  We study the total cross section and angular distribution in Rayleigh
scattering by hydrogen atom in the ground state, within the framework of Dirac
relativistic equation and second-order perturbation theory. The relativistic
states used for the calculations are obtained by making use of the finite basis
set method and expressed in terms of B-splines and B-polynomials. We pay
particular attention to the effects that arise from higher (non-dipole) terms
in the expansion of the electron-photon interaction. It is shown that the
angular distribution of scattered photons, while it is symmetric with respect
to the scattering angle $\theta$=90$^\circ$ within the electric dipole
approximation, becomes asymmetric when higher multipoles are taken into
account. The analytical expression of the angular distribution is parametrized
in terms of Legendre polynomials. Detailed calculations are performed for
photons in the energy range 0.5 to 10 keV. When possible, results are compared
with previous calculations.
