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DPG Tagung, 15.03.10
Breathing mode in an improved transport modelBreathing mode in an improved transport model
T. Gaitanos, A.B. Larionov, H. Lenske, U. MoselT. Gaitanos, A.B. Larionov, H. Lenske, U. Mosel
IntroductionIntroduction
Improved relativistic transport (Giessen-BUU) modelImproved relativistic transport (Giessen-BUU) model
ResultsResultsApplication: properties of Giant Monopole Resonances (GMR)
Final remarksFinal remarks
DPG Tagung, 15.03.10
Introduction…Introduction…
Giant resonances = highly collective (vibrational) modeshighly collective (vibrational) modes of nuclear excitation
Monopol (breathing Monopol (breathing mode)mode)
Monopol (breathing Monopol (breathing mode)mode)
•Giant Monopole Resonance (GMR, breathing mode):
Excitation energy E* --> compression modulus
Width → explore many-body features of finite nuclear system
•Simultaneous description of E* and important, but not trivial
•Here: semi-classical dynamical description of GMR within full BUU
perfect dynamical description of ground state nuclei essential
DPG Tagung, 15.03.10
Relativistic BUU:Relativistic BUU:
Numerical realization (Test-Particle Ansatz):Numerical realization (Test-Particle Ansatz):
+
Initialization Propagation (Vlasov, collisions)
Nuclear ground states in BUU:
„test particles“ initialized according to empirical density distributions
Problem: density profiles not consistent with mean-field used in propagation
nucleus not in its „real“ groundstate, but in an „excited“ state
affects stability
DPG Tagung, 15.03.10
New initialization: method…New initialization: method…
Use the same energy density functional [p,n] for initialization & propagation
Relativistic Thomas Fermi (RTF) for spherical nuclei
Relativistic Thomas-Fermi (RTF) equationsRelativistic Thomas-Fermi (RTF) equations
+ meson field equations (for the different meson fields)+ meson field equations (for the different meson fields)
RTF densitiesRTF densities
DPG Tagung, 15.03.10
New initialization: density distributions & stability in Vlasov New initialization: density distributions & stability in Vlasov dynamics…dynamics…
old initialization
new initialization
DPG Tagung, 15.03.10
New initialization: Binding energy & rms-radius in Vlasov New initialization: Binding energy & rms-radius in Vlasov dynamics…dynamics…
Old initialization
Old initialization
new initialization
new initialization
RTF-binding energy
DPG Tagung, 15.03.10
Simulation of a collective isoscalar vibration in Vlasov & full BUU…Simulation of a collective isoscalar vibration in Vlasov & full BUU…
Vlasov dynamics
GiBUU dynamics
DPG Tagung, 15.03.10
Giant Monopol Resonances (GMR) – excitation energy & width…Giant Monopol Resonances (GMR) – excitation energy & width…
Exp.:Exp.:Shlomo/Youngblood PRC47, 529 (93)
(Q)RPA: Quasiparticle (Q)RPA: Quasiparticle RPARPA
QTBA: Quasiparticle QTBA: Quasiparticle Time Blocking Approx.Time Blocking Approx.
Tselyaev et al., Tselyaev et al., 0912.53280912.5328
DPG Tagung, 15.03.10
Conclusions…Conclusions…
Giant monopole resonancesGiant monopole resonances important tool to explore the many-body features of nuclear systems
simultaneous description of E* and G necessary
Semi-classical treatmentSemi-classical treatment stability of ground state essential improved transport model for collective nuclear dynamics
GiBUU resultsGiBUU resultsGood simultaneous description of E* and ! comparison with RPA & extensions: missing quantal effects
FutureFutureStudy of other giant resonance modes (dipole → symmetry energy)
DPG Tagung, 15.03.10
Pauli blocking: full BUU dynamics…Pauli blocking: full BUU dynamics…
Full BUUFull BUU: time consuming less TP; 1000 TP/N affects accuracy Of Pauli
Improvement of PauliImprovement of Pauli: mom. dep. radius in momentum space rp(r,p), provides sharper profiles near the Fermi surface.
Reduction of spurious particle emission to a minimum, still not perfect.
Spurious escape width of GMR, which has to be excluded (back-up slides…)
DPG Tagung, 15.03.10
Pauli blocking: full BUU dynamics…Pauli blocking: full BUU dynamics…
Full BUUFull BUU: time consuming less TP; 1000 TP/N affects accuracy Of Pauli
Improvement of PauliImprovement of Pauli: mom. dep. radius in momentum space rp(r,p), provides sharper profiles near the Fermi surface.
Reduction of spurious particle emission to a minimum, still not perfect.
Spurious escape width of GMR, which has to be excluded
DPG Tagung, 15.03.10
Ground state in BUU-II: Ground state in BUU-II: Results (application to proton-induced reactions)Results (application to proton-induced reactions)
DPG Tagung, 15.03.10
New initialization: relativistic fields (scalar, vector, etc) & New initialization: relativistic fields (scalar, vector, etc) & stability…stability…
old initialization
new initialization
Fluctuations in different Lorentz-components of nuclear self energy (scalar, vector)
V ~ (vector – scalar) fluctuates considerably!
Almost perfect stability + agreement with ground state
scalar partscalar part vector partvector part
DPG Tagung, 15.03.10
New initialization: relativistic potential (scalar-vector) & stability…New initialization: relativistic potential (scalar-vector) & stability…
old initialization
new initialization
DPG Tagung, 15.03.10
New initialization: relativistic fields (scalar, vector, isocvector, New initialization: relativistic fields (scalar, vector, isocvector, coulomb) & stability…coulomb) & stability…
DPG Tagung, 15.03.10
New initialization: Fermi energies in RTF…New initialization: Fermi energies in RTF…
EF (protons)
EF (neutrons)
DPG Tagung, 15.03.10
New initialization: Fermi energies in BUU…New initialization: Fermi energies in BUU…
old initialization
new initialization
DPG Tagung, 15.03.10
Giant Resonances – preliminaries…Giant Resonances – preliminaries…
Giant resonances = highly collective modeshighly collective modes of nuclear excitation
CollectivityCollectivity
CoherentCoherent super-position of many single-particle transitions from one shell to another
Collective motionCollective motion of an appreciable fraction of nucleons of
nucleus
Monopol (L=0)Monopol (L=0)Monopol (L=0)Monopol (L=0) Dipol (L=1)Dipol (L=1)Dipol (L=1)Dipol (L=1) Oktupol (L=2)Oktupol (L=2)Oktupol (L=2)Oktupol (L=2) … … (L>3)(L>3)… … (L>3)(L>3)
DPG Tagung, 15.03.10
Giant Monopol Resonances (GMR) - Importance…Giant Monopol Resonances (GMR) - Importance…
Indirect determination of the nuclear compression modulus (important for EoS ~sat)
Microscopic approaches (RPA) : Determine E*E* with several nuclear models
and NM properties (compression moduluscompression modulus)
Excitation energy of GMRExcitation energy of GMR
Compression modulus of NM
Compression modulus of NM
Effective interactionsEffective interactions
208Pb
90Zr
Exp. data
EGMR~A-1/3
