Search for hyperheavy toroidal nuclear structures formed in heavy ion collisions

1. Search for hyperheavy toroidal nuclear structures formed in heavy ion collisions Anna Sochocka and Roman Płaneta, M. Smoluchowski Institute of Physics, Jagellonian University, Cracow, Poland

3. The theoretical analysis of properties of super-heavy nuclei do not predict any long living nuclei with compact shapes beyond the island of stability (N ~ 184, Z ~ 114). Liquid drop model with shell corrections and Hartree – Fock – Bogoliubov theory with the Gogny D1S force calculations have shown that metastable islands of nuclear bubbles can exist for nucleon numbers in the range A=450-3000 K. Dietrich, K.Pomorski Phys. Rev. Lett. 80, 37 (1998) J. Decharge et al. Nucl. Phys.A 716, 55 (2003 )

4. Predictions of the HFB model with the Gogny D1S force bubbles semi - bubbels ordinary nuclei typical density profiles corresponding to the above configurations J. Decharge et all. Phys. Lett. B (1999) 275 - 282 The lightest semi bubbels are foreseen around mass A300, while the true bubble appear at A400, the lighter nuclei prefer ordinary solution

5. Torus is another topology which is investigated M.Warda, Int. J. Mod. Phys. E 16, 2 (452-458),2006 Q 2- quadrupole moment RMSR – root mean square radius d – tube radius d Minimum potential energy for the toroidal shape RMSR

6. Prediction for the toroidal shapes • The energy of the toroidal minimum decrease relatively to the potential energy of the spherical configuration with increase of the mass of the system • For Z>140 , the global minimum of potential energy corresponds to the toroidal shape M. Warda, poster on XIII Nuclear Physics Workshop in Kazimierz 2006

7. y x Dynamical model predictions: • BUU transport calculations showed that exotic nuclear shapes may be created in central heavy ion collisions at intermediate energiesL. G. Moretto et al., Phys. Rev. Lett. 78 ( 1997 824 -827) z beam direction x BUU calculations Lien-Ven Chen et all. Phys. Rev. C 68 (2003 ) 014605

8. Boltzmann – Uehling – Uhlenbeck model The BUU transport equation for the nucleonic one-body density distribution function f = is given by: d /d - nucleon-nucleon cross section v12 - relative velocity for the colliding nucleons, U - mean-field potential consisting of the Coulomb potential and a nuclear potential with isoscalar and symmetry terms.

9. The potential field is approximated by 0 - normal nuclear matter density, , n , p- nucleon, neutron, and proton densities, z - equals 1 or -1 for neutrons or protons, respectively.  = (n - p) /(n+ p) – asymmetry parameter

10. x z beam direction Simulation results for central collisions of Au+Au K=200MeV E=15MeV/nucleon E=23MeV/nucleon y z E=40MeV/nucleon y y x x BUU calculations

11. Simulation results for central collisions of Au+Au K=380 MeV K=200 MeV flat sphere flat bubble Ksym =-69MeV – blue line E=15 MeV/A Ksym =61 MeV – red line toroid disc E=23MeV/A Central density  ( x=0, y=0, z=0 ) toroid toroid E=40MeV/A BUU calculations

12. Simulation results for non-central Au+Au at 23 MeV/A b=1.25 fm y z’ x  b=3fm z y x’ z beam direction x’ b=8fm Time = 200 fm/c z’ x x’ K=200 MeV y

13. Results for central collisions of124Sn+124Sn K=200MeV E=25MeV/nucleon E=35MeV/nucleon z y E=50MeV/nucleon x x BUU calculations

14. Decay characteristics for non compact nuclear objects (dynamical model predictions) • more of intermediate mass fragments ( Z > 3) should be generated than would beexpected for the decay of a compact object at the same temperature • enhanced similarity in the charges of fragments

15. ETNA – Expecting Toroidal Nuclear Agglomeration Flow diagram ACN = AT + AP ZCN = ZT + ZP -minus preequilibrium nucleons Non - central collisions are taken into acount up to give impact parameter b Partition of the available energy: • Drawing of fragments: • Gaussian distribution Eava = ECM + Q –ECOULOMB Acceleration in mutual Coulomb field Established : Zi , Ai ; i = 1,N ( N=5 ) Detection of particles in the CHIMERA detector All the fragments are placed in ball, bubble and toroidal configuration with additional condition: Rij > Ri + Rj + 2fm ,   detector number  rand ,rand Ethr=1 MeV/A

16. Global characteristics of ETNA code simulation for Au+Au

17. Definition of sphericity and coplanarity From the Cartesian components of fragment (Z 5) momenta in the centre of mass one may construct the tensor where p(n)iis the i-th Cartesian momentum component of the n-th particle, and is the n-th fragment momentum vector. For eigenvalues t1 < t2 < t3 of the tensor F one dehines the reduced quantities: Then sphericity and coplanarity parameters are defined as:

