  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.
