Impact of the in-medium cross section on cluster spectra in ${}^{40,48}\mathrm{Ca}+{}^{58,64}\mathrm{Ni}$ collisions at $56$ and $140$ $\mathbf{\mathrm{MeV}}/\mathrm{\mathbf{nucleon}}$

TL;DR

This study investigates how in-medium nucleon-nucleon cross sections influence mid-rapidity light-cluster spectra in central ${}^{40,48} ext{Ca}+{}^{58,64} ext{Ni}$ collisions at 56 and 140 MeV/nucleon. Using the Antisymmetrized Molecular Dynamics (AMD) transport model with a density- and momentum-dependent in-medium cross section $ ilde{\sigma}_{NN}$ controlled by a screening parameter $oldsymbol{\eta}$, the authors compare simulated spectra to experimental data filtered to reproduce the same centrality selection. They find that a stronger in-medium suppression is required at 56 MeV/n ($oldsymbol{\eta}=0.35$) than at 140 MeV/n ( $oldsymbol{\eta}=0.85$), implying the in-medium effect reflects the dynamical state of the medium rather than solely density. These results demonstrate the need to tune in-medium cross sections in AMD to reliably constrain the symmetry-energy term in the nuclear equation of state from heavy-ion collision observables. The work highlights the energy-dependent nature of in-medium effects and their critical role in linking reaction dynamics to the density dependence of the symmetry energy.

Abstract

Although significant efforts have been made to investigate the density dependence of the nuclear symmetry energy, the influence of the in-medium cross section on particle production in transport models is not well constrained. The in-medium cross section reflects the dynamic situation of the medium such as a nontrivial phase space distribution. In this study, we analyze the transverse momentum spectra of $p$, $d$, $t$, ${}^3{\mathrm{He}}$ and $α$ particles emitted near mid-rapidity in central $^{40,48}\mathrm{Ca}$ + $^{58, 64}\mathrm{Ni}$ reactions at $56$ and $140$ $\mathrm{MeV}/\mathrm{nucleon}$. The Antisymmetrized Molecular Dynamics ($\mathrm{AMD}$) model is chosen as the transport model for data comparison. Central events are selected based on charged-particle multiplicity in both the experimental data and AMD calculations after applying an experimental filter. Our results show that the in-medium nucleon-nucleon scattering cross-sections are more strongly reduced at $56$ $\mathrm{MeV}/\mathrm{nucleon}$ than at $140$ $\mathrm{MeV}/\mathrm{nucleon}$ incident energy.

Figures (7)

• Figure 1: Charged-particle hit pattern of the Microball and HiRA10 detectors. The boundaries of each rectangular block represent CsI(Tl) crystals in Microball. The coverage at $\theta_\mathrm{lab} \in (30^\circ, 75^\circ)$ corresponds to charged particles detected by HiRA10.
• Figure 2: Effect of the screening parameter $\eta$ on $\tilde{\sigma}_{np}$ at saturation density. This $\tilde{\sigma}_{np}$ is used to obtain the matrix element $|M|^2$ in medium, which then determines the $NN$ cross section by Eq. \ref{['amd_coll_sigma']}.
• Figure 3: Differential cross section $d\sigma(N_C)/db$ from AMD calculation. The dashed lines are fits to the distribution with the equation $2\pi b / (1 + \exp((b-b_0)/\Delta b))$, see Ref. INDRA:2020kyj.
• Figure 4: Left : Correlation between the impact parameter and the charged-particle multiplicities in $\mathrm{AMD}$ after filtering out events according to experimental gates. Right : The calculated mapping between charged-particle multiplicity $N_C$ and the estimated impact parameter in the experiment (black triangle) and $\mathrm{AMD}$ with $\eta=0.35$ (blue line) and $\eta=0.85$ (red line). The top and bottom panels refer to the reactions $^{48}$Ca + $^{64}$Ni at $56$ (top) and $140$ (bottom) $\mathrm{MeV}/\mathrm{nucleon}$, respectively.
• Figure 5: Integrated yields of $p$, $d$, $t$, ${}^3\mathrm{He}$, $\alpha$ of $^{40,48}\mathrm{Ca}+{}^{58,64}\mathrm{Ni}$ reactions at $56$ (top) and $140$ (bottom) $\mathrm{MeV}/\mathrm{nucleon}$. Data are represented by black markers and $\mathrm{AMD}$ calculations with $\eta=0.85$ and $\eta=0.35$ are represented by red and blue lines respectively. The integration is over the mid-rapidity region $0.4 < y_\mathrm{lab}/y_\mathrm{beam}<0.6$ and in the $p_\mathrm{T}/\mathrm{A}$ range showed in Fig. \ref{['fig:5x2-pt-e56']} and Fig. \ref{['fig:5x2-pt-e140']}. Statistical uncertainties are smaller than the data points.