Probing the Three-dimension Emission Source and Neutron Skin via $π$-$π$ Correlations in Heavy-Ion Collisions

TL;DR

The work addresses reconstructing the 3D emission-source function $S(\mathbf{r})$ from two-pion correlations $C(\mathbf{q})$ in heavy-ion collisions. It extends the Richardson–Lucy deconvolution to a 3D kernel derived from the KP femtoscopy framework and the Coulomb-modified pion wave function. Validation with Gaussian sources and HADES Au+Au data demonstrates accurate 3D reconstruction and reveals non-Gaussian tails in the emission source. UrQMDPb+Pb simulations with varying neutron-skin thickness show that the RL-imaged source broadens with thicker neutron skins, indicating the method’s potential as a direct probe of nuclear density distributions in heavy-ion collisions.

Abstract

The Richardson-Lucy algorithm is applied to reconstruct the three-dimensional source function of identical pions from their two-particle correlation functions. The algorithm's performance is first evaluated through simulations with Gaussian-type initial source functions. Its imaging quality and robustness are further demonstrated with experimental data from Au+Au collisions at 1.23 A GeV, collected by the HADES Collaboration. Additionally, using UrQMD simulations of Pb+Pb collisions at 1.5 A GeV, we show that the deblurred source functions exhibit sensitivity to the initial neutron skin thickness of the colliding nuclei. This highlights the potential of the Richardson-Lucy algorithm as a tool for probing the neutron density distribution in heavy nuclei.

Figures (7)

• Figure 1: Coulomb wave function modulus square $|\Psi(x, q_x)|^2$ as a function of coordinate space position $x$ and momentum space component $q_x$. The color intensity represents the probability density, with brighter regions indicating higher values.
• Figure 2: (a)--(c) Reconstructed correlation functions along the out, side, and long directions, compared with the true correlation functions. The restored results accurately reproduce the Coulomb-induced suppression at low relative momentum while reducing statistical noise. (d)--(e) Comparison between the reconstructed source functions and the true Gaussian distributions, showing excellent agreement in both shape and magnitude.
• Figure 3: Evolution of $\chi^2$ with the number of iterations
• Figure 4: Convergence of the imaged source function. Open symbols are the reconstructed profile at $10^{\rm th}$, $100^{\rm th}$ and $500^{\rm th}$ iteration, evolving from the initial guess (dashed) toward the final deblurred distribution (filled circles), which overlaps with the input known distribution (solid).
• Figure 5: (a)--(c) Reconstructed correlation functions along the out, side, and long directions, compared with the experimental data from HADES. The light red bands indicate experimental uncertainties. Slight discrepancies in the central region may result from the algorithm's treatment of Coulomb repulsion effects. (d)--(f) Comparison between the imaged source functions and the Gaussian-parameterized source functions from HADES. The reconstructed profiles show an upward deviation at large relative distances $r$ particularly on the longitudinal side, suggesting non-Gaussian characteristics in the emission source.