Short-range expansion for the quantum many-body problem

TL;DR

This paper develops a systematic short-range expansion of the many-body wave function, enabling improved descriptions of strongly-interacting systems and connecting experimental observables with low-energy nuclear physics.

Contribution

It introduces a novel short-range expansion framework for many-body wave functions, applicable across nuclear, atomic, and condensed matter systems.

Findings

Accurate description of two-body densities and momentum distributions

Validation of the expansion in neutron matter and two-body systems

Potential to analyze high-momentum transfer reactions in nuclear physics

Abstract

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.