  Using a relativistic version of Landau theory of Fermi liquid with
$\sigma-\omega$ and $\rho$ mesons exchange, we have obtained an equation of
state for dense neutron star matter in presence of strong quantizing magnetic
field. It is found that in this scenario the self energies of both neutron and
proton components of dense neutron star matter become complex under certain
physical conditions. To be more specific, it is observed that in the exchange
diagrams of $\sigma$, $\omega$ and neutral $\rho$ transfer processes and in the
direct interaction diagram with $\rho_\pm$ transfer reactions, the nucleon
self-energies become complex in nature.
