Relativistic shock acceleration: A Hartree-Fock approach

We examine the problem of particle acceleration at a relativistic shocks assuming pitch‐angle scattering and using a Hartree‐Fock method to approximate the associated eigenfunctions. This leads to a simple transcendental equation determining the power‐law index, s, given the up and downstream velocities. We compare our results with accurate numerical solutions obtained using the eigenfunction method. In addition to the power‐law index this method yields the angular and spatial distributions upstream of the shock.