  We show that for a general system of N s-wave point scatterers, there are
always N eigenmodes. These eigenmodes or eigenchannels play the same role as
spherical harmonics for a spherically symmetric target--they give a phase shift
only. In other words, the T matrix of the system is of rank N and the
eigenmodes are eigenvectors corresponding to non-0 eigenvalues of the T matrix.
The eigenmode expansion approach can give insight to the total scattering cross
section; the position, width, and superradiant or subradiant nature of
resonance peaks; the unsymmetric Fano lineshape of sharp proximity resonance
peaks based on the high energy tail of a broad band; and other properties.
Off-resonant eigenmodes for identical proximate scatterers are approximately
angular momentum eigenstates.
