# Contact formalism for coupled channels

## TL;DR

This paper extends the contact formalism to systems with coupled channels, deriving a generalized framework that explains short-range correlations in nuclear physics, including the simplification to a single contact in certain regimes.

## Contribution

It introduces a generalized contact formalism for coupled channels, deriving asymptotic forms and contact matrices, and explains the reduction to a single contact in specific coupling regimes.

## Key findings

- Derivation of asymptotic form for coupled channels
- Introduction of contact matrices for two-channel systems
- Explanation of single contact approximation in weak or strong coupling regimes

## Abstract

The contact formalism, a useful tool for analyzing short-range correlations, is generalized here for systems with coupled channels, such as in nuclear physics. The relevant asymptotic form is presented and contact matrices are defined. Generally, for the case of two coupled channels, two two-body functions are included in the asymptotic form, resulting a 2 x 2 contact matrix. Nevertheless, it is shown that if the coupling terms of the potential are very weak or very strong, only a single two-body function is needed, resulting a single contact. This universal result is directly relevant to nuclear systems, and provides a theoretical explanation for the fact that proton-neutron short-range correlations can be described using the single bound-state deuteron wave function. It is achieved by applying an appropriate boundary condition on the two-body functions. This boundary condition can be interpreted as a mean field potential imposed on the correlated pair due to the residual system.