  In this work we derive a systematic short-range expansion of the many-body
wave function. At leading order, the wave function is factorized to a
zero-energy $s$-wave correlated pair and spectator particles, while terms that
include energy derivatives and larger orbital angular momentum two-body
functions appear at subleading orders. The validity of the expansion is tested
for the two-body case, as well as the many-body case, where infinite neutron
matter is considered. An accurate and consistent description of both
coordinate-space two-body densities and the one-body momentum distribution is
obtained. These results show the possibility to utilize such an expansion for
describing different observables in strongly-interacting many-body systems,
including nuclear, atomic and condensed-matter systems. This work also enables
a systematic description of large momentum transfer reactions in nuclear
systems sensitive to short-range correlations, provides a link between such
experiments and low-energy nuclear physics, and motivates measurement of new
observables in these experiments.