18. ETNA`s simulation results

19. ETNA`s simulation results planarity

20. Conclusions • Microscopic models of the nuclear system predict that for Z>130 the exotic shapes ( bubbles, toroids ) corresponds to the stable configuration of very heavy nuclear matter • The threshold energy for toroidal shapes formation decrease with increasing mass of the system ( BUU predictions ) • This threshold energy depends on the stiffness of the nuclear equations of the state ( BUU predictions ) • Preliminary predictions of ETNA code indicate that at 23 MeV/A the proposed signitures able to distinguish between different freeze-out configurations • Comparison with other dynamical models in progress

21. Conclusions • Przewidywania modeli mikroskopowych wskazuja na egzotyczne ksztalty dla systemow o duzych masach bedacych w rownowadze • Energia progowa na formowanie sie toroidalnych ksztaltow maleje wraz z rosnaca masa zderzajacych sie jader • Dla rownania stanu ksztalty toroidalne tworza sie przy wyzszych energiach w porownaniu dla przewidywan dla miekkiego rownania stanu

22. Characterizaton of the dynamical models Vlasov model – paricles experience only the self – consistent effective field, leading to a single dynamical trajectory Boltzman model – various possible outcomes of the residual collisions are being averaged at each step, leading to a different but still single dynamical trajectory Langevin model – various stochastic collisions outcomes to develop independently, leading to a continual trajectory branching, corresponding ensemble of histories Vlasov Boltzman Langevin

23. A.Sochockag*, C.Agodia, R.Albaa, F.Amorinia, A.Anzalonea, L.Auditored, V.Barane, I.Berceanue, J.Blicharskaf, J.Brzychczykg, B.Borderieh, R.Bougaulti, M.Brunoj, G.Cardellab, S.Cavallaroa, R.Coniglionea, M.B.Chatterjeek, A.Chbihil, J.Ciborm, M.Colonnaa, M.D’Agostinoj, E.DeFilippob, R. Dayraso, A.DelZoppoa, M.DiToroa, J.Franklandl, E.Galicheth, W. Gawlikowiczg, E.Geracij, F.Giustolisia,A.Grzeszczukf, P.Guazzonip, D.Guinetq, P.Hachaju, M.Iacono-Mannoa, S.Kowalskif, E. La Guidaraa, G.Lanzanòb, G.Lanzalonea, C.Maiolinoa, N.LeNeindreh, N.G.Nicolist , Z.Majkag, A.Paganob, M.Papab, M.Petrovicie, E.Piaseckir, S.Pirroneb, R.Płanetag, G.Politib, A.Pope, F.Portoa, M.F.Riveth, E.Rosatos, F.Rizzoa, S.Russop, P.Russottol, D.Santonocitoa, M.Sassip, K.Schmidtf, K.Siwek-Wilczyńskar, I.Skwirar, M.L.Sperdutob, L.Świderskir, A.Trifiròd, M.Trimarchid, G.Vanninij, G.Verdeb, M.Vigilantes, J.P.Wieleczkol, J.Wilczyńskic, L.Zettap, and W.Zipperf CHIMERA - ISOSPINCollaboration a) INFN, Laboratori Nazionali del Sud and Dipartimento di Fisica e Astronomia, Università di Catania, Italy b) INFN, Sezione di Catania and Dipartamento di Fisica e Astronomia, Università di Catania, Italy c) A. Sołtan Institute for Nuclear Studies, Swierk/Warsaw, Poland d) INFN, Gruppo Collegato di Messina and Dipartamento di Fisica, Università di Messina, Italy e) Institute for Physics and Nuclear Engineering, Bucharest, Romania f) Institute of Physics, University of Silesia, Katowice, Poland g) M. Smoluchowski Institute of Physics, Jagellonian University, Cracow, Poland h) Institute de Physique Nuclèaire, IN2P3-CNRS, Orsay, France i) LPC, ENSI Caen and Universitè de Caen, France j) INFN, Sezione di Bologna and Dipartimento di Fisica, Università di Bologna, Italy k) Saha Institute of Nuclear Physics, Kolkata, India l) GANIL, CEA, IN2P3 – CNRS, Caen, France m) H. Niewodniczanski Institute of Nuclear Physics, Cracow, Poland o) DAPNIA / SPhN, CEA – Saclay, France p) INFN, Sezione di Milano and Dipartimento di Fisica, Università di Milano, Italy q) IPN, IN2P3 – CNRS and Universitè Claude Bernard, Lyon, France r) Institute for Experimental Physics, Warsaw University, Warsaw, Poland s) INFN, Sezione Napoli and Dipartamento di Fisica, Università di Napoli, Italy t) Department of Physics, University of Ioannina, Ioannina, Greece u) Cracow University of Technology, Cracow, Poland * Corresponding author, e-mail: ania_sochocka@poczta.fm

