Strong potential in a box for applications to femtoscopy

TL;DR

This paper develops an analytical model using a square-well potential to describe the strong nucleon-nucleon interaction, improving the interpretation of femtoscopy measurements in high-energy nuclear collisions.

Contribution

It introduces a new analytical framework for modeling two-nucleon interactions that accounts for Coulomb effects and multiple partial waves, enhancing femtoscopy analysis accuracy.

Findings

The model accurately reproduces correlation functions for realistic source sizes.

It shows the Lednicky-Lyuboshits approximation overestimates signals for small sources.

Good agreement with numerical calculations using Argonne v18 potential.

Abstract

Understanding the short-range nucleon-nucleon interaction is essential for the interpretation of correlation femtoscopy measurements in high-energy hadronic and nuclear collisions. We present an analytical treatment of the strong interaction in two-nucleon systems by modelling it with a square-well potential and solving the Schroedinger equation in the presence of the Coulomb interaction. The resulting pair wave function is regular at small relative distances and allows for the inclusion of multiple partial waves. We apply this framework to proton-proton femtoscopy and compute theoretical correlation functions for realistic source sizes. We demonstrate that the commonly used Lednicky-Lyuboshits asymptotic approximation overestimates the correlation signal for small sources. Comparisons with numerical calculations using the CATS framework and the Argonne v18 potential show good agreement within current experimental uncertainties. The proposed analytical approach provides a practical and flexible tool for femtoscopic analyses of nucleon and baryon pairs.