  We show that it is possible to define shape-independent three-dimensional
short-range quantum interactions in two parameter form for non-spherical
angular momentum channels through double rescaling of potential strength.
Unlike the special case of $l=0$, where the zero range limit of the system is
renormalizable, the effective ranges diverge for $l /ne 0$ channels, and the
system becomes trivial at zero-size limit. It is also shown that the
two-parameter representation with finite interaction range is useful in
analyzing phase shifts with accuracy and describing resonances in non-spherical
scatterings.
