  In this paper we have studied the effect of external magnetic field in the
co-existing phase of superconducting and anti-ferromagnetism of rare earth
nickel borocarbides. The anti-ferromagnetism in these systems might have
originated due to both localized 'f' electrons as well as itinerant electrons
which are responsible for conduction. On the other hand, superconductivity is
due to spin density wave, arising out of Fermi surface instability. The
anti-ferromagnetism order is mostly influenced by hybridization of the 'f'
electron with the conduction electron. Here we have obtained the dependence of
superconducting energy gap as well as staggered magnetic field on temperature T
and energy $\epsilon_k$ in a framework based on mean field Hamiltonian using
double time electron Green's function. We have shown in our calculation the
effect of external magnetic field on superconducting and anti-ferromagnetic
order parameter for $YNi_2B_2C$ in the presence of hybridization. The ratio of
the calculated effective gap and $T_C$ is close to BCS value which agrees quite
well with experimental results.
