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 The lightest semi bubbels are foreseen around mass A  300, while the true bubble appear at A  400, the lighter nuclei prefer ordinary solution J. Decharge et all. Phys. Lett. B (1999) 275 - 282

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

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

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 v 12 - 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 EOSA[MeV]B[MeV]  K[MeV] STIFF-124.6974.242380 SOFT-356306.17/6200

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

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

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

13. Results for central collisions of 124 Sn+ 124 Sn y x z x E=35MeV/nucleon E=50MeV/nucleon E=25MeV/nucleon K=200MeV 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 be expected 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 Drawing of fragments: Gaussian distribution Established : Z i, A i ; i = 1,N ( N=5 ) All the fragments are placed in ball, bubble and toroidal configuration with additional condition: R ij > R i + R j + 2fm A CN = A T + A P Z CN = Z T + Z P - minus preequilibrium nucleons Partition of the available energy: E ava = E CM + Q –E COULOMB Acceleration in mutual Coulomb field Detection of particles in the CHIMERA detector ,   detector number   rand,  rand Non - central collisions are taken into acount up to give impact parameter b E thr =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) i is the i-th Cartesian momentum component of the n-th particle, and is the n-th fragment momentum vector. For eigenvalues t 1 < t 2 < t 3 of the tensor F one dehines the reduced quantities: Then sphericity and coplanarity parameters are defined as:

18. ETNA`s simulation results

19. planarity 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. VlasovBoltzmanLangevin 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

23. A.Sochocka g *, C.Agodi a, R.Alba a, F.Amorini a, A.Anzalone a, L.Auditore d, V.Baran e, I.Berceanu e, J.Blicharska f, J.Brzychczyk g, B.Borderie h, R.Bougault i, M.Bruno j, G.Cardella b, S.Cavallaro a, R.Coniglione a, M.B.Chatterjee k, A.Chbihi l, J.Cibor m, M.Colonna a, M.D’Agostino j, E.DeFilippo b, R. Dayras o, A.DelZoppo a, M.DiToro a, J.Frankland l, E.Galichet h, W. Gawlikowicz g, E.Geraci j, F.Giustolisi a, A.Grzeszczuk f, P.Guazzoni p, D.Guinet q, P.Hachaj u, M.Iacono-Manno a, S.Kowalski f, E. La Guidara a, G.Lanzanò b, G.Lanzalone a, C.Maiolino a, N.LeNeindre h, N.G.Nicolis t, Z.Majka g, A.Pagano b, M.Papa b, M.Petrovici e, E.Piasecki r, S.Pirrone b, R.Płaneta g, G.Politi b, A.Pop e, F.Porto a, M.F.Rivet h, E.Rosato s, F.Rizzo a, S.Russo p, P.Russotto l, D.Santonocito a, M.Sassi p, K.Schmidt f, K.Siwek-Wilczyńska r, I.Skwira r, M.L.Sperduto b, L.Świderski r, A.Trifirò d, M.Trimarchi d, G.Vannini j, G.Verde b, M.Vigilante s, J.P.Wieleczko l, J.Wilczyński c, L.Zetta p, and W.Zipper f 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 CHIMERA - ISOSPIN Collaboration

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

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

27. Definition of TKE TKE – total mesured c.m kinetic energy of detected charged products TKE = E C.M + Q -  E neutron -  E  Where E C.M, Q,  E neutron,  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  70 0  = 2,6 mb G.Tabacaru Nucl. Phys. A 764 ( 2006 ) 371-386

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

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

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

32. G.Tabacaru Nucl.Phys. A 764 ( 2006 ) 371-386 i ) Z i,j  5 ii ) 5  Z i,j  20 iii ) Z i  Z max Black line – experimental data Red symbols - dynamical 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 BOB simulation

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

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 - two particle coincidence yield - background yield obtained by event mixing relative velocity - relative velocity v red = reduced velocity - reduced velocity -

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

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

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

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

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

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

44. 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 E available =E *( T ) + E th ( T )

49. Invariant velocity plots E = E* Energia wzbudzenia Energia ruchu termicznego E = E Th E available = E* E th =0 E available =E th E*= 0 Hachaj prescription

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

51. Common temperature of thermal motion and fragments excitation Temperature T Common temperature of thermal motion and fragments excitation Hachaj prescriptionGaussian distribution

52. 16O + Au _60MeV We observed energy spectrum for oxygen in reaction 16O + Au at 60MeV Elastic scattering Elab_p vs yield abs(theta_p-74 o ).lt. 4 o Detector 850; 305  m Si; =74 o

53. 58Ni + Au _100MeV We observed energy spectrum for nickel in reaction 58Ni + Au at 100MeV Detector 850; 305  m Si; =74 o Elab_p vs yield abs(theta_p-74 o ).lt. 4 o Elastic scattering

54. 16O + Au _100MeV We observed energy spectrum for oxygen in reaction 16O + Au at 100MeV Elastic scattering Detector 850; 305  m Si; =74 o Elab_p vs yield abs(theta_p-74 o ).lt. 4 o

55. Detector 850; 305  m Si; =74 o 16O + Au at 60MeV E 160 el. scater. = 52.25MeV E 160 el. scater. = 88.02MeV 16O + Au at 100MeV 58Ni + Au at 100MeV E 58Ni el. scater. = 88.02MeV Calculations

56. Alpha line Desilpg 218.31 272.3 Time 2565.1 2599.5 Carbon line Desilpg 218.31 272.3 Time 2565.1 2599.5 3H punch through Desilpg 205.62 208.13 Time 2605 2612.5 Detector 850; 305  m Si; =74 o Au + C at 15MeV/A Experimental data

57. Simulation results for central collisions Ar + Sc at 80 MeV/nucleon 10fm/c 50fm/c 100fm/c 150fm/c x y z beam direction BUU calculations D.O. Handzy et al. Phys. Rev. C 51, 2237 (1995) Decay characteristics for non compact nuclear objects ( model predictions)  more of intermediate mass fragments ( Z > 3 ) should be generated than would be expected for the decay of a compact object at the same temperature  enhanced similarity in the charges of fragments  suppressed sphericity in the emission of fragments

58. Detector 850; 305  m Si; =74 o Au + Au at 15MeV/A Au fission Desilpg 262.77 637.47 Time 2339.3 2479 Alpha punch through E alpha = 24.7 Mev Experimental data

59. Mass spectrum Au + C at 15MeV/A Yield vs mass C 

61. BUU equation is solved by test – particle method Each nucleon is replaced by N test- particles N A - number of nucleons A nucleus N B - number of nucleons B nucleus N B * N N A * N A B = + ( N A +N B )*N  ( r ) = N’/[N(N A + N B )](  r ) 3 N’ - number of test particles in small volume (  r ) 3 around the point Test particles collide with a cross section  nn /N

62. Multiplicity distribution of the heavy fragments

63.  R =8 barn  /  R =3,5% for b=3fm