Neutrino Bremsstrahlung Process in highly degenerate magnetized electron gas

In this article the neutrino bremsstrahlung process is considered in presence of strong magnetic field, though the calculations for this process in absence of magnetic field are also carried out simultaneously. The electrons involved in this process are supposed to be highly degenerate and relativistic. The scattering cross sections and energy loss rates for both cases, in presence and absence of magnetic field, are calculated in the extreme-relativistic limit. Two results are compared in the range of temperature $5.9\times 10^{9}$ K $< T\leq 10^{11}$ K and magnetic field $10^{14} - 10^{16}$ G at a fixed density $\sim 10^{15}$ $gm/cc$, a typical environment during the cooling of magnetized neutron star. The interpretation of our result is briefly discussed and the importance of this process during the stellar evolution is speculated.