Strong potential in a box for applications to femtoscopy

TL;DR

The paper addresses the challenge of modeling short-range strong nucleon–nucleon interactions in femtoscopy by developing an analytic framework that combines Coulomb coupling with a square-well representation of the strong force. By solving the Schrödinger equation in the center-of-mass frame and expanding in partial waves, the authors obtain a regular two-body wave function that includes multiple angular momenta and is tractable for phenomenology. They demonstrate that the Lednicky–Lyuboshits asymptotic treatment overestimates correlation signals for small emission sources, and they validate the analytic solution against CATS calculations using realistic potentials (e.g., Argonne $v18$). The approach offers a practical tool for femtoscopy, enabling robust analysis of nucleon and baryon pairs and potential extraction of effective short-range interaction characteristics, with implications for studies of rare baryons and three-body correlations.

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.

Figures (5)

• Figure 1: Square-well potential.
• Figure 2: Proton-proton CFs calculated for different effective source sizes with the Coulomb+SW model. Left: the Coulomb+SW model accounting for strong interaction in the s-wave (continuous lines) is compared to the LL approach (dashed lines). Right: the s-wave calculation (continuous lines) with the Coulomb+SW model is compared to the sp-wave configuration (dashed lines).
• Figure 3: Proton-proton CFs with the CATS package employing the Argonne $v18$ strong potential model compared to the Coulomb+SW model for the two separate cases in which the strong potential is included in the s- (left) and sp-waves (right).
• Figure 4: p-p phase shifts fitted with Eq. (\ref{['eq_A2_5']}) to extract the effective strong potential parameters (Tab. \ref{['tab1']}) in a shape of a square-well for different pair states: $^1S_0$ (top left), $^3P_0$ (top right), $^3P_1$ (bottom left), $^3P_2$ (bottom right). The green line corresponds to the upper limit of the fit range.
• Figure 5: p-p phase shifts fitted with Eq. (\ref{['eq_A2_7']}) to extract the effective range parameters (Tab. \ref{['tab2']}) for different pair states: $^1S_0$ (top left), $^3P_0$ (top right), $^3P_1$ (bottom left), $^3P_2$ (bottom right). Green line corresponds to the upper limit of the fit range.