  The Bose-Hubbard Hamiltonian of spin-2 cold bosons with repulsive interaction
in an optical lattice is proposed. After neglecting the hopping term, the
site-independent Hamiltonian and its energy eigenvalues and eigenstates are
obtained. We consider the hopping term as a perturbation to do the calculations
in second order and draw the phase diagrams for different cases. The phase
diagrams show that there is a phase transition from Mott insulator with integer
number bosons to superfluid when the ratio $c_0/t$ ($c_0$ is the
spin-independent on-site interaction and $t$ the hopping matrix element between
adjacent lattice sites) is decreased to a critical value and that there is
different phase boundary between superfluid and Mott insulator phase for
different Zeeman level component in some ground states. We find that the
position of phase boundary for different Zeeman level component is related to
its average population in the Mott ground state.