24. Outlook • Incorporation of angular momentum into the ETNA code • Additional calculation with BUU code • Introduction of novel signatures of exotic shapes • Test of signatures for systems with different masses: Au+Au @ 40 MeV/nucleons; INDRA, GSI U+U @ 24 MeV/nucleons; INDRA, GANIL Sn + Sn @ 35 MeV/nucleon, CHIMERA, INFN-LNS

25. Definition of sphericity and coplanarity From the cartesian components of fragment Z 5 momenta in the centre of mass may construct the tensor where p(n)iis the i-th Cartesian momentum component of the n-th particle, and is the n-th fragment momentum vector. Main axis of events flow Beam direction

26. Events selection for central collisions Total reaction cross section R = 6500 mb events located in „3” are well measured events : 120 Ztot  ( ZP+ZT =156) 0.8  Ptot II /Pproj  1.1  = 93mb II J.D Frankland et al., Nucl. Phys. A 689 (2001),905-939

27. Definition of TKE TKE – total mesured c.m kinetic energy of detected charged products TKE = EC.M + Q -  Eneutron -  E Where EC.M , Q,  Eneutron, E are the available centre of mass energy, the mass balance of the reaction and total neutron and gamma ray kinetic energies, respectively

28. Events selection flow  700  = 2,6 mb G.Tabacaru Nucl. Phys. A 764 ( 2006 ) 371-386

29. Ftotal Results The average kinetic energy of the largest fragment is smaller than energy of the other fragments and show maximum for Z30-35 date simulation G.Tabacaru Nucl. Phys A 764 ( 2006 ) 371-386

30. In the region Z=15-25 the heaviest fragment, Zmax, has always the lowest average kinetic energy date simulation G.Tabacaru Nucl.Phys. A 764 ( 2006 ) 371-386

31. G.Tabacaru Nucl.Phys A 764 ( 2006 ) 371-386

32. BOB simulation The one body density evolution calculated in a Boltzmann-Nordheim-Vlasov approach (BNV) up to 40 fm/c (the instant of maximum compression) after Brownian One Body (BOB) dynamics i ) Zi,j5 ii ) 5  Zi,j 20 iii ) Zi  Zmax Black line – experimental data Red symbols - dynamical simulation G.Tabacaru Nucl.Phys. A 764 ( 2006 ) 371-386

33. L 35 1500 L [hbar] Here is the place for other event geometries 2,6 mb Sharp cut off approximation Experimatal event selection

35. Binding energy per nucleon e( , )as a function of density  and isospin asymmetry parameter  : Where: • N - density of neutron P - density of proton

36. Experimental observables where: - two particle coincidence yield • background yield obtained by event mixing - relative velocity v red = - reduced velocity -

38. Space distribution of fragments for disc and torusconfigurations; (  = 0/3 ) Au+Au at 15 MeV/nucleons y z beam direction x

39. Invariant velocity plots Au+Au at 15 MeV/nucleons Common temperature

40. General decay characteristics for Au + Au reaction at 15 MeV/nucleons Common temperature Granulation of the CHIMERA detector taken into account

41. Simulation predictions Planarity is able to disantangle between ball, disc and toroidal shapes for the heavy Au + Au system and unable for the lighter system

42. Simulation predictions Noticeable differences in 1+R function are observed for the heavier system, for the lighter system are less visible

43. Definition of 1+R correlation function where: - two particle coincidence yield • background yield obtained by event mixing - relative velocity - reduced velocity v red =

44. G.Tabacaru Nucl.Phys. A 764 ( 2006 ) 371-386

45. G.Tabacaru Nucl.Phys. A 764 ( 2006 ) 371-386

46. Summary and conclusions: • preliminary simulations with ETNA code were performed • observables discriminating different exotic shapes were found ( 1+R, planarity) for heavy Au + Au system, for lighter Sn + Sn system discrimation is less obvious • it is necessery to performed additional simulations for more realistic mass distribution ( experimental data ) • simulations with dynamical models are necessery in order to rushed more light at the dynamics of exotic systems formation

48. Angular momentum Eavailable=E*( T ) + Eth( T )

49. Invariant velocity plots Eavailable =Eth E*= 0 Eavailable = E* Eth=0 Energia ruchu termicznego E = ETh Energia wzbudzenia E = E* Hachaj prescription

50. BUU predictions for central collisions of Mo + Mo at 75 MeV/nucleon K = 200 MeV K = 540 MeV 20fm/c 60fm/c 120fm/c 180fm/c