HADRONS@FAIR, 25.06.08 Fragment formation of nuclei and hypernuclei within a combined BUU+SMM model...

HADRONS@FAIR, 25.06.08

Fragment formation of nuclei and hypernuclei Fragment formation of nuclei and hypernuclei within a combined BUU+SMM modelwithin a combined BUU+SMM model

T. Gaitanos, H. Lenske, U. MoselT. Gaitanos, H. Lenske, U. Mosel

IntroductionIntroduction

Outline of the relativistic transport modelOutline of the relativistic transport modelThe transport equation (GiBUU) in the relativistic framework (Walecka model)Numerical aspects (conservation of energy-momentum tensor, ground-conservation of energy-momentum tensor, ground-statestate)Hybrid GiBUU+SMM model

Applications-I: Fragment formation in p+X & X+XDynamical aspects, statistical aspects, comparison with exp.

Applications-II: Formation of hypernuclei in X+X & p+X

Final remarks & outlookFinal remarks & outlook

Many thanks to GiBUU-group


Introduction…Introduction…Introduction…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

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 ApplicationsRecent Applications

Production of hypernuclei in X+X@2AGeV (HypHI-Phase I, GSI)

In future: HypHI@FAIR (X+X@20AGeV), PANDA (pbar+X) & J-PARC (p+X@50GeV)

Recent ApplicationsRecent Applications

Production of hypernuclei in X+X@2AGeV (HypHI-Phase I, GSI)

In future: HypHI@FAIR (X+X@20AGeV), PANDA (pbar+X) & J-PARC (p+X@50GeV)

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) ?

Production of light nuclei with strangeness (hypernuclei)

Knowledge of YN & YY interaction (strangeness sector of hadronic EoS) ?

N.K. Glendenning, astro-ph/9707.351v1; F. Weber et. al., astro-ph/0705.2708v2


Relativistic Hypernuclei…Relativistic Hypernuclei…

Production of Hypernuclei in Relativistic HICProduction of Hypernuclei in Relativistic HICProduction of many hyperons from BB->BYK (3-body PS)

Secondary rescattering (NYK)Multiple coalescence of hyperons with fragments

Theoretical FrameworkTheoretical 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?Description of hypernuclei formation?(presently) simple coalescence in coordinate and in momentum space(future) SMM with strangeness (Botvina & Pochodzalla)


Theoretical description…Theoretical description…Theoretical description…Theoretical description…Initial non-equilibrium stageInitial non-equilibrium stage

Relativistic transport equation of Boltzmann-type (GiBUU)

Initial non-equilibrium stageInitial non-equilibrium stage

Relativistic transport equation of Boltzmann-type (GiBUU)

http://gibuu.physik.uni-giessen.de/GiBUU/

++ ++IcollIcoll

(R)BUU exactly conservs energy-momentum tensor:(R)BUU exactly conservs energy-momentum tensor:

Total energy (Etot=∫dxT00) of a „source“, local Pressures (Plong(x)=Tzz,Ptr(x)=Txx,yy)

Excitation energyExcitation energy: Eexc=Etot-Ebind, of a „source“

Total energy (Etot=∫dxT00) of a „source“, local Pressures (Plong(x)=Tzz,Ptr(x)=Txx,yy)

Excitation energyExcitation energy: Eexc=Etot-Ebind, of a „source“


Asymptotic equilibrated stageAsymptotic 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)

Asymptotic equilibrated stageAsymptotic 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*

Ai,Zi

E*

Ai,Zi

E*-

Ad,Zd

E*-

Ad,Zd

j,j,

AiAi Ad+nAd+n SMM code: Botvina & Mishustin, PR257(´95) 133

Non-Equilibrium dynamics within BUU until source(s) approaches stable configuration

and local equilibration at t=tf

Determination of mass (A), charge (Z) and excitation energy Eexcitation energy Eexcexc of a source at time t=tf,

then apply SMM

Non-Equilibrium dynamics within BUU until source(s) approaches stable configuration

and local equilibration at t=tf

Determination of mass (A), charge (Z) and excitation energy Eexcitation energy Eexcexc of a source at time t=tf,

then apply SMM

Combination: GiBUU+SMM (hybrid model)…Combination: GiBUU+SMM (hybrid model)…Combination: GiBUU+SMM (hybrid model)…Combination: GiBUU+SMM (hybrid model)…


Ground state in simulations: Stability…Ground state in simulations: Stability…Ground state in simulations: Stability…Ground state in simulations: Stability…

Important in calculating EImportant in calculating Eexcexc

Energy must be conserved!

