  Implying perturbation theory, the impact of the dipole dipole interaction
(DDI) on the thermodynamic properties of a homogeneous electron gas at zero
temperature is investigated. Through the second quantization formalism, the
analytic expressions for the ground state energy and the DDI energy are
obtained. In this paper, the DDI energy has similarities with the previous
works done by others. We show that its general behavior depends on density and
the total angular momentum. Especially, it is found that the DDI energy has a
highly state-dependent behavior. With the growth of density, the magnitude of
DDI energy, which is found to be the summation of all energy contributions of
the states with even and odd total angular momenta, grows linearly. It is also
found that for the states with even and odd total angular momenta, the DDI
energy contributions are corresponding to the positive and negative values,
respectively. In particular, an increase of total angular momentum leads to
decline in the magnitude of energy contribution. Therefore, the dipole dipole
interaction reveals distinct characteristics in comparison with central like
interactions.
