Unlocking the initial neutron density distribution from the two-pion HBT correlation function in heavy-ion collisions

TL;DR

The paper addresses how to constrain the initial neutron density distribution and neutron skin in nuclei using heavy-ion collisions. It employs the UrQMD transport model with a Droplet-model neutron density controlled by $f_n$, followed by the CRAB afterburner to compute two-pion HBT correlations and extract radii $R_L$, $R_O$, $R_S$ and the emission volume $V_{fo}$, with observables wrapped in $π^{-}/π^{+}$ and HBT analyses. Key findings show that the charged-pion yield ratio and the two-pion HBT observables are sensitive to $f_n$, while the centrality dependence is comparatively weak for momentum-space correlations; the STAR-compatible $R_O/R_S$ trends are achieved for $f_n<3$, supporting the use of HBT as a probe of neutron density. The results offer a potential experimental pathway to constrain neutron density distributions and the nuclear equation of state, though further cross-model validation and Bayesian analyses are needed to isolate competing effects.

Abstract

Revealing the neutron density distribution in the nucleus is one of the crucial tasks of nuclear physics. Within the framework of the ultrarelativistic quantum molecular dynamic model followed by a correlation afterburner program, we investigate the effects of the initial neutron density distribution on the charged-pion yield ratio $π^{-}/π^{+}$, the two-pion momentum correlation function, and the emission source dimension. It is found that the $π^{-}/π^{+}$ ratio is sensitive to the initial neutron density distribution and the impact parameter, especially for collisions at large impact parameter. However, the charge splitting in the correlation functions between positively $π^{+}π^{+}$ and negatively $π^{-}π^{-}$, as well as the source radii and volumes extracted exhibit a stronger dependence on the initial neutron density distribution, but a weaker dependence on the impact parameter. The present study highlights that $π^{+}π^{+}$ and $π^{-}π^{-}$ correlation functions in heavy-ion collisions could be used to probe the initial neutron density distribution of nuclei.

Figures (8)

• Figure 1: (Color online) The proton (left), neutron (middle), and total (right) density distributions of the target nucleus $^{197}\rm{Au}$ calculated with $f_{n}$ varies from 1 to 6 in Eq. \ref{['fiti']}. The top panels display the initial density profiles, while the bottom panels present the density profiles at $t=20$ fm/c.
• Figure 2: (Color online) The dependence of $\pi^{-}/\pi^{+}$ on the diffuseness parameter of neutron density distribution $f_{n}$ [panel (a)] and the impact parameter $b$ [panel (b)] under the condition of $0.15<p_{T}<1.0$ GeV/c for Au+Au at $\sqrt{s_{NN}}=3$ GeV.
• Figure 3: (Color online) The dependence of $\pi^{-}/\pi^{+}$ ratio on transverse momentum $p_{T}$ in Au+Au collisions at $\sqrt{s_{NN}}=3$ GeV for $0.15<p_{T}<1.0$ GeV/c. Results from simulations with varying $b$ (left panels) and $f_{n}$ (right panels) are represented by different symbols.
• Figure 4: (Color online) Top panels: the one-dimensional $\pi^{+}\pi^{+}$ and $\pi^{-}\pi^{-}$ correlation functions as a function of the invariant relative momentum $q_{\rm{inv}}$ in Au+Au at $\sqrt{s_{NN}}=3$ GeV with various $b$ and different $f_{n}$. Bottom panels: the corresponding correlation function ratios between $\pi^{-}\pi^{-}$ and $\pi^{+}\pi^{+}$. The horizontal dotted lines represent unity.
• Figure 5: (Color online) The HBT correlation function ratios between $\pi^{-}\pi^{-}$ and $\pi^{+}\pi^{+}$ for $f_{n}=1$ (left panel) and $f_{n}=6$ (right panel) with various $b$.