  In this paper, we consider the Dirac-Hartree-Fock equations for system has
many-particles. The difficulties associated with Gaussians model are likely to
be more complex in relativistic Dirac-Hartree-Fock calculations. To processing
these problem, we use accurate techniques. The four-component spinors will be
expanded into a finite basis-set, using Gaussian basis-set type dyall.2zp to
describe 4-component wave functions, in order to describe the upper and lower
two components of the 4-spinors, respectively. 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 the heavy element 83 Bi. We adopt 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 a
system has many-particle. Our obtained results for the heavy atom (Z=83),
including the total energy, energy for each spinor in atom, and expectation
value of <r n > give are good compared with relativistic Visscher treatment.
This accuracy is attributed to the use of the Gaussian basis-set type Dyall to
describe the four-component spinors.
