The nonadditive entropy for the ground state of helium-like ions using Hellmann potential

Abstract

We are calculating the Tsallis entropy $\left(S_q\right)$ for the ground state of helium isoelectronic series that interrelates with the Yukawa and Hellmann-type potentials in the position (r) space. The calculation has been done by solving the Schrödinger equation in the Hylleraas-coordinate system and within the framework of the Ritz’s variational principle. Simple wave functions have been used in the calculation to reach informative discussions. The scaling behaviour of Tsallis entropy as a function of the nuclear charge Z, the Tsallis index $q$, and screening parameter $\mu$, is defined and discussed. Due to the nonadditive property of our system, the modified Tsallis index $Q_q$ is proposed and calculated as a function of $\mu$. The calculations for two-electron systems in Hellmann potential (HP) are carried out for the first time in the literature.

GRAPHICAL ABSTRACT

KEYWORDS:

• Ritz’s variation method
• scaling
• helium atom
• Hylleraas coordinates
• nonadditive entropy
• Tsallis entropy
• Shannon entropy

Acknowledgments

We sincerely thank the kind referee for his/her constructive and valuable comments, from which the manuscript has greatly benefited.

Disclosure statement

No potential conflict of interest was reported by the authors.