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Hybrid Approach for Fragments with Finite Strangeness using GiBUU+SMM: Applications and Benchmarks in HypNuc Production

This study focuses on the production of hypernuclei in high-energy reactions, employing a hybrid GiBUU+SMM approach to investigate the formation of hyperons and exotic hypernuclei. The theoretical framework, involving transport equations and statistical models, guides the understanding of hypernuclei formation mechanisms. Experimental benchmarks in spallation reactions and heavy-ion collisions provide insights into the dynamics of relativistic hypernuclei. The research aims to enhance knowledge of strangeness sector interactions and properties of strange baryons in neutron-rich environments, crucial for understanding phenomena like hyperon stars.

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Hybrid Approach for Fragments with Finite Strangeness using GiBUU+SMM: Applications and Benchmarks in HypNuc Production

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  1. Production of fragments with finite strangeness in reactions wihtin a GiBUU+SMM combined approach Th. Gaitanos, H. Lenske, U. Mosel • Introduction • Theoretical aspects • Formation of relativistic hypernuclei in simulations • Non-equlibrium transport dynamics (Giessen-BUU) • Fragmentation mechanism (coalescence, statistical approaches, e.g. SMM) • Hybrid approach (GiBUU+SMM) • Applications • Benchmark: p+X@SIS/GSI (spallation reactions), X+X@SIS/GSI, (ALADIN) • X+X@2AGeV (HypHI), p+X@50GeV, X+X@20AGeV (J-PARC) • Final remarks Many thanks to GiBUU-group

  2. Introduction… • Knowledge of YN & YY interaction (strangeness sector of hadronic EoS) ? • important for physics of neutron stars • „Hyperon Stars“, ~60% neutron, but ~20% occupation of protons and strange baryons • (N.K. Glendenning, astro-ph/9707.351v1; F. Weber et. al., astro-ph/0705.2708v2) • So far mainly from nuclear structure studies • Info on properties of strange baryons in neutron rich matter needed •  e.g. (exotic) hypernuclei, e.g. 3HeY, 5HeY (Y=L,S) • Formation of (exotic?) hypernuclei accessible in high-energy reactions (p+X, X+X) • HypHI: 12C(6Li)+12C@SIS (in progress…) • J-PARC: p+12C@50GeV, 12C+12C@20AGeV (in future…) • PANDA: Antiproton-Nucleus (in future…)

  3. K L L,S,p,K,... L p p L L L,S,p,K,... K Relativistic Hypernuclei… • Production of Hypernuclei in Relativistic HIC • Production of many hyperons from BB->BYK (3-body PS) • Secondary rescattering (pNYK) • Multiple coalescence of hyperons with fragments • Theoretical Framework • Phase-Space evolution • Transport equations of Boltzmann type, e.g. Giessen-BUU model •  http://www.physik.uni-giessen.de/GiBUU/ • Description of fragment formation ? • Statistical picture (SMM, A.Botvina & I.Mishustin), coalescence • Description of hypernuclei formation? • simple coalescence in coordinate (Y inside fragmenting source) and in momentum space

  4. (http://theorie.physik.uni-giessen.de/GiBUU) • Asymptotic equilibrated stage • Fission/spallation, evaporation, multifragmentation… (with increasing excitation) • Statistical determination of partial decay widths  Monte-Carlo method • (basic method similar to numerical treatment of collisions in transport approaches) j,e E* Ai,Zi E*-e Ad,Zd Ad+n Ai Theoretical description (pre-equilibrium dynamics, statistical decay)… • Initial non-equilibrium stage • Relativistic transport equation of Boltzmann-type • Giessen-Boltzmann-Uehling-Uhlenbeck (GiBUU) Q.Li, J.Q. Wu, C.M. Ko, Phys. Rev. C39 (1989) 849 B. Blättel, V. Koch, U. Mosel, Rep. Prog. Phys. 56 (1993) 1 SMM code: Bondorf, Botvina & Mishustin, PR257(´95) 133

  5. Total energy (Etot=∫dxT00) of a „source“  Excitation energy: Eexc=Etot-Ebind, of a „source“ • local Pressures (Plong(x)=Tzz,Ptr(x)=Txx,yy)  Anisotropy ratios Qc (equilibration) Theoretical description (hybrid GiBUU+SMM approach)…

  6. Dynamical aspects in p+X and X+X reactions (properties of „fragmenting source“)… • Definition of residual nucleus: r>rsat/100. • Non-Equilibrium dynamics within GiBUU until system(s) approach local equilibrium at t=tf • Determination of A,Z and Eexc at time tf, and then apply SMM p+Au@0.8GeV Phys. Lett. B 663, 197 (2008)

  7. Benchmark-I: p+X reactions (global characteristics)… Exp. data: J. Benlliure et al., Nucl. Phys. A683 (2001) 513. F. Rejmund et al., Nucl. Phys. A683 (2001) 540 Charge distribution… Mass distribution… Phys. Lett. B 663, 197 (2008)

