  We have studied a spinor (F = 1) Bose gas in presence of the density-density
interaction through the mean field approach and the perturbation theory for
either sign of the spin dependent interaction, namely the antiferromagnetic
(AF) and the ferromagnetic cases. In the AF case, the charge density wave (CDW)
phase appears to be sandwiched between the Mott insulating (MI) and the
supersolid phases for small values of the extended interaction strength. But
the CDW phase completely occupies the MI lobe when the extended interaction
strength is larger than a certain critical value related to the width of the MI
lobes and hence opens up the possibilities of spin singlet and nematic CDW
insulating phases. In the ferromagnetic case, the phase diagram shows similar
features as that of the AF case and are in complete agreement with a spin-0
Bose gas. The perturbation expansion calculations nicely corroborate the mean
field phase results in both these cases. Further, we extend our calculations in
presence of a harmonic confinement and obtained the momentum distribution
profile that is related to the absorption spectra in order to distinguish
between different phases.