Important in calculating EImportant in calculating Eexcexc

Energy must be conserved!

Important in determing the Important in determing the sourcesource

No spurious particle emission!

Important in determing the Important in determing the sourcesource

No spurious particle emission!


Dynamical aspects in Dynamical aspects in p+Xp+X and X+X reactions… and X+X reactions…Dynamical aspects in Dynamical aspects in p+Xp+X and X+X reactions… and X+X reactions…

Residual fireball-like source equlibrates after t>50-70fm/cResidual fireball-like source equlibrates after t>50-70fm/c

Definition of residual nucleus: >sat/100.Definition of residual nucleus: >sat/100.

time (fm/c)time (fm/c) time (fm/c)time (fm/c)

HADRONS@FAIR, 25.06.08Phys. Lett. B Phys. Lett. B 663663, 197 , 197 (2008)(2008)

Definition of residual nucleus: >sat/100.Definition of residual nucleus: >sat/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

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

Dynamical aspects in Dynamical aspects in p+Xp+X and X+X reactions ( and X+X reactions (properties of „fragmenting properties of „fragmenting source“source“)…)…Dynamical aspects in Dynamical aspects in p+Xp+X and X+X reactions ( and X+X reactions (properties of „fragmenting properties of „fragmenting source“source“)…)…

[email protected]

[email protected]

Impact parameterImpact parameter


Benchmark-I: Benchmark-I: p+Xp+X reactions (global characteristics)… reactions (global characteristics)…Benchmark-I: Benchmark-I: p+Xp+X reactions (global characteristics)… reactions (global characteristics)…

Charge distribution…Charge distribution…

Mass distribution…

Mass distribution…

Phys. Lett. B Phys. Lett. B 663663, 197 , 197 (2008)(2008)

GSI-dataGSI-dataJ. Benlliure et al., Nucl. Phys. A683 (2001) 513.F. Rejmund et al., Nucl. Phys. A683 (2001) 540



Benchmark-I: Benchmark-I: p+Xp+X reactions (details)… reactions (details)…Benchmark-I: Benchmark-I: p+Xp+X reactions (details)… reactions (details)…

Phys. Lett. B Phys. Lett. B 663663, 197 , 197 (2008)(2008)




Benchmark-I: Benchmark-I: [email protected][email protected] reactions (more details)… reactions (more details)…Benchmark-I: Benchmark-I: [email protected][email protected] reactions (more details)… reactions (more details)…

Pre-Equilibrium (BUU): high-energy n-emission, QE-pick

Pre-Equilibrium (BUU): high-energy n-emission, QE-pickAsymptotic equilibreated state (SMM): Statistical decay of excited sourceAsymptotic equilibreated state (SMM): Statistical decay of excited source

Final Result: Hybrid GiBUU+SMMFinal Result: Hybrid GiBUU+SMMFinal Result: Hybrid GiBUU+SMMFinal Result: Hybrid GiBUU+SMM

Data: (Saclay) S. Leray et al., PRC65,044621 Data: (Saclay) S. Leray et al., PRC65,044621

neutronsneutrons


Dynamical aspects in p+p and Dynamical aspects in p+p and X+XX+X reactions (Spectators)… reactions (Spectators)…Dynamical aspects in p+p and Dynamical aspects in p+p and X+XX+X reactions (Spectators)… reactions (Spectators)…

SpectatorsSpectators

Well defined conditions after onset of instability…


Well defined conditions after onset of instability…


…and onset of equilibration


…and onset of equilibration

Def. ofSpectatorsDef. ofSpectators

Y(0)>0.75 +>sat/100

To be submitted very soon To be submitted very soon (07.2008)(07.2008)