  8. Benchmark-I: p+X reactions (details)… Exp. data: J. Benlliure et al., Nucl. Phys. A683 (2001) 513. F. Rejmund et al., Nucl. Phys. A683 (2001) 540 Phys. Lett. B 663, 197 (2008)

  9. Pre-Equilibrium (BUU): high-energy n-emission, QE-pick • Asymptotic equilibreated state (SMM): Statistical decay of excited source • Final Result: Hybrid GiBUU+SMM Benchmark-I: p+208Pb@0.8GeV reactions (more details)… data: S. Leray et al., PRC65,044621 neutrons

  10. Dynamical aspects in p+p and X+X reactions (Spectators)… • Def. ofSpectators • Y(0)>0.75 (ALADIN)+r<rsat/100 • Spectators • Well defined conditions after onset of instability… • Anisotropy • …and onset of equilibration submitted (2008)

  11. Benchmark-II: X+X reactions (spectator fragmentation in Au+Au@0.4AGeV)… submitted (2008)

  12. Heavy System Light System Formation mechanism of spectator-hypernuclei …(X+X@3AGeV) • Hyperons formed from high- phase(pB->YK,BB->BYK+PYTHIA) rescattering with „spectator“-particles • captured by cold „spectator“-clusters with high probability, e.g. 4,6He •  In collisions of heavy nuclei (Au) difficult separation from pion-background (fireball) •  Possible in collisions of light systems (Ca+Ca,C+C) with minor problems of pion-background (Fireball)

  13. Hypernuclei from spectator fragmentation…(HypHI, 12C+12C@2AGeV) Formation of hypernuclei from spectator fragmentation via coalescence (condition: Y inside radius of fragmenting source+momentum coalescence) Note: extremely low total yields, e.g. orders of only view mb for light He-hypernuclei Consistent with previous studies: M.Wakai, NPA547(92)89c Very small systemsless compressionless pions available for rescattering inside spectators Very small systemssmall interaction radius for pions passing through spectator submitted (2008)

  14. Hypernuclei from high energy proton-induced reactions…(J-PARC, p+12C@50GeV) submitted (2008) Two sources (residual target+moving source) Stable conditions after resonance decay Most of hyperons created & rescatter inside moving source

  15. Final remarks & Outlook… • Fragmentation in reactions within “hybrid” GiBUU+SMM •  BUU: non-equilibrium dynamics, info on onset of equilibration & instabilities •  Ground state stability important in extracting Ex •  SMM(Botvina/Mishustin): statistical decay of excited configuration • Fragmentation in proton-induced reactions & HIC •  GiBUU+SMM combined approach for fragmentation reactions •  reasonable description of a wide selection of exp. data • First transport predictions for future HypHI-project at GSI •  Light hyperfragment production from spectators with high probability • (however, coalescence picture too simple…) • Future/under progress developments •  Better description for strangeness sector of mean-field (in progress) •  Hyperfragment description more consistent: • GiBUU+HypSMM: would be an important extension for HypHI A.S. Botvina, J. Pochodzalla, Phys. Rev. C76 (2007) 024909.

  16. Relativistic Thomas-Fermi…

  17. Improved ground state in BUU…

  18. Transport equations of Boltzmann-type, very old story… • 1. Primer L. Boltzmann, Wien. Ber. 66 (1872) 275 • 2. Primer…L. Nordheim, Proc. R. Soc. London A119 (1928) 689 • E.A. Uehling, G.E. Uhlenbeck, Phys. Rev. 43 (1933) 552 • Theoretical background • Non-Relativistic kinetic theory • L.P. Kadanoff, G. Baym, „Quantum Statistical Mechanics“ (Benjamin, N.Y. 1962) • Relativistic kinetic theory • S.R. de Groot, W.A. van Leeuwen, C.G. van Weert • „Relativistic kinetic theory“ (North Holland, Amsterdam, 1980) • Modern Relativistic Quantum Transport Theory • W. Botermans, R. Malfliet, Phys. Rep. 198 (1990) 115 (difficult to understand…) • First applications to HIC… • P. Danielewicz, Ann. Phys. 152 (1984) 239 & 305 • G.F. Bertsch, S. Das Gupta, Phys. Rep. 160 (1988) 189 • First relativistic applications to HIC… • Giessen-group (PhD-Thesis of B. Blättel, V. Koch & U. Mosel/W. Cassing ~1990) • B. Blättel, V. Koch, U. Mosel, Rep. Prog. Phys. 56 (1993) 1 Q.Li, J.Q. Wu, C.M. Ko, Phys. Rev. C39 (1989) 849

  19. Spectator matter properties (BUU)… Nice stable conditions… …before instability sets in • Spectator very well suited for studies on fragments & hyperfragments

  20. Mean-field vs cascade – the role of the MDI…(J-PARC, p+12C@50GeV) central peripheral

  21. 136Xe+208Pb@1AGeV (spectator fragmentation…)

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