[Paper Review] The influence of the neutron skin and the asymmetry energy on the $π^-/π^+$ ratio

C. Hartnack, A. Le Fèvre+2 more|arXiv (Cornell University)|Aug 29, 2018

Quantum Chromodynamics and Particle Interactions3 citations

TL;DR

This study uses the Isospin Quantum Molecular Dynamics (IQMD) model to disentangle the contributions of neutron skin thickness, density-dependent asymmetry energy, and Pauli blocking in $π^{-}/\pi^{+}$ ratios in heavy-ion collisions. It demonstrates that centrality-dependent measurements at different beam energies can isolate these effects, enabling experimental determination of neutron skin and asymmetry energy properties.

ABSTRACT

We use the Isospin Quantum Molecular Dynamics model (IQMD) to analyze the centrality dependence of the isospin ratio of pions, $π^-/π^+$. We find that the density dependence of the asymmetry potential, the Pauli blocking of the $Δ$-decay and the thickness of the neutron skin influence in different ways this observable. Using the centrality dependence of this ratio at different beam energies we can disentangle the different contributions and open the way for their experimental determination.

Motivation & Objective

• To disentangle the individual contributions of neutron skin thickness, density-dependent asymmetry energy, and Pauli blocking on the $π^{-}/\pi^{+}$ ratio in heavy-ion collisions.
• To establish a method for experimentally determining neutron skin thickness and the density dependence of the asymmetry energy using centrality-resolved $π^{-}/\pi^{+}$ ratios.
• To investigate how these effects vary with beam energy and collision centrality, particularly distinguishing their roles at 400 AMeV versus 1 AGeV.
• To validate the robustness of this disentanglement procedure through systematic simulations in $^{48}$Ca and $^{208}$Pb systems.

Proposed method

• Modified IQMD model to initialize protons and neutrons with different root-mean-square (rms) radii, allowing for controlled neutron skin thickness $s$ via $\Delta R = R_N - R_P = s$.
• Used three initialization schemes: $R_P = R_N$ (standard), $R_P < R_N$ (large skin), and $\Delta R = s$ (intermediate skin, $s \approx 0.2-0.3$ fm for $^{208}$Pb).
• Simulated $^{48}$Ca+$^{48}$Ca and $^{208}$Pb+$^{208}$Pb collisions at 400 AMeV and 1 AGeV beam energies across a range of impact parameters.
• Varied the density dependence of the asymmetry potential via the equation of state parameter $\gamma$, testing soft to hard stiffness.
• Incorporated Pauli blocking effects on $\Delta$-baryon decay channels, particularly suppressing $n\pi^{+}$ production in neutron-rich environments.
• Analyzed the centrality dependence of the $\pi^{-}/\pi^{+}$ ratio to isolate sensitivity to each physical effect.

Experimental results

Research questions

• RQ1 How does the neutron skin thickness influence the centrality dependence of the $\pi^{-}/\pi^{+}$ ratio at different beam energies?
• RQ2 To what extent is the $\pi^{-}/\pi^{+}$ ratio sensitive to the density dependence of the asymmetry energy, and how does this vary with collision centrality and beam energy?
• RQ3 What is the role of Pauli blocking in $\Delta$-baryon decay channels, and how does it affect the $\pi^{-}/\pi^{+}$ ratio in neutron-rich matter?
• RQ4 Can the centrality dependence of the $\pi^{-}/\pi^{+}$ ratio at multiple beam energies be used to disentangle the contributions of neutron skin, asymmetry energy, and Pauli blocking?

Key findings

• The $\pi^{-}/\pi^{+}$ ratio is most sensitive to neutron skin thickness in peripheral collisions, where the density dependence of the asymmetry potential has minimal influence.
• At 400 AMeV, the ratio shows a significant dependence on the density dependence of the asymmetry potential, particularly in central collisions, but this effect vanishes at 1 AGeV.
• Pauli blocking of $\Delta$-baryon decay enhances the $\pi^{-}/\pi^{+}$ ratio at 400 AMeV, especially in peripheral collisions, but has negligible impact at 1 AGeV due to large phase space.
• The centrality dependence of the $\pi^{-}/\pi^{+}$ ratio at 400 AMeV allows for the extraction of neutron skin thickness, which can then be used to isolate the asymmetry energy contribution in central collisions.
• The method is robust: systematic variation of beam energy and centrality enables clear disentanglement of neutron skin, asymmetry energy, and Pauli blocking effects.
• The $\pi^{-}/\pi^{+}$ ratio in peripheral collisions at 400 AMeV is primarily sensitive to neutron skin, while central collisions at the same energy are sensitive to the asymmetry energy and Pauli blocking.