Benchmark-II: Benchmark-II: X+XX+X reactions (spectator fragmentation in [email protected]) reactions (spectator fragmentation in [email protected])……Benchmark-II: Benchmark-II: X+XX+X reactions (spectator fragmentation in [email protected]) reactions (spectator fragmentation in [email protected])……


data:ALADIN (GSI)ALADIN (GSI)

data:ALADIN (GSI)ALADIN (GSI)


Hypernuclei from spectator fragmentationHypernuclei from spectator fragmentation……(HypHI@GSI(Phase-I), (HypHI@GSI(Phase-I), 1212C+C+1212C@2AGeV)C@2AGeV)Hypernuclei from spectator fragmentationHypernuclei from spectator fragmentation……(HypHI@GSI(Phase-I), (HypHI@GSI(Phase-I), 1212C+C+1212C@2AGeV)C@2AGeV)Formation of hypernuclei from spectator fragmentation via coalescencecoalescence

(condition: Y inside radius of fragmenting source+momentum coalescence)

Formation of hypernuclei from spectator fragmentation via coalescencecoalescence

(condition: Y inside radius of fragmenting source+momentum coalescence)

Extremely lowExtremely low total yields, ~1-3b, pionic contribution~0.03-0.2b!

Consistent with previous studies: M.Wakai, NPA547(92)89cM.Wakai, NPA547(92)89c

In progress: X+X@(>3-20)AGeV (FAIR), pbar+X (PANDA)In progress: X+X@(>3-20)AGeV (FAIR), pbar+X (PANDA)

Extremely lowExtremely low total yields, ~1-3b, pionic contribution~0.03-0.2b!

Consistent with previous studies: M.Wakai, NPA547(92)89cM.Wakai, NPA547(92)89c

In progress: X+X@(>3-20)AGeV (FAIR), pbar+X (PANDA)In progress: X+X@(>3-20)AGeV (FAIR), pbar+X (PANDA)



Dynamical aspects in high energy proton-induced reactionsDynamical aspects in high energy proton-induced reactions……(J-PARC, (J-PARC, p+p+1212C@50GeV)C@50GeV)Dynamical aspects in high energy proton-induced reactionsDynamical aspects in high energy proton-induced reactions……(J-PARC, (J-PARC, p+p+1212C@50GeV)C@50GeV)

Density profiles along beam (z) axisDensity profiles along beam (z) axis

Two sources (residual target+moving source)Two sources (residual target+moving source)


Hypernuclei from high energy proton-induced reactions…Hypernuclei from high energy proton-induced reactions…(J-PARC, (J-PARC, p+p+1212C@50GeV)C@50GeV)Hypernuclei from high energy proton-induced reactions…Hypernuclei from high energy proton-induced reactions…(J-PARC, (J-PARC, p+p+1212C@50GeV)C@50GeV)

Two sources (residual target+moving source)

Stable conditions after resonance decay

Most of hyperons created & rescatter inside moving source

Two sources (residual target+moving source)

Stable conditions after resonance decay

Most of hyperons created & rescatter inside moving source

To be submited very soon To be submited very soon (07.2008)(07.2008)


Final remarks & Outlook…Final remarks & Outlook…

Fragmentation in reactions within “hybrid” GiBUU+SMMFragmentation 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 & HICFragmentation in proton-induced reactions & HIC

GiGiBUU+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 Transport predictions for HypHI-project at GSI (PANDA & J-PARC in future)future) Light hyperfragment production from spectator fragmentation~b (however, coalescence picture too simple…)

Future/under progress developmentsFuture/under progress developments Hyperfragment description more consistent: GiBUU+HypSMM: would be an important extension for HypHI

Studies on FAIR@GSI: HypHI(X+X) PANDA (pbar+X) being studied…

A.S. Botvina, J. Pochodzalla, Phys. Rev. C76 (2007) 024909.


