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

I. Nasser; Mostafa Zeama; Afaf Abdel-Hady

doi:10.1016/j.rinp.2017.10.013

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

I. Nasser^*, Mostafa Zeama, Afaf Abdel-Hady

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

Research output: Contribution to journal › Article › peer-review

23 Scopus citations

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.

Original language	English
Pages (from-to)	3892-3900
Number of pages	9
Journal	Results in Physics
Volume	7
DOIs	https://doi.org/10.1016/j.rinp.2017.10.013
State	Published - 2017

Bibliographical note

Publisher Copyright:
© 2017 The Authors

Keywords

Helium isoelectronic series
Hylleraas coordinates
Rényi entropy
Scaling
Shannon entropy
Variation method

ASJC Scopus subject areas

General Physics and Astronomy

Access to Document

10.1016/j.rinp.2017.10.013

Cite this

@article{f13f883074f64288a832bae33db6f566,

title = "The R{\'e}nyi entropy, a comparative study for He-like atoms using the exponential-cosine screened Coulomb potential",

abstract = "A comparative study of the atomic R{\'e}nyi entropies for the exponential-cosine screened Coulomb potential (ECSCP), has been discussed. The study has been done by solving the Schr{\"o}dinger 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 R{\'e}nyi 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 R{\'e}nyi 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 = "Helium isoelectronic series, Hylleraas coordinates, R{\'e}nyi entropy, Scaling, Shannon entropy, Variation method",

author = "I. Nasser and Mostafa Zeama and Afaf Abdel-Hady",

note = "Publisher Copyright: {\textcopyright} 2017 The Authors",

year = "2017",

doi = "10.1016/j.rinp.2017.10.013",

language = "English",

volume = "7",

pages = "3892--3900",

journal = "Results in Physics",

issn = "2211-3797",

publisher = "Elsevier B.V.",

}

TY - JOUR

T1 - The Rényi entropy, a comparative study for He-like atoms using the exponential-cosine screened Coulomb potential

AU - Nasser, I.

AU - Zeama, Mostafa

AU - Abdel-Hady, Afaf

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

KW - Helium isoelectronic series

KW - Hylleraas coordinates

KW - Rényi entropy

KW - Scaling

KW - Shannon entropy

KW - Variation method

UR - https://www.scopus.com/pages/publications/85033567949

U2 - 10.1016/j.rinp.2017.10.013

DO - 10.1016/j.rinp.2017.10.013

M3 - Article

AN - SCOPUS:85033567949

SN - 2211-3797

VL - 7

SP - 3892

EP - 3900

JO - Results in Physics

JF - Results in Physics

ER -

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Fingerprint

Cite this