavity with .5 au, we found that this energy correction is fifty times higher than the corresponding value for the free hydrogen atom. For a finite value of V₀,we found that the maximum of the energy correction is reached at a value  which very is close to the position at which the electron density is most compact around to the nucleus. This is confirmed though the Shannon entropy in configuration space.