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Calculation of Particle Pair Correlation Functions with Classical Trajectory Approximation

Sheng Xiao, Yijie Wang, Zhigang Xiao

TL;DR

This work addresses the challenge of extracting spatio-temporal information about particle emission sources in heavy-ion collisions at Fermi energies by developing a Monte Carlo model based on a classical trajectory approximation (CTA-I) that self-consistently couples thermal emission, a central mean-field for the residual source, and three-body final-state interactions. The model samples thermally equilibrated emission and propagates particle pairs under the combined source potential and inter-particle forces to compute two-particle correlation functions, $C(q)$. Application to IMF-IMF and LCP-LCP data demonstrates that $C(q)$ is highly sensitive to the Gaussian source size $\sigma_R$ but largely insensitive to the temperature $T$, aligning with experimental trends and allowing robust inference of the source’s spatio-temporal extent. This approach provides a practical tool to constrain emission-source sizes in the Fermi-energy regime and enhances the utility of femtoscopy for probing nuclear matter properties and reaction dynamics.

Abstract

Femtoscopic interferometry is a powerful tool for probing the spatio-temporal evolution of emission sources in heavy-ion collisions. A major challenge in the field is formulating a self-consistent description of the source function, final-state interactions between the particle pair, and interactions inherent to the source itself. To address this, we have developed a novel Monte Carlo model for calculating two-particle correlation functions in a classic framework. The model incorporates self-consistently the emission source of thermal equilibrium and three-body final state interactions. Application of the model shows satisfactory fit to experimental data, revealing that the correlation function is highly sensitive to the source's spatio-temporal extent. In contrast, the temperature parameter governing the emitted particles' energy spectra has a negligible influence. Our approach offers the potential to extract the spatio-temporal information from the emission source, thereby advancing the applicability of femtoscopic interferometry in the Fermi energy domain.

Calculation of Particle Pair Correlation Functions with Classical Trajectory Approximation

TL;DR

This work addresses the challenge of extracting spatio-temporal information about particle emission sources in heavy-ion collisions at Fermi energies by developing a Monte Carlo model based on a classical trajectory approximation (CTA-I) that self-consistently couples thermal emission, a central mean-field for the residual source, and three-body final-state interactions. The model samples thermally equilibrated emission and propagates particle pairs under the combined source potential and inter-particle forces to compute two-particle correlation functions, . Application to IMF-IMF and LCP-LCP data demonstrates that is highly sensitive to the Gaussian source size but largely insensitive to the temperature , aligning with experimental trends and allowing robust inference of the source’s spatio-temporal extent. This approach provides a practical tool to constrain emission-source sizes in the Fermi-energy regime and enhances the utility of femtoscopy for probing nuclear matter properties and reaction dynamics.

Abstract

Femtoscopic interferometry is a powerful tool for probing the spatio-temporal evolution of emission sources in heavy-ion collisions. A major challenge in the field is formulating a self-consistent description of the source function, final-state interactions between the particle pair, and interactions inherent to the source itself. To address this, we have developed a novel Monte Carlo model for calculating two-particle correlation functions in a classic framework. The model incorporates self-consistently the emission source of thermal equilibrium and three-body final state interactions. Application of the model shows satisfactory fit to experimental data, revealing that the correlation function is highly sensitive to the source's spatio-temporal extent. In contrast, the temperature parameter governing the emitted particles' energy spectra has a negligible influence. Our approach offers the potential to extract the spatio-temporal information from the emission source, thereby advancing the applicability of femtoscopic interferometry in the Fermi energy domain.
Paper Structure (10 sections, 50 equations, 4 figures)

This paper contains 10 sections, 50 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Model Construction
  3. Thermal Equilibrium Treatment
  4. Mean Field
  5. Dynamics and Correlation
  6. Parameterization
  7. Result and Discussions
  8. Correlation functions of IMF-IMF pair
  9. Correlation functions of LCP-LCP pair
  10. Conclusion

Figures (4)

  • Figure 1: The mean field a triton experiences at different settings of $k_{\rm B}T$, $\sigma_{\rm R}$ and $\gamma_{\rm c}$. Here $\gamma_{\rm{d}}=0.3$ and $U_0=3$ MeV are fixed, with the reaction system is $^{86}$Kr+$^{208}$Pb.
  • Figure 2: Correlation function of B-B pairs in comparison with the CTA-I model predictions for the reactions MeV/u . Data points taken from PhysRevLett.67.14.
  • Figure 3: Correlation function of triton-triton pair in 25 MeV/u $^{86}$Kr+$^{\rm nat}$Pb reactions in comparison with the CTA-I model predictions.
  • Figure 4: Correlation function of $\rm ^3He \text{-} ^3He$ pair in 25 MeV/u $^{86}$Kr+$^{\rm nat}$Pb reactions in comparison with the CTA-I model predictions.