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The self-consistent field approach for the electric dipolar ultracoldspin-1/2 fermions is discussed. Contribution of the exchange part of theelectric dipole interaction is found. Hence we obtain a model of dipolarfermions beyond the self-consistent field approximation. It is shown that theexchange interaction of electric dipolar fermions depends on thespin-polarisation of the system. For instance the electric dipole exchangeinteraction equals to zero for spin-unpolarised systems, namely all low layingquantum states occupied by two-particles with opposite spins. In opposite limitof the full spin polarisation of the degenerate fermions, then we have oneparticle in each quantum states, the exchange interaction has maximum value,which is comparable with the self-consistent field part of the dipole-dipoleinteraction. The self-consistent part of the electric dipole-dipole interactiongives a positive contribution into the spectrum of collective excitations,while the exchange part of the dipole-dipole interaction leads to a negativeterm in the spectrum. At angles between the equilibrium polarisation and thedirection of wave propagation close to $\pi/2$ the full dipolar part of thespectrum becomes negative. At the electric dipole moment of fermions of orderof several Debay the dipolar part is large enough to exceed the Fermi pressure,that reveals in an instability.

Destabilization effect of exchange dipole-dipole interaction on the spectrum of electric dipolar ultracold Fermi gas