Fermi γ-ray pulsars: Spectral and generation order parameters

We examine the theory of generation order parameters. Three kinds of generation order parameters are introduced, which describe the production of high-energy gamma photons in a cascade process scenario. We find a correlation between the average power-law photon index Gamma and spin-down rate P in 38 common FERMI gamma-ray pulsars, and find that the third generation order parameter, which implies that the magnetic field may have the most significant effect on the high-energy gamma photon absorption in the cascade processes, is the best one. The statistical work shows that the theory of generation order parameters can be applied to describe the the gamma-ray pulsar radiation mechanisms in the cascade processes.