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In-medium \(\Delta (1232)\) potential, pion production in heavy-ion collisions and the symmetry energy

  • Regular Article - Theoretical Physics
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Abstract

Using the dcQMD transport model, the isoscalar and isovector in-medium potentials of the \(\Delta \)(1232) baryon are studied and information regarding their effective strength is obtained from a comparison to experimental pion production data in heavy-ion collisions below 800 MeV/nucleon impact energy. The best description is achieved for an isoscalar potential moderately more attractive than the nucleon optical potential and a rather small isoscalar relative effective mass \(\hbox {m}^*_\Delta \approx \) 0.45. For the isovector component only a constraint between the potential’s strength at saturation and the isovector effective mass difference can be extracted, which depends on quantities such as the slope of the symmetry energy and the neutron-proton effective mass difference. These results are incompatible with the usual assumption, in transport models, that the \(\Delta \)(1232) and nucleon potentials are equal. The density dependence of symmetry energy can be studied using the high transverse momentum tail of pion multiplicity ratio spectra. Results are however correlated with the value of neutron-proton effective mass difference. This region of spectra is shown to be affected by uncertain model ingredients such as the pion potential or in-medium correction to inelastic scattering cross-sections at levels smaller than 10%. Extraction of precise constraints for the density dependence of symmetry energy above saturation will require experimental data for pion production in heavy-ion collisions below 800 MeV/nucleon impact energy and experimental values for the high transverse momentum tail of pion multiplicity ratio spectra accurate to better than 5%.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: The results of model calculations can be obtained directly from the corresponding author upon request.]

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Acknowledgements

The authors acknowledge financial support from the U.S. Department of Energy, USA under Grant Nos. DE-SC00145 30, US National Science Foundation, United States Grant No. PHY- 1565546. The research of M.D.C. has been financially supported in part by the Romanian Ministry of Education and Research through Contract No. PN 19 06 01 01/2019–2022. M.D.C. acknowledges the hospitality of NSCL / MSU where part of this study was performed. The authors express their gratitude to Maria Colonna, Pawel Danielewicz, Justin Estee, Che-Ming Ko, William Lynch, Hermann Wolter and TMEP Collaboration for stimulating discussions. The computing resources have been partly provided by the Institute for Cyber-Enabled Research (ICER) at Michigan State University.

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  1. National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI, 48824, USA

    M. D. Cozma & M. B. Tsang

  2. Department of Theoretical Physics, IFIN-HH, Reactorului 30, 077125, Mǎgurele-Bucharest, Romania

    M. D. Cozma

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Cozma, M.D., Tsang, M.B. In-medium \(\Delta (1232)\) potential, pion production in heavy-ion collisions and the symmetry energy. Eur. Phys. J. A 57, 309 (2021). https://doi.org/10.1140/epja/s10050-021-00616-3

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