Plasma Confined Ground and Excited State Helium Atom: A Comparison Theorem Study Using Variational Monte Carlo and Lagrange Mesh Method

Salah B Doma,Kalidas D Sen,Mahmoud A Salem

doi:10.3390/computation9120138

Abstract

The energy eigenvalues of the ground state helium atom and lowest two excited states corresponding to the configurations 1s2s embedded in the plasma environment using Hulthén, Debye–Hückel and exponential cosine screened Coulomb model potentials are investigated within the variational Monte Carlo method, starting with the ultracompact trial wave functions in the form of generalized Hylleraas–Kinoshita functions and Guevara–Harris–Turbiner functions. The Lagrange mesh method calculations of energy are reported for the He atom in the ground and excited 1S and 3S states, which are in excellent agreement with the variational Monte Carlo results. Interesting relative ordering of eigenvalues are reported corresponding to the different screened Coulomb potentials in the He ground and excited electronic states, which are rationalized in terms of the comparison theorem of quantum mechanics.

Highlights

The theoretical studies of atomic systems in dense plasmas at different temperatures play a very important role in some physical situations and have gained considerable interest in recent years [1,2,3,4,5,6,7,8]
We investigated the effect of the plasma environment by using the screened Coulomb potential (SCP) and the exponential cosine screened Coulomb potential (ECSCP) models on the energy eigenvalues of the helium atom
For the value of the ground state energy of the He atom that corresponds to Debye screening length λ D = ∞ with screening parameter μ = 0.0 and expresses the case of pure Coulomb potential, we obtained the value −2.902662 a.u., which nearly coincides with the value

Summary

Introduction

The theoretical studies of atomic systems in dense plasmas at different temperatures play a very important role in some physical situations and have gained considerable interest in recent years [1,2,3,4,5,6,7,8]. The dilute plasma environment is represented by the screened. Coulomb potentials given by the Debye–Hückel model (DHM) or screened Coulomb potential (SCP) [9], which provides a suitable treatment of nonideality in plasma via the screening effect under the low-density and high-temperature conditions. Hulthén potential is used as a model potential for the dilute plasma environment in which the atoms are embedded. The dense quantum plasmas environment is represented by using the modified Debye–Hückel model (MDHM) [10] or exponential cosine screened Coulomb potential (ECSCP). Considerable attention has been given to the screened Coulomb potentials and exponential cosine screened Coulomb potential in field theory, nuclear, and plasma physics [11,12,13,14,15,16,17]

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