  The spin-1 anisotropic Heisenberg model with a single-ion anisotropy is
studied using the Oguchi's pair approximation. Although the theory is developed
for lattices with general coordination number, we treat in detail the
three-dimensional lattice with the lowest coordination number, i.e. diamond
lattice, where the critical and tricritical behavior of the system is analyzed
as a function of both the single-ion anisotropy and exchange anisotropy.
