  For a finite-dimensional (but possibly noncompact) symplectic manifold with a
compact group acting with a proper moment map, we show that the square of the
moment map is an equivariantly perfect Morse function in the sense of Kirwan,
and that the set of critical points of the square of the moment map is a
countable discrete union of compact sets. We show that certain integrals of
equivariant cohomology classes localizes as a sum of contributions from these
compact critical sets, and we bound the contribution from each critical set. In
the case (1) that the contribution from higher critical sets grows slowly
enough that the overall integral converges rapidly and (2) that 0 is a regular
value of the moment map, we recover Witten's result \cite{Witten92} identifying
the polynomial part of these integrals as the ordinary integral of the image of
the class under the Kirwan map to the symplectic quotient.
