  In this article we propose a definition of super Gromov-Witten invariants by
postulating a torus localization property for the odd directions of the moduli
spaces of super stable maps and super stable curves of genus zero. That is, we
define super Gromov-Witten invariants as the integral over the pullback of
homology classes along the evaluation maps divided by the equivariant Euler
class of the normal bundle of the embedding of the moduli space of stable spin
maps into the moduli space of super stable maps. This definition sidesteps the
difficulties of defining a supergeometric intersection theory and works with
classical intersection theory only. The properties of the normal bundles, known
from the differential geometric construction of the moduli space of super
stable maps, imply that super Gromov-Witten invariants satisfy a generalization
of Kontsevich-Manin axioms and allow for the construction of a super small
quantum cohomology ring. We describe a method to calculate super Gromov-Witten
invariants of $\mathbb{P}^n$ of genus zero by a further geometric torus
localization and give explicit numbers in degree one when dimension and number
of marked points are small.
