Atomic Form Factor Calculations of S-states of Helium

S Diallo ,Ibrahima Faye ,Louis Gomis ,Moustapha Tall ,I Diédhiou

doi:10.11648/j.ajmp.20190804.12

S Diallo , Ibrahima Faye + Show 3 more

Open Access

https://doi.org/10.11648/j.ajmp.20190804.12

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Abstract

Variational calculations of the helium atom states are performed using highly compact 26-parameter correlated Hylleraas-type wave functions. These correlated wave functions used here yield an accurate expectation energy values for helium ground and two first excited states. A correlated wave function consists of a generalized exponential expansion in order to take care of the correlation effects due to N-corps interactions. The parameters introduced in our model are determined numerically by minimization of the total atomic energy of each electronic configuration. We have calculated all integrals analytically before dealing with numerical evaluation. The 1S2 11S and 1S2S 21, 3S states energies, charge distributions and scattering atomic form factors are reported. The present work shows high degree of accuracy even with relative number terms in the trial Hylleraas wave functions definition. The results presented here, indicate that the highly compact twenty-six variational parameters model will have the quantitative and qualitative applicability for the study of electronic correlation. The correlated wave functions are used to calculate the atomic form factor for the diffusion of electrons by the helium atom. The atomic form factor is evaluated as the Fourier transform of the electron density distribution of an atom or ion, which is calculated from theoretical correlated wave functions for free atoms. Finally, suggestions are made as to the way the atomic form factor of the helium atom may be approximated by a sum of Gaussians for efficiency use.

Highlights

Several theories and methods of calculations have been elaborated these last years to calculate energy levels and electronic charge distribution of atoms and molecules
The stationary Schrödinger equation can be solved analytically in a very restricted number of case Most problems of the chemistry and quantum mechanics are solved with the help of approximate methods
A comparative study of two-electron systems with different potentials is done by authors of Ref. [7]

Summary

Introduction

Several theories and methods of calculations have been elaborated these last years to calculate energy levels and electronic charge distribution of atoms and molecules. The second term takes into account both the electron–electron interaction and the correlation between all the parts of the system elements This second terms can be constructed by a sum with a large number of parameters or by a specific mathematical function. Saïdou Diallo et al.: Atomic Form Factor Calculations of S-states of Helium representation of the correlation function [9,10,11,12]. The 1 and 2 , states energies of the helium atom are calculated by using Hylleraas basis wave functions that introduces the coordinates ( , , ). The calculation of charge distribution is important for the determination of scattering atomic form factor. An accurate calculation of wave function is very important to determine the spatial distribution that governs the shape of the atomic form factor.

Variational Calculations

Atomic Form Factor

Results and Discussions

Conclusion