Back up transparencies

Back up transparencies


Spectator matter properties (BUU)…Spectator matter properties (BUU)…

Spectator very well suited for studies on fragments & Spectator very well suited for studies on fragments & hyperfragmentshyperfragments

Nice stable Nice stable conditions…conditions…

……before instability sets inbefore instability sets in


Ground state in BUU-I: Binding energies…Ground state in BUU-I: Binding energies…Ground state in BUU-I: Binding energies…Ground state in BUU-I: Binding energies…

Important in calculating EImportant in calculating Eexcexc: use for Etot and Ebind the same model/technical parameters, for consistency!

Important in calculating EImportant in calculating Eexcexc: use for Etot and Ebind the same model/technical parameters, for consistency!

Distributing „test particles“ to density profiles acc. empirical systematics (NOTNOT consistent with RMF)

Neglecting spatial derivatives of meson-field equations (NONO surface effects)

Neglecting iso-vector field (NONO isospin-asymmetry)

Distributing „test particles“ to density profiles acc. empirical systematics (NOTNOT consistent with RMF)

Neglecting spatial derivatives of meson-field equations (NONO surface effects)

Neglecting iso-vector field (NONO isospin-asymmetry)


Ground state in BUU-II: Ground state in BUU-II: (RTF; account for surface & isospin-asymmetry)(RTF; account for surface & isospin-asymmetry)Ground state in BUU-II: Ground state in BUU-II: (RTF; account for surface & isospin-asymmetry)(RTF; account for surface & isospin-asymmetry)

Eqs. of motion + meson-field Eqs. including (spatial) gradients (ADI-method):Eqs. of motion + meson-field Eqs. including (spatial) gradients (ADI-method): Eqs. of motion + meson-field Eqs. including (spatial) gradients (ADI-method):Eqs. of motion + meson-field Eqs. including (spatial) gradients (ADI-method):

++

From RMF approach of QHD:From RMF approach of QHD:

Variational method…Variational method…

Relativistic Thomas-Fermi (RTF) equationsRelativistic Thomas-Fermi (RTF) equationsRelativistic Thomas-Fermi (RTF) equationsRelativistic Thomas-Fermi (RTF) equations

RTF densitiesRTF densities

T.G., A.B. Larionov, work in progress… T.G., A.B. Larionov, work in progress… (2008)(2008)


Ground state in BUU-II: Ground state in BUU-II: (under study…)(under study…)Ground state in BUU-II: Ground state in BUU-II: (under study…)(under study…)

16O16O„Std init“ (+ gradient terms)„Std init“ (+ gradient terms)

Improved init (consistent RTF)Improved init (consistent RTF)

T.G, A.B. Larionov, work in progress… T.G, A.B. Larionov, work in progress… (2008)(2008)

Eqs. of motion + meson-field Eqs. including (spatial) gradients (ADI-method):Eqs. of motion + meson-field Eqs. including (spatial) gradients (ADI-method): Eqs. of motion + meson-field Eqs. including (spatial) gradients (ADI-method):Eqs. of motion + meson-field Eqs. including (spatial) gradients (ADI-method):

++

Improved init (consistent RTF)Improved init (consistent RTF)

„Std init“ (+ gradient terms)„Std init“ (+ gradient terms)


Ground state in BUU-II: Ground state in BUU-II: (RTF and BUU test-particles densities)(RTF and BUU test-particles densities)Ground state in BUU-II: Ground state in BUU-II: (RTF and BUU test-particles densities)(RTF and BUU test-particles densities)

T.G, A.B. Larionov, work in progress… T.G, A.B. Larionov, work in progress… (2008)(2008)


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


Mean-field vs cascade – the role of the MDI…Mean-field vs cascade – the role of the MDI…(J-PARC, p+(J-PARC, p+1212C@50GeV)C@50GeV)Mean-field vs cascade – the role of the MDI…Mean-field vs cascade – the role of the MDI…(J-PARC, p+(J-PARC, p+1212C@50GeV)C@50GeV)

centralcentral

peripheralperipheral

HADRONS@FAIR, 25.06.08 Fragment formation of nuclei and hypernuclei within a combined BUU+SMM model...

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