The Rényi entropy, a comparative study for He-like atoms using the exponential-cosine screened Coulomb potential

Abstract

A comparative study of the atomic Rényi entropies for the exponential-cosine screened Coulomb potential (ECSCP), has been discussed. The study has been done by solving the Schrödinger equation in the Hylleraas-space, and within the framework of Ritz’s variational principle. Different wave functions for the 1s2-state of the helium isoelectronic series, in the Hylleraas-space with few variational parameters, have been used to calculate the Shannon and Rényi entropies. They are used to create a comparative study and discuss the scaling behavior of different physical quantities close to the ionization limit. The 3-dimension visualization of the Shannon and Rényi charge densities, as a function of the nuclear charge Z and the screening parameter μ, will be explained and discussed. Comparison with literature results is made, whenever possible. Keywords: Variation method, Scaling, Helium isoelectronic series, Hylleraas coordinates, Shannon entropy, Rényi entropy