  In this theoretical study, the problem of self-focusing of an X-ray intense
laser beam in the thermal quantum plasma is studied. Using a relativistic fluid
model and taking into account the hydrodynamic pressure of degenerate electrons
in the zero temperature limit, the nonlinear momentum equation of electrons is
solved by means of a perturbative method and the nonlinear current density of
the relativistic degenerate electrons is obtained. Saving only the third-order
nonlinearity of the laser beam amplitude, a nonlinear equation describing the
interaction of laser beam with the quantum plasma is derived. It is shown that
considering the nonlinearity of system through solving nonlinear equation of
degenerate electron leads to the originally different wave equation in
comparison with outcomes of the approach in which the permittivity of
longitudinal waves of quantum plasma is problematically extended to the
relativistic case. The evolution of laser beam spot size with Gaussian profile
is considered and the effect of quantum terms on the self-focusing quality is
studied. It is shown that considering quantum effects leads to the decrease in
the self-focusing property and the effect of Bohm tunneling potential is more
dominant than the degenerate electrons pressure term.
