Relaxation rate spectrum of the linearized Boltzmann equation for hard spheres: cases l=2 and l=3

The solutions of the linearized Boltzmann collision operator for hard spheres can be separated into spherical harmonics and investigated respectively for each angular index l. The fact that an infinite sequence of discrete eigenvalues exists below a continuum has veen established elsewhere for the cases l=0 and l=1. For the case l=2, however, the single gas and the foreign gas problems have markedly different spectral profiles below the continuum. For the latter, there is no discrete eigenvalue in that region while there is still an infinite sequence for the former. For the l=3 case, no discrete eigenvalue exists below the continuum for both problems