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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 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.

Using Gaussian Basis-Sets with Gaussian Nuclear Charge Distribution to Solve Dirac-Hartree-Fock Equation for 83Bi-Atom