22 th Winter Workshop on Nuclear Dynamics La Jolla, New Clues on Fission Dynamics from Systems of Intermediate Fissility E.V., A. Brondi, G. La Rana, R. Moro, M.Trotta, A. Ordine, A. Boiano Istituto Nazionale di Fisica Nucleare and Dipartimento di Scienze Fisiche dell’Università di Napoli, I Napoli, Italy M. Cinausero, E. Fioretto, G. Prete, V. Rizzi, D. Shetty Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Legnaro I Legnaro (Padova), Italy M. Barbui, D. Fabris, M. Lunardon, S. Moretto, G. Viesti Istituto Nazionale di Fisica Nucleare and Dipartimento di Fisica dell’Università di Padova, I Padova, Italy F. Lucarelli, N. Gelli Istituto Nazionale di Fisica Nucleare and Dipartimento di Fisica dell’Università di Firenze, I Firenze, Italy P.N. Nadtochy Department of Theoretical Physics, Omsk State University, Omsk,Russia V.A. Rubchenya Department of Physycs, University of Jyvaskyla, Finland

22 th Winter Workshop on Nuclear Dynamics La Jolla, Fusion-Fission Light particles and  emission can provide a moving picture of the time evolution Multiplicity is a sensible observable for time scales

22 th Winter Workshop on Nuclear Dynamics La Jolla, Fission Dynamics in Systems of Intermediate Fissility Prologue: FISSION TIME SCALE Excess of pre-scission n, p,  with respect to statistical model predictions Dynamical effect: path from equilibrium to scission slowed- down by the nuclear viscosity 0  d  ssc time Equilibrium Saddle-Point Scission-Point

22 th Winter Workshop on Nuclear Dynamics La Jolla, O Au Excitation Energy (MeV) a f /a n Neutron Multiplicity Statistical Model  = (35 ± 15) x s D. J. Hinde et al.  pp nn ff Statistical Model   d  f =  BW D. J. Hinde et al.,PRC45 (1992)

22 th Winter Workshop on Nuclear Dynamics La Jolla, Inclusion of  d (step function)  <  d   f = 0  >  d  f =  BW - Fission Barriers from A. J. Sierk Phys. Rev. C33 (1986) - a n from Toke and Swiatecki, Nucl. Phys. A372 (1981) Calculations performed for different values of a f / a and  d : 0.94 < a f / a < <  d < 40 x s  -Different sets of transmission coefficients: default, OM, IWBCM - Inclusion of  d (step function)  <  d   f = 0  >  d  f =  BW - Fission Barriers from A. J. Sierk Phys. Rev. C33 (1986) - a n from Toke and Swiatecki, Nucl. Phys. A372 (1981) Calculations performed for different values of a f / a and  d : 0.94 < a f / a < <  d < 40 x s  -Different sets of transmission coefficients: default, OM, IWBCM Multiplicity Analysis with SM

22 th Winter Workshop on Nuclear Dynamics La Jolla, Modified Statistical Model Fission as a diffusion process (Kramer Prescription) : 1.the presence of nuclear viscosity reduces the fission rate  BW 2.the full BW fission rate is never attained.   nuclear viscosity parameter  1 overdamped   reduced dissipation coefficient  f  transient buildup time of the flux over the barrier

22 th Winter Workshop on Nuclear Dynamics La Jolla, Time Scales n  f = (35 ± 15) x s D. J. Hinde et al.  f = (120 ± 10) x s L. M. Pant et al. n, p,  d = 10 x s  ssc = 50 x s J. P. Lestone et al. p,  d  0 H. Ikezoe et al. GDR  d = x s Shaw et al., Thoennessen et al. Dynamical fission time scale :  f =  d +  ssc The determination of the fission time scale and of the average deformation relies on Statistical Model calculations. Use as many observables as possible to constraint the relevant model parameters GOAL: To reproduce many observables with one set of input parameters

22 th Winter Workshop on Nuclear Dynamics La Jolla, Collective Transport Models 1.Lagrange equation (deterministic) 2.Transport equations (stochastic): Fokker-Planck and Langevin equations Dissipation from TKE, n multiplicity Dynamics of fission consists in the study of the gradual change of the shape of a fissioning nucleus. The shape is characterized in terms of collective variables (i.e. elongation parameter, the neck radius, mass asymmetry of exit fragments). The internal degrees of freedom (not collective) constitute the surrounding “heat bath”. The time evolution of these collective variables (interaction the “heat bath” ) describes the fission dynamics.

22 th Winter Workshop on Nuclear Dynamics La Jolla, …but.. NucleusE* (MeV)    s   Exp. Observ. ref. 200 Pb M n (pre) P f L + K 178 W – 251 Es neck 30 sci Mn(pre) P f L + K 181,185,187 Ir M n (pre) FP 181,185,187 Ir16422 M n (pre) WF 158 Er M n (pre) KG + SM 158 Er M n (pre) SML 224 Th6420 ± 6 M GDR KG + SM 175 Ta12320 M GDR KG + SM 90 Sr TKEKG + SM 141 Eu9020 M n (pre), M p (pre) M  (pre) M n (ER), M p (ER) M  (ER)  fiss KG + SM L+K: Langevin and Kramer; FP: Fokker-Plank; KG: Kramers-Grangé; SM: Statistical Model; WF: wall formula.

