1. DPG Tagung, 15.03.10 Breathing mode in an improved transport model T. Gaitanos, A.B. Larionov, H. Lenske, U. Mosel Introduction Improved relativistic transport (Giessen-BUU) model Results Application: properties of Giant Monopole Resonances (GMR) Final remarks

2. DPG Tagung, 15.03.10 Introduction… highly collective (vibrational) modes Giant resonances = highly collective (vibrational) modes of nuclear excitation Monopol (breathing 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

3. DPG Tagung, 15.03.10 Relativistic BUU: 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

4. DPG Tagung, 15.03.10 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) equations  Relativistic Thomas-Fermi (RTF) equations + meson field equations (for the different meson fields) RTF densities

5. DPG Tagung, 15.03.10 New initialization: density distributions & stability in Vlasov dynamics… old initialization new initialization

6. DPG Tagung, 15.03.10 New initialization: Binding energy & rms-radius in Vlasov dynamics… Old initialization new initialization RTF-binding energy

7. DPG Tagung, 15.03.10 Simulation of a collective isoscalar vibration in Vlasov & full BUU… Vlasov dynamics GiBUU dynamics

8. DPG Tagung, 15.03.10 Giant Monopol Resonances (GMR) – excitation energy & width… Exp.: Exp.:Shlomo/Youngblood PRC47, 529 (93) (Q)RPA: Quasiparticle RPA QTBA: Quasiparticle Time Blocking Approx. Tselyaev et al., 0912.5328

9. DPG Tagung, 15.03.10 Conclusions… Giant monopole resonances  important tool to explore the many-body features of nuclear systems  simultaneous description of E* and G necessary Semi-classical treatment  stability of ground state essential  improved transport model for collective nuclear dynamics GiBUU results  Good simultaneous description of E* and  !  comparison with RPA & extensions: missing quantal effectsFuture Study of other giant resonance modes (dipole → symmetry energy)

10. DPG Tagung, 15.03.10 Pauli blocking: full BUU dynamics… Full BUU Full BUU: time consuming  less TP; 1000 TP/N  affects accuracy Of Pauli Improvement of Pauli Improvement of Pauli: mom. dep. radius in momentum space r p (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…)

11. DPG Tagung, 15.03.10 Pauli blocking: full BUU dynamics… Full BUU Full BUU: time consuming  less TP; 1000 TP/N  affects accuracy Of Pauli Improvement of Pauli Improvement of Pauli: mom. dep. radius in momentum space r p (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

12. DPG Tagung, 15.03.10 Ground state in BUU-II: Results (application to proton-induced reactions)

13. DPG Tagung, 15.03.10 New initialization: relativistic fields (scalar, vector, etc) & 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 part vector part

14. DPG Tagung, 15.03.10 New initialization: relativistic potential (scalar-vector) & stability… old initialization new initialization

15. DPG Tagung, 15.03.10 New initialization: relativistic fields (scalar, vector, isocvector, coulomb) & stability…

16. DPG Tagung, 15.03.10 New initialization: Fermi energies in RTF… E F (protons) E F (neutrons)

17. DPG Tagung, 15.03.10 New initialization: Fermi energies in BUU… old initialization new initialization

18. DPG Tagung, 15.03.10 Giant Resonances – preliminaries… highly collective modes Giant resonances = highly collective modes of nuclear excitationCollectivity Coherent Coherent super-position of many single-particle transitions from one shell to another Collective motion Collective motion of an appreciable fraction of nucleons of nucleus Monopol (L=0) Dipol (L=1) Oktupol (L=2) … (L>3)

19. DPG Tagung, 15.03.10 Giant Monopol Resonances (GMR) - Importance… Indirect determination of the nuclear compression modulus (important for EoS ~  sat ) E* Microscopic approaches (RPA) : Determine E* with several nuclear models compression modulus and NM properties (compression modulus) Excitation energy of GMR Compression modulus of NM Effective interactions 208 Pb 90 Zr Exp. data E GMR ~A -1/3