We develop a unified treatment of the non-Abelian Aharonov-Bohm (AB) effect
in isotropic multiband systems, namely, the scattering of particles on a gauge
field corresponding to a noncommutative Lie group. We present a complex contour
integral representation of the scattering states for such systems, and, using
their asymptotic form, we calculate the differential scattering cross section.
The angular dependence of the cross section turns out to be the same as that
obtained originally by Aharonov and Bohm in their seminal paper, but this time
it depends on the polarization of the incoming plane wave. As an application of
our theory, we perform the contour integrals for the wave functions explicitly
and calculate the corresponding cross section for three non-trivial isotropic
multiband systems relevant to condensed matter and particle physics. To have a
deeper insight into the nature of the scattering, we plot the probability and
current distributions for different incoming waves. This paper is a
generalization of our recent results on the Abelian AB effect providing an
extension of exactly solvable AB scattering problems.Comment: 10 pages, 5 figure