Inverse Compton scattering on laser beam and monochromatic isotropic radiation

Most of the known literature on inverse compton scattering (ICS) is based on earliest theoretical attempts and later approximations led by F.C. Jones and J.B. Blumenthal. We found an independent and more general analytical procedure which provide both relativistic and ultrarelativistic limits for ICS. These new analytical expressions can be derived in a straightforward way and they contain the previously reminded Jones' results. Our detailed solutions may be probed by already existing as well future ICS experiments.