22 th Winter Workshop on Nuclear Dynamics La Jolla, From the theoretical point of view the predictions vary almost by two or three orders of magnitude. Most of the theories predict indeed an overdamped motion (  > 2x10 21 s -1 ) …but..

22 th Winter Workshop on Nuclear Dynamics La Jolla, The role of isospin in the dissipation W. Ye, Eur. Phys. J. A18 (2003) 571 N/Z N/Z

22 th Winter Workshop on Nuclear Dynamics La Jolla, Open Questions in Fission Dynamics 1.Fission time scale; 2.Strength and Nature of dissipation: one-body or two-body; 3.Dependence of the viscosity on the temperature and on the shape. 1.Fission time scale; 2.Strength and Nature of dissipation: one-body or two-body; 3.Dependence of the viscosity on the temperature and on the shape.

22 th Winter Workshop on Nuclear Dynamics La Jolla, More constraint on the model’s parameters (  ER, lp multiplicities in ER channel)  ~0.60  >0.60 Systems of Intermediate Fissility  ) sscpre   deformation effects on lcp emission  no much data on these systems  deformation effects on lcp emission  no much data on these systems

22 th Winter Workshop on Nuclear Dynamics La Jolla, Target 8  LP layout 34.0° 116 Si- CsI Telescopes (E-DE & TOF) 126 Si- CsI Telescopes (E-DE & PSD) 4 PPACs ring G 4.7° 60cm 15cm FF ring A

22 th Winter Workshop on Nuclear Dynamics La Jolla, The 8  LP setup MAX ENERGY Wall: up to 64 AMeV Ball : up to 34 AMeV TRIGGERS Fission Fragments in ring E/F/G Evaporation Residues (4 PPAC- PPAC) CORSET (under construction) ENERGY THRESHOLDS 0.5 AMeV for p and  2-3 AMeV for 12 C

22 th Winter Workshop on Nuclear Dynamics La Jolla, What observables ?  particle – FF coincidences  particle – ER coincidences  particle – FF coincidences  particle – ER coincidences 8  LP + Trigger for ER and FF

22 th Winter Workshop on Nuclear Dynamics La Jolla, Systems Studied G. La Rana et al., EPJ A16 (2003) 199 E. Vardaci et al., Phys.Atomic Nuclei 66, (2003) 1182, Nucl.Phys. A734 (2004) 241 dd Fast Fission R. Lacey et al., Phys. Rev. C37 (1988) 2540 W. Parker et al., Nucl. Phys. A568 (1994) 633 SystemCNEx (MeV)  d ( s) 32 S Ag 141 Eu O Sm 168 Yb93? 32 S Mo 132 Ce122? 121 Sb + 27 Al 149 Gd Ar + nat Ag 147,9 Tb Ar + nat Ag 147,9 Tb S Mo 132 Ce1520

22 th Winter Workshop on Nuclear Dynamics La Jolla, MeV 32 S Mo  132 Ce: Fragment-Fragment Correlations Ring F-GRing G-G E1 E2 E1

22 th Winter Workshop on Nuclear Dynamics La Jolla, Fragment-Fragment-Particle Coincidences Particle Energy Spectra can arise from several sources: in order to extract the pre- and post-scission integrated multiplicity it is necessary to unfold the contribution of these sources. Three main sources: -Composite System prior to scission - The two fission fragments The Statistical code GANES is used to unfold the spectra and extract the multiplicities.

22 th Winter Workshop on Nuclear Dynamics La Jolla, In-Plane Multiplicity Spectra 12 in-plane correlation angles CS F1 F2 43 o 78 o 102 o 120 o 137 o 156 o 204 o 223 o 241 o 258 o 282 o 299 o E lab (MeV) d 2 M/d   dE  (ster -1 MeV -1 )  =78°  =102°  =120°  =43°  =156°  =204°  =223°  =137°  =258°  =241°  =282°  =299° 200 MeV 32 S Mo  132 Ce

22 th Winter Workshop on Nuclear Dynamics La Jolla, ring G  = in-plane angle  out-of-plane angle d 2 M/d   dE   ster -1 MeV -1 ) E lab (MeV)  = 35.4°   = 24.9°   = 9.2°   = 335.1°   = 324.6°   = 318.9°   = 41.1°   = 350.8°  200 MeV 32 S Mo  132 Ce CS F1 F2 Out-Of-Plane Multiplicity Spectra

22 th Winter Workshop on Nuclear Dynamics La Jolla, ring E  = in-plane angle  out-of-plane angle E lab (MeV)  = 74.2°   = 66.6°   = 38.8°   = 293.4°   = 285.8°   = 77.0°   = 321.2°  d 2 M/d   dE  (ster -1 MeV -1 )  = 283.0°  200 MeV 32 S Mo  132 Ce CS F1 F2 Out-Of-Plane Multiplicity Spectra

