Some general features of the scattering of boson-based anyons with an added
non-statistical interaction are discussed. Periodicity requirements of the
phase shifts are derived, and used to illustrate the danger inherent in
separating these phase shifts into the well-known pure Aharanov-Bohm phase
shifts, and an additional set which arise due to the interaction. It is proven
that the added phase shifts, although due to the non-statistical interaction,
necessarily change as the statistical parameter is varied, keeping the
interaction fixed. A hard-disk interaction provides a concrete illustration of
these general ideas. In the latter part of the paper, scattering with an
additional hard-disk interaction is studied in detail, with an eye towards
providing a criterion for the validity of the mean-field approximation for
anyons, which is the first step in virtually any treatment of this system. We
find, consistent with previous work, that the approximation is justified if the
statistical interaction is weak, and that it must be more weak for boson-based
than for fermion-based anyons.Comment: 17 pages plus 3 encoded/compressed post-script figures,
UdeM-LPN-TH-94-18
