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New Clues on Fission Dynamics from Systems of Intermediate Fissility

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-80125 Napoli, Italy

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New Clues on Fission Dynamics from Systems of Intermediate Fissility

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  1. 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-80125 Napoli, Italy M. Cinausero, E. Fioretto, G. Prete, V. Rizzi, D. Shetty Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Legnaro I-36020 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-35131 Padova, Italy F. Lucarelli, N. Gelli Istituto Nazionale di Fisica Nucleare and Dipartimento di Fisica dell’Università di Firenze, I-50125 Firenze, Italy P.N. Nadtochy Department of Theoretical Physics, Omsk State University, Omsk,Russia V.A. Rubchenya Department of Physycs, University of Jyvaskyla, Finland 22th Winter Workshop on Nuclear Dynamics La Jolla, 2006

  2. Fusion-Fission Reactions @10MeVA Light particles and g emission can provide a moving picture of the time evolution Multiplicity is a sensible observable for time scales 22th Winter Workshop on Nuclear Dynamics La Jolla, 2006

  3. 0 tdtssctime Fission Dynamics in Systems of Intermediate Fissility Prologue: FISSION TIME SCALE Dynamical effect: path from equilibrium to scission slowed-down by the nuclear viscosity Excess of pre-scission n, p, awith respect to statistical model predictions EquilibriumSaddle-PointScission-Point 22th Winter Workshop on Nuclear Dynamics La Jolla, 2006

  4. 16O + 197Au 4 Gp Gf Statistical Model 3 Gn Ga a / a f n Neutron Multiplicity 2 1.00 1 1.06 40 60 80 Excitation Energy (MeV) Statistical Model t < tdGf = 0 t > tdGf = GBW t= (35 ± 15) x 10-21s D. J. Hinde et al. D. J. Hinde et al.,PRC45 (1992) 22th Winter Workshop on Nuclear Dynamics La Jolla, 2006

  5. Multiplicity Analysis with SM • Inclusion of td (step function) • t < td Gf = 0 • t > td Gf = GBW • -Fission Barriers from A. J. Sierk Phys. Rev. C33 (1986) • -an from Toke and Swiatecki, Nucl. Phys. A372 (1981) • Calculations performed for different values ofaf/ anandtd: • 0.94 < af/ an< 1.12 0 < td < 40 x 10-21 s • -Different sets of transmission coefficients: default, OM, IWBCM 22th Winter Workshop on Nuclear Dynamics La Jolla, 2006

  6. Modified Statistical Model • Fission as a diffusion process (Kramer Prescription): • the presence of nuclear viscosity reduces the fission rate GBW • the full BW fission rate is never attained. g nuclear viscosity parameter g < 1 underdampedg > 1 overdamped b reduced dissipation coefficient tf transient buildup time of the flux over the barrier 22th Winter Workshop on Nuclear Dynamics La Jolla, 2006

  7. ntf = (35 ± 15) x 10-21 s D. J. Hinde et al. tf = (120 ± 10) x 10-21 s L. M. Pant et al. n, p, atd = 10 x10-21 s tssc= 50 x 10-21 sJ. P. Lestone et al. p,a td  0 H. Ikezoe et al. GDR td = 30-200 x 10-21 s Shaw et al., Thoennessen et al. Time Scales Dynamical fission time scale: tf = td + tssc 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 22th Winter Workshop on Nuclear Dynamics La Jolla, 2006

  8. Collective Transport Models 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. • Lagrange equation (deterministic) • Transport equations (stochastic): Fokker-Planck and Langevin equations Dissipation from TKE, n multiplicity 22th Winter Workshop on Nuclear Dynamics La Jolla, 2006

  9. …but.. L+K: Langevin and Kramer; FP: Fokker-Plank; KG: Kramers-Grangé; SM: Statistical Model; WF: wall formula. 22th Winter Workshop on Nuclear Dynamics La Jolla, 2006

  10. …but.. 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 (b > 2x1021 s-1) 22th Winter Workshop on Nuclear Dynamics La Jolla, 2006

  11. N/Z 1.49 1.40 1.32 N/Z 1.25 1.40 1.52 The role of isospin in the dissipation W. Ye, Eur. Phys. J. A18 (2003) 571 22th Winter Workshop on Nuclear Dynamics La Jolla, 2006

  12. Open Questions in Fission Dynamics • Fission time scale; • Strength and Nature of dissipation: one-body or two-body; • Dependence of the viscosity on the temperature and on the shape. 22th Winter Workshop on Nuclear Dynamics La Jolla, 2006

  13. c>0.60 c~0.60 t >> t pre ssc Systems of Intermediate Fissility(c  0.5 - 0.6) More constraint on the model’s parameters (sER, lp multiplicities in ER channel) • deformation effects on lcp emission • no much data on these systems 22th Winter Workshop on Nuclear Dynamics La Jolla, 2006

  14. FF 34.0° 15cm 60cm 4.7° ring A 4 PPACs ring G Target 8pLP layout 116 Si- CsI Telescopes (E-DE & TOF) 126 Si- CsI Telescopes (E-DE & PSD) 22th Winter Workshop on Nuclear Dynamics La Jolla, 2006

  15. The 8pLP setup MAX ENERGYWall: up to 64 AMeV Ball : up to 34 AMeV ENERGY THRESHOLDS0.5 AMeV for p and a 2-3 AMeV for 12C TRIGGERSFission Fragments in ring E/F/G Evaporation Residues (4 PPAC- PPAC) CORSET (under construction) 22th Winter Workshop on Nuclear Dynamics La Jolla, 2006

  16. What observables ? • particle – FF coincidences • particle – ER coincidences 8pLP + Trigger for ER and FF 22th Winter Workshop on Nuclear Dynamics La Jolla, 2006

  17. td Fast Fission 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 R. Lacey et al., Phys. Rev. C37 (1988) 2540 W. Parker et al., Nucl. Phys. A568 (1994) 633 22th Winter Workshop on Nuclear Dynamics La Jolla, 2006

  18. Ring F-G Ring G-G 200 MeV 32S + 100Mo132Ce: Fragment-Fragment Correlations E2 E2 E1 E1 22th Winter Workshop on Nuclear Dynamics La Jolla, 2006

  19. 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. 22th Winter Workshop on Nuclear Dynamics La Jolla, 2006

  20. a=78° a=102° a=120° a=43° 78o 102o 120o 43o 137o a=137° a=156° a=204° a=223° d2M/dWadEa (ster-1 MeV-1) 156o 204o 223o 241o 258o 282o 299o a=241° a=258° a=282° a=299° CS F1 F2 Elab (MeV) 200 MeV 32S + 100Mo132Ce In-Plane Multiplicity Spectra 12 in-plane correlation angles 22th Winter Workshop on Nuclear Dynamics La Jolla, 2006

  21. a = 35.4° b = 25.9° a = 24.9° b = 36.1° a = 41.1° b = 13.5° a = 9