Astrophysical models need calculations in cross section. It is believed that inverse Comptonrnscattering in strong magnetic fields near the surfaces of Neutron stars is one of the possiblernmechanisms responsible for X-ray and -ray emissions. Spin sum is one fundamental variable inrncalculations of scattering cross sections involving charged fermions in magnetic field. In thisrnthesis we explicitly calculate the spin-sum of the solutions of Dirac equation and using it werncalculate spin-sum corrected total cross of the inverse Compton scattering in the presence ofrnuniform and strong magnetic field