22 th Winter Workshop on Nuclear Dynamics La Jolla, d 2 M/d   dE  (ster -1 MeV -1 ) E lab (MeV)  = 113.0°   = 140.8°   = 247.0°   = 254.5°   = 257.3°   = 102.7°   = 219.2°   = 105.5°  200 MeV 32 S Mo  132 Ce  = in-plane angle  out-of-plane angle ring D CS F1 F2 Out-Of-Plane Multiplicity Spectra

22 th Winter Workshop on Nuclear Dynamics La Jolla, M p ER M  ER M p pre M  pre  ff [mb]  ER [mb] 0,90 (0.14) 0,56 (0.09) 0,055 (0,007) 0,038 (0,005) 70 ± 7576 ± MeV 32 S Mo  132 Ce:

22 th Winter Workshop on Nuclear Dynamics La Jolla, Important to measure M n 200 MeV 32 S Mo  FF

22 th Winter Workshop on Nuclear Dynamics La Jolla, particle-ER coincidences 1.The SM code Lilita_N97 (no fission included) reproduces the angular distribution 2.It overestimates p and  multiplicities by the same factor It well reproduces the energy spectra shapes of p and  ABCDEFG Lilita_N97 exp alpha dM/d  (ster -1 ) ABCDEFG exp Lilita_N proton Detector #

22 th Winter Workshop on Nuclear Dynamics La Jolla, dM/d  (ster -1 ) ABCDEFG Detector # exp PACE exp PACE ABCDEFG Detector # proton alpha particle-ER coincidences: PACE (1) 1.The SM code PACE (fission included) reproduces the a.d. 2.It overestimates p (by 1.8) and  (by 3.1) multiplicities 3.No selection of input parameters improves the agreement 4.The energy spectra are generally too hard

22 th Winter Workshop on Nuclear Dynamics La Jolla, Q & A If the model does not work where it is supposed to work, why do we use it in another regime to estimate time scales ? With respect to what baseline number is the excess to be determined? What are the effects of this inability of the model to predict correctly the particle competition in the fission channel? In principle, if the charged particle multip. are overestimated, the neutron multiplicity should be underestimated......(?) Excitation Energy (MeV) Neutron Multiplicity Statistical Model a f /a n 16 O Au This means that the time delay may be overestimated if only neutrons are measured in the FF channel....

22 th Winter Workshop on Nuclear Dynamics La Jolla, MeV 18 O Sm  168 Yb n p  Newton et al.Nucl.Phys.A483 (1988)  d (x ) PreScission Multiplicity

22 th Winter Workshop on Nuclear Dynamics La Jolla, What do we do? By using a more realistic approach we can try to put this picture together! 3D Langevin approach + Statistical Model Karpov, Nadtochy et al. Phys.Rev. C63, 2001 LILITA_N97 for light particle evaporation along trajectories

22 th Winter Workshop on Nuclear Dynamics La Jolla, D Langevin Eq. (1) 1.The shape is characterized in terms of collective variables (i.e. elongation parameter, the neck radius, mass asymmetry of exit fragments). 2.The internal degrees of freedom (not collective) constitute the surrounding ‘heat bath’. 3.The heat bath induces fluctuations on the collective variables Langevin equations describe the time evolution of the collective variables like the evolution of Brownian particle that interact stochastically with a ‘heat bath’ (internal degrees of freedom). Dynamical approach of fission consists into the study of the gradual change of the shape of a fissioning nucleus.

22 th Winter Workshop on Nuclear Dynamics La Jolla, D Langevin Eq. (2) Inertia Tensor Friction Tensor q 1 = deformation q 2 = neck size q 3 = mass asymmetry

22 th Winter Workshop on Nuclear Dynamics La Jolla, E coll - the energy connected with collective degrees of freedom E int - the energy connected with internal degrees of freedom E evap - the energy carried away by the evaporated particles PES Time Evolution

22 th Winter Workshop on Nuclear Dynamics La Jolla, fission eventsEvaporation residue events - starting point (sphere) - saddle point For each fissioning trajectory it is possible to calculate masses (M 1 and M 2 ) and kinetic energies (E K ) of fission fragments, fission time (t f ), the number of evaporated light prescission particles. Samples of Trajectories scission line

22 th Winter Workshop on Nuclear Dynamics La Jolla, MeV 32 S Mo: Fission Rate t (x ) Fission Rate L = 60 L = 50 L = 40 L = 0-20

22 th Winter Workshop on Nuclear Dynamics La Jolla, ER channelPrescission channel MpMp MM MpMp MM  FF (mb)  ER (mb) Exp. 0,91 ± ,56 ± ,055 ± 0,007 0,038 ± 0, ± ± 50 Theor MeV 32 S Mo Transient time for fission, ranging from 15 to 20 x at high angular momentum of the composite system, where fission is relevant

22 th Winter Workshop on Nuclear Dynamics La Jolla, Conclusions The current implementations of the SM do not reproduce correctly particle competitions in the ER channel The extraction of the fission time scale is affected by the reliability of the SM ingredients used The SM is unable to reproduce a sizeable set of observable which involve the Fission and the ER channel Dynamical models seems to be a promising approach capable of reproducing a more complete set of data More tests and measurement need to be performed