New Scaling Relations for Nucleons in Three-Nucleon Short-Range Correlations

Abstract

The search for three nucleon short range correlations~(3N- SRCs) in nuclei is one of the intensive areas of research in high density nuclear physics. It is in part motivated by the prediction of the above two-solar mass neutron stars based on 3N short-range forces and the subsequent observation of such stars. The 3N-SRCs serve as a "laboratory" for probing the dynamics of largely unknown irreducible 3N-forces. However, the identification of 3N-SRCs in high energy nuclear processes is still elusive making the prospects of their investigation problematic. In this work we introduced new dynamical parameters for 2N- and 3N- SRCs, $β_{2N}$ and $β_{3N}$ respectively, which characterize the strength of SRCs beyond combinatorial counting of nucleons in SRCs. For 2N-SRCs the introduction of $β_{2N}$ parameter resulted in a previously known and experimentally verified relation for proton and neutron momentum distributions in 2N-SRCS. For 3N-SRCs the $β_{3N}$ parameter allowed to factorize momentum distributions of nucleons in the correlation resulting in a prediction of a new scaling relation between proton and neutron momentum distributions in 3N SRCs. This relation, if valid gives a new venue for identification of 3N-SRCs in electro-nuclear processes. Even though the obtained scaling relation is relevant in the relativistic domain, the possibility of separating center of mass motion of SRCs on the light-front allows to check the validity of predicted scaling using non-relativistic ab-initio wave functions. We found surprisingly reasonable confirmation of our prediction analyzing ab-initio wave functions of nuclei in the range $3\le A\le 12$. This indicates the robustness of the scaling relation and opens up a new direction in searching for 3N-SRCs experimentally.