Correction Four-Component Dirac-Coulomb Using Gaussian Basis-Set and Gaussian Model Distribution for Super Heavy Element (Z=115)

TL;DR

This paper develops a Gaussian basis-set approach to solve the Dirac-Coulomb equation for super heavy element 115, incorporating a Gaussian charge distribution model to accurately describe nuclear charge effects.

Contribution

It introduces a Gaussian basis-set method combined with a Gaussian nuclear charge model for relativistic calculations of super heavy elements, addressing singularity issues at the nucleus.

Findings

Successfully applied to element 115 with accurate energy level calculations.

Implemented Gaussian charge distribution to handle nuclear charge singularity.

Enhanced relativistic quantum calculations with flexible Gaussian basis functions.

Abstract

In this paper, we consider the Dirac-Coulomb equation for many-particles, to describe the interaction between electrons in the system having many electrons. The four-component wave function will expanding into a finite basis-set, using Gaussian basis function technique, in order to describe the upper and lower two components of the 4-spinors, respectively. Gaussian basis-set type dyall.v2z has been adopted to describe the correlation and polarization of 4-component wave function. The small component Gaussian basis functions have been generated from large component Gaussian basis functions using kinetic balance relation. The considered techniques have been applied for super heavy element 115 Uup, in which the nuclei has large charge and the inner spinors s 1/2 is strongly contracted. To solve the problem resulted from singularity at the origin for the 1s 1/2 spinors. We adopting the Gaussian charge distribution model to describe the charge of nuclei. To calculate accurate properties of the atomic levels, we used Dirac-Hartree-Fock method, which have more flexibility through Gaussian basis-set to treat relativistic quantum calculation for system has many-particle.