Tsallis entropy: A comparative study for the 1s2-state of helium atom

The Tsallis entropies are reported, as a function of the Tsallis index q and the screening parameter mu, in position space, for the ground state of the helium atom. Three different potentials, namely Coulomb, Yukawa, and exponential cosine screened Coulomb potentials and their combinations are used in the calculations. The simple Hylleraas correlated wave function, with a three-parameter, is applied to focus on getting the most characteristic physical features of the electron-electron repulsion results. The values are calculated in one- and two-electron charge densities. Moreover, for a comparative study, the Hartree-Fock approximation, which implements a numerical grid method, is employed. Additionally, the modified Tsallis index, Q(q), is proposed and calculated to predict the best value of q in the combined potentials, and it was found that 0.5 <= q < 1.0. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

The study investigates the Tsallis entropies as a function of the Tsallis index q and screening parameter mu in position space for the ground state of the helium atom. Different potentials and wave functions are used to characterize the electron-electron repulsion results, with a focus on calculating one- and two-electron charge densities. Additionally, a modified Tsallis index is proposed and calculated to predict the optimal q value in the combined potentials, finding that 0.5 <= q < 1.0.