Comparison of heavy-ion transport simulations: Collision integral with pions and $\mathrm{\ensuremath{\Delta}}$ resonances in a box

Comparison of heavy-ion transport simulations: Collision integral with pions and $Δ$ resonances in a box

Akira Ono, Jun Xu, Maria Colonna, Pawel Danielewicz, Che Ming Ko, Manyee Betty Tsang, Yong-Jia Wang, Hermann Wolter, Ying-Xun Zhang, Lie-Wen Chen, Dan Cozma, Hannah Elfner, Zhao-Qing Feng, Natsumi Ikeno, Bao-An Li, Swagata Mallik, Yasushi Nara, Tatsuhiko Ogawa, Akira Ohnishi, Dmytro Oliinychenko, Jun Su, Taesoo Song, Feng-Shou Zhang, and Zhen Zhang

Phys. Rev. C 100, 044617 – Published 30 October 2019

Abstract

Background: Simulations by transport codes are indispensable for extracting valuable physical information from heavy-ion collisions. Pion observables such as the $π^{-} / π^{+}$ yield ratio are expected to be sensitive to the symmetry energy at high densities.

Purpose: To evaluate, understand, and reduce the uncertainties in transport-code results originating from different approximations in handling the production of $Δ$ resonances and pions.

Methods: We compare ten transport codes under controlled conditions for a system confined in a box, with periodic boundary conditions, and initialized with nucleons at saturation density and at a temperature of 60 MeV. The reactions $N N \leftrightarrow N Δ$ and $Δ \leftrightarrow N π$ are implemented, but the Pauli blocking and the mean-field potential are deactivated in the present comparison. Thus, these are cascade calculations including pions and $Δ$ resonances. Results are compared to those from the two reference cases of a chemically equilibrated ideal gas mixture and of the rate equation.

Results: For the numbers of $Δ$ and $π$ , deviations from the reference values are observed in many codes, and they depend significantly on the size of the time step. These deviations are tied to different ways in ordering the sequence of reactions, such as collisions and decays, that take place in the same time step. Better agreements with the reference values are seen in the reaction rates and the number ratios among the isospin species of $Δ$ and $π$ . Both the reaction rates and the number ratios are, however, affected by the correlations between particle positions, which are absent in the Boltzmann equation, but are induced by the way particle scatterings are treated in many of the transport calculations. The uncertainty in the transport-code predictions of the $π^{-} / π^{+}$ ratio, after letting the existing $Δ$ resonances decay, is found to be within a few percent for the system initialized at $n / p = 1.5$ .

Conclusions: The uncertainty in the final $π^{-} / π^{+}$ ratio in this simplified case of particles in a box is sufficiently small so that it does not strongly impact constraining the high-density symmetry energy from heavy-ion collisions. Most of the sources of uncertainties have been understood, and individual codes may be further improved in future applications. This investigation will be extended in the future to heavy-ion collisions to ensure the problems identified here remain under control.

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Received 5 April 2019
Revised 1 September 2019

DOI:https://doi.org/10.1103/PhysRevC.100.044617

Physics Subject Headings (PhySH)

Low & intermediate energy heavy-ion reactions Models & methods for nuclear reactions Particle & resonance production Symmetry energy

Molecular dynamics Test-particle methods

Nuclear Physics

Authors & Affiliations

Akira Ono ^1,*, Jun Xu^2,3,†, Maria Colonna⁴, Pawel Danielewicz⁵, Che Ming Ko⁶, Manyee Betty Tsang⁵, Yong-Jia Wang⁷, Hermann Wolter⁸, Ying-Xun Zhang^9,10, Lie-Wen Chen¹¹, Dan Cozma¹², Hannah Elfner^13,14,15, Zhao-Qing Feng¹⁶, Natsumi Ikeno^17,18, Bao-An Li¹⁹, Swagata Mallik²⁰, Yasushi Nara²¹, Tatsuhiko Ogawa²², Akira Ohnishi²³, Dmytro Oliinychenko²⁴, Jun Su²⁵, Taesoo Song¹³, Feng-Shou Zhang^26,27, and Zhen Zhang²⁵

¹Department of Physics, Tohoku University, Sendai 980-8578, Japan
²Shanghai Advanced Research Institute, Chinese Academy of Sciences, Shanghai 201210, China
³Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, China
⁴INFN-LNS, Laboratori Nazionali del Sud, 95123 Catania, Italy
⁵National Superconducting Cyclotron Laboratory and Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
⁶Cyclotron Institute and Department of Physics and Astronomy, Texas A&M University, College Station, Texas 77843, USA
⁷School of Science, Huzhou University, Huzhou 313000, China
⁸Physics Department, University of Munich, D-85748 Garching, Germany
⁹China Institute of Atomic Energy, Beijing 102413, China
¹⁰Guangxi Key Laboratory Breeding Base of Nuclear Physics and Technology, Guilin 541004, China
¹¹School of Physics and Astronomy and Shanghai Key Laboratory for Particle Physics and Cosmology, Shanghai Jiao Tong University, Shanghai 200240, China
¹²IFIN-HH, Reactorului 30, 077125 Măgurele-Bucharest, Romania
¹³GSI Helmholtzzentrum für Schwerionenforschung, Planckstrasse 1, 64291 Darmstadt, Germany
¹⁴Institute for Theoretical Physics, Goethe University, Max-von-Laue-Strasse 1, 60438 Frankfurt am Main, Germany
¹⁵Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe University, Ruth-Moufang-Strasse 1, 60438 Frankfurt am Main, Germany
¹⁶School of Physics and Optoelectronics, South China University of Technology, Guangzhou 510640, China
¹⁷Department of Life and Environmental Agricultural Sciences, Tottori University, Tottori 680-8551, Japan
¹⁸RIKEN Nishina Center, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
¹⁹Department of Physics and Astronomy, Texas A&M University–Commerce, Commerce, Texas 75429-3011, USA
²⁰Physics Group, Variable Energy Cyclotron Centre, 1/AF Bidhan Nagar, Kolkata 700064, India
²¹Akita International University, Akita 010-1292, Japan
²²Research Group for Radiation Transport Analysis, Japan Atomic Energy Agency, Shirakata, Tokai, Ibaraki 319-1195, Japan
²³Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan
²⁴Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, USA
²⁵Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-sen University, Zhuhai 519082, China
²⁶Key Laboratory of Beam Technology and Material Modification of Ministry of Education, College of Nuclear Science and Technology, Beijing Normal University, Beijing 100875, China
²⁷Beijing Radiation Center, 100875 Beijing, China

^*ono@nucl.phys.tohoku.ac.jp
^†xujun@zjlab.org.cn

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Vol. 100, Iss. 4 — October 2019

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Physical Review C

covering nuclear physics

Comparison of heavy-ion transport simulations: Collision integral with pions and $Δ$ resonances in a box

Phys. Rev. C 100, 044617 – Published 30 October 2019

Abstract

Physics Subject Headings (PhySH)

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Article Text (Subscription Required)

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Physical Review C

covering nuclear physics

Comparison of heavy-ion transport simulations: Collision integral with pions and Δ resonances in a box

Phys. Rev. C 100, 044617 – Published 30 October 2019

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Authors & Affiliations

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Comparison of heavy-ion transport simulations: Collision integral with pions and $Δ$ resonances in a box