  We find self-similar solutions to describe the interaction of spherically
symmetric ejecta expanding at relativistic speeds with an ambient medium having
a power law density distribution. Using this solution, the time evolution of
the Lorentz factor of the outer shock is derived as a function of the explosion
energy, the mass of the ejecta, and parameters for the ambient medium. These
solutions are an ultra-relativistic version of the solutions for the
circumstellar interaction of supernova ejecta obtained by Chevalier and
extensions of the relativistic blast wave solutions of Blandford & Mckee.
