Fragment formation of nuclei and hypernuclei within a combined BUU+SMM model T. Gaitanos, H. Lenske, U. Mosel Introduction Outline of the relativistic transport model The transport equation (GiBUU) in the relativistic framework (Walecka model) conservation of energy-momentum tensor, ground-state Numerical aspects (conservation of energy-momentum tensor, ground-state) Hybrid GiBUU+SMM model Applications-I: Fragment formation in p+X & X+X Dynamical aspects, statistical aspects, comparison with exp. Applications-II: Formation of hypernuclei in X+X & p+X Final remarks & outlook Many thanks to GiBUU-group

Introduction… Production of light nuclei in reactions (fragmentation) Standard approach: combination of dynamical & statistical models Spallation reactions: useful tool to study/test long-time scales of fragmentation process Heavy-ion reactions: testing hybrid models in spectator fragmentation Recent Applications Production of hypernuclei in (HypHI-Phase I, GSI) In future: PANDA (pbar+X) & J-PARC J. Cugnon et al., NPA620 (97) 475, Mishustin et al., PLB359 (95) 261; NPA624 (97) 706 Production of light nuclei with strangeness (hypernuclei) Knowledge of YN & YY interaction (strangeness sector of hadronic EoS) ? N.K. Glendenning, astro-ph/ v1; F. Weber et. al., astro-ph/ v2

Relativistic Hypernuclei…         Production of Hypernuclei in Relativistic HIC Production of many hyperons from BB->BYK (3-body PS) Secondary rescattering (  N  YK) Multiple coalescence of hyperons with fragments Theoretical Framework Phase-Space evolution Phase-Space evolution Transport approaches (INC,BUU,RBUU,CBUU,(Ur)QMD,HSD,…) Description of fragment formation Description of fragment formation Statistical picture (SMM, Botvina & Mishustin) Description of hypernuclei formation? (presently) simple coalescence in coordinate and in momentum space (future) SMM with strangeness (Botvina & Pochodzalla)

Theoretical description… Initial non-equilibrium stage Relativistic transport equation of Boltzmann-type (GiBUU) ++ I coll (R)BUU exactly conservs energy-momentum tensor: Total energy (E tot =∫dxT 00 ) of a „source“, local Pressures (P long (x)=T zz,P tr (x)=T xx,yy ) Excitation energy Excitation energy: E exc =E tot -E bind, of a „source“

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) E* A i,Z i E*-  A d,Z d j,  AiAi A d +n SMM code: Botvina & Mishustin, PR257(´95) 133 Non-Equilibrium dynamics within BUU until source(s) approaches stable configuration and local equilibration at t=t f excitation energy E exc Determination of mass (A), charge (Z) and excitation energy E exc of a source at time t=t f, then apply SMM Combination: GiBUU+SMM (hybrid model)…

Ground state in simulations: Stability… Important in calculating E exc Energy must be conserved! Important in determing the source No spurious particle emission!

Dynamical aspects in p+X and X+X reactions… Residual fireball-like source equlibrates after t>50-70fm/c Definition of residual nucleus:  >  sat /100. time (fm/c)

Phys. Lett. B 663, 197 (2008) Definition of residual nucleus:  >  sat /100. Non-Equilibrium dynamics within GiBUU until system(s) approach local equilibrium at t=t f Determination of A,Z and E exc at time t f, and then apply SMM Dynamical aspects in p+X and X+X reactions ( properties of „fragmenting source“ )… Impact parameter

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

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

Benchmark-I: reactions (more details)… Pre-Equilibrium (BUU): high-energy n-emission, QE-pick Asymptotic equilibreated state (SMM): Statistical decay of excited source Final Result: Hybrid GiBUU+SMM Data: (Saclay) S. Leray et al., PRC65, neutrons

Dynamical aspects in p+p and X+X reactions (Spectators)… Spectators Well defined conditions after onset of instability… Spectators …and onset of equilibration Def. ofSpectators Y (0) >  >  sat /100 To be submitted very soon ( )

Benchmark-II: X+X reactions (spectator fragmentation in To be submitted very soon ( ) data: ALADIN (GSI)

Hypernuclei from spectator fragmentation 12 C+ 12 coalescence Formation of hypernuclei from spectator fragmentation via coalescence (condition: Y inside radius of fragmenting source+momentum coalescence) Extremely low Extremely low total yields, ~1-3  b, pionic contribution~  b! M.Wakai, NPA547(92)89c Consistent with previous studies: M.Wakai, NPA547(92)89c In progress: (FAIR), pbar+X (PANDA) To be submitted very soon ( )

Dynamical aspects in high energy proton-induced reactions …(J-PARC, p+ 12 Density profiles along beam (z) axis Two sources (residual target+moving source)

Hypernuclei from high energy proton-induced reactions…(J-PARC, p+ 12 Two sources (residual target+moving source) Stable conditions after resonance decay Most of hyperons created & rescatter inside moving source To be submited very soon ( )

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 E x  SMM(Botvina/Mishustin): statistical decay of excited configuration Fragmentation in proton-induced reactions & HIC  Gi  GiBUU+SMM combined approach for fragmentation reactions  reasonable description of a wide selection of exp. Data Transport predictions for HypHI-project at GSI (PANDA & J-PARC in future)  Light hyperfragment production from spectator fragmentation~  b (however, coalescence picture too simple…) Future/under progress developments  Hyperfragment description more consistent: GiBUU+HypSMM: would be an important extension for HypHI  Studies on HypHI(X+X) PANDA (pbar+X) being studied… A.S. Botvina, J. Pochodzalla, Phys. Rev. C76 (2007)

Back up transparencies

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

Ground state in BUU-I: Binding energies… Important in calculating E exc Important in calculating E exc : use for E tot and E bind the same model/technical parameters, for consistency! NOT Distributing „test particles“ to density profiles acc. empirical systematics (NOT consistent with RMF) NO Neglecting spatial derivatives of meson-field equations (NO surface effects) NO Neglecting iso-vector field (NO isospin-asymmetry)

Ground state in BUU-II: (RTF; account for surface & isospin-asymmetry)  Eqs. of motion + meson-field Eqs. including (spatial) gradients (ADI-method): + From RMF approach of QHD: Variational method… Relativistic Thomas-Fermi (RTF) equations  Relativistic Thomas-Fermi (RTF) equations RTF densities T.G., A.B. Larionov, work in progress… (2008)

Ground state in BUU-II: (under study…) 16 O „Std init“ (+ gradient terms) Improved init (consistent RTF) T.G, A.B. Larionov, work in progress… (2008)  Eqs. of motion + meson-field Eqs. including (spatial) gradients (ADI-method): + Improved init (consistent RTF) „Std init“ (+ gradient terms)

Ground state in BUU-II: (RTF and BUU test-particles densities) T.G, A.B. Larionov, work in progress… (2008)

Ground state in BUU-II: Results (application to proton-induced reactions)

Mean-field vs cascade – the role of the MDI…(J-PARC, p+ 12 central peripheral