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Improved initial colliding nuclei density profile method for QMD-type transport models

Xilong Xiang, Manzi Nan, Pengcheng Li, Yongjia Wang, Ling Liu, Qingfeng Li

TL;DR

The paper tackles how initial nuclear density distributions in QMD-type transport models influence the extraction of the high-density nuclear equation of state (EoS) from heavy-ion collisions. It introduces a Fourier-series expansion (FSE) filtering method to construct objective 3D density profiles by deriving a filtering function g(r_i) from Fourier coefficients of the target density. The method is validated by recreating bubble-like densities for the nucleus $^{96}$Ru and integrating it into the UrQMD framework, followed by simulations of $^{96}$Ru+$^{96}$Ru at $E_ ext{lab}=1500~$MeV/nucleon. Results show that FSE initialization increases the maximum system density and enhances collective flow, and that EoS constraints inferred from observables depend on the initialization method (WS suggesting $K_0>280$ MeV vs FSE suggesting $K_0=200$–$280$ MeV). Overall, the FSE filtering approach provides a robust means to sample exotic density profiles, improving the link between nuclear structure and dense-matter EoS in heavy-ion collision studies.

Abstract

Accurate modeling of the initial density profile is essential for studying heavy-ion collisions (HICs) with a transport model. Within the framework of the quantum molecular dynamics (QMD)-type model, a novel method for generating nuclear density distributions based on a Fourier series expansion (FSE) is proposed. In this approach, the objective density distribution is expanded into a Fourier series to construct a filter function, which is then applied to select the randomly sampled nucleon coordinates in phase space to generate a three-dimensional nuclear density distribution that matches the desired profile. This new initialization method is further incorporated into the ultrarelativistic quantum molecular dynamics (UrQMD) model, and the bubble-like density distribution of $^{96}$Ru is constructed, showing good stability. Then, by simulating $^{96}$Ru+$^{96}$Ru collisions at $E_\mathrm{lab}=1500$ MeV/nucleon with different equations of state (EoS) and initialization methods, the effects of the initialization method on the final state observables and the constrained information of EoS are analyzed. It is found that the maximum system density increases when the new FSE initialization method is adopted, and results in an enhanced collective flow. Moreover, a relatively stiff EoS with $K_0>280$ MeV is favored when adopting the Woods-Saxon initialization method, whereas an EoS of $K_0$ = 200-280 MeV is supported when using the FSE initialization. These results indicate that, within QMD-like transport models, the FSE filtering method provides a reliable means to sample nuclei with exotic density profiles, offering new insight to investigate nuclear structure and dense nuclear matter EoS through HICs.

Improved initial colliding nuclei density profile method for QMD-type transport models

TL;DR

The paper tackles how initial nuclear density distributions in QMD-type transport models influence the extraction of the high-density nuclear equation of state (EoS) from heavy-ion collisions. It introduces a Fourier-series expansion (FSE) filtering method to construct objective 3D density profiles by deriving a filtering function g(r_i) from Fourier coefficients of the target density. The method is validated by recreating bubble-like densities for the nucleus Ru and integrating it into the UrQMD framework, followed by simulations of Ru+Ru at MeV/nucleon. Results show that FSE initialization increases the maximum system density and enhances collective flow, and that EoS constraints inferred from observables depend on the initialization method (WS suggesting MeV vs FSE suggesting – MeV). Overall, the FSE filtering approach provides a robust means to sample exotic density profiles, improving the link between nuclear structure and dense-matter EoS in heavy-ion collision studies.

Abstract

Accurate modeling of the initial density profile is essential for studying heavy-ion collisions (HICs) with a transport model. Within the framework of the quantum molecular dynamics (QMD)-type model, a novel method for generating nuclear density distributions based on a Fourier series expansion (FSE) is proposed. In this approach, the objective density distribution is expanded into a Fourier series to construct a filter function, which is then applied to select the randomly sampled nucleon coordinates in phase space to generate a three-dimensional nuclear density distribution that matches the desired profile. This new initialization method is further incorporated into the ultrarelativistic quantum molecular dynamics (UrQMD) model, and the bubble-like density distribution of Ru is constructed, showing good stability. Then, by simulating Ru+Ru collisions at MeV/nucleon with different equations of state (EoS) and initialization methods, the effects of the initialization method on the final state observables and the constrained information of EoS are analyzed. It is found that the maximum system density increases when the new FSE initialization method is adopted, and results in an enhanced collective flow. Moreover, a relatively stiff EoS with MeV is favored when adopting the Woods-Saxon initialization method, whereas an EoS of = 200-280 MeV is supported when using the FSE initialization. These results indicate that, within QMD-like transport models, the FSE filtering method provides a reliable means to sample nuclei with exotic density profiles, offering new insight to investigate nuclear structure and dense nuclear matter EoS through HICs.

Paper Structure

This paper contains 10 sections, 20 equations, 6 figures, 1 table.

Table of Contents

  1. Introduction
  2. Methodology
  3. Initialization of QMD-type transport models
  4. UrQMD model
  5. Filtering method
  6. Results and discussion
  7. Reconstruction of the objective density distribution
  8. Applying the FSE method to the UrQMD model
  9. Analysis of model simulation results
  10. SUMMARY and Outlook

Figures (6)

  • Figure 1: (Color online) Comparison of the density distributions obtained from the WS function Eq. \ref{['MBF3']} approximated by a Fourier series truncated at twenty terms and from the FSE filtering method in the one-dimensional ($z$) case.
  • Figure 2: (Color online) Proton (top) and neutron (bottom) density distributions of $^{96}$Ru. The eSHF denotes the objective density distributions taken from Ref. Li:2019kkh, while the WS and the FSE represent results obtained using Eqs. \ref{['wsd']} and \ref{['fes_3D']} as filtering functions, respectively.
  • Figure 3: (Color online) Initial density distribution of $^{96}$Ru obtained from the UrQMD model with WS and FSE filtering method.
  • Figure 4: (Color online) Time evolution of the density distributions in semi-central $^{96}$Ru+$^{96}$Ru collisions ($0.25 < b_0 < 0.45$) at a beam energy of $E_{\mathrm{lab}}=1500~\mathrm{MeV/nucleon}$, obtained within the UrQMD model using the WS and FSE filtering methods.
  • Figure 5: (Color online) Reduced rapidity dependence of the directed flow $v_{1}$ (top) and elliptic flow $v_{2}$ (bottom) of free protons in semi-central $^{96}$Ru+$^{96}$Ru collisions ($0.25 < b_{0} < 0.45$) at $E_{\mathrm{lab}} = 1500~\mathrm{MeV/nucleon}$ with transverse momentum $u_{t0} > 0.4$. Left panels correspond to calculations with the incompressibility coefficient $K_{0} = 200~\mathrm{MeV}$, while right panels show the results calculated with $K_{0} = 280~\mathrm{MeV}$. The experimental data are taken from FOPI Collaboration FOPI:2011aa. The lines are fits to the calculated results and data (see text).
  • ...and 1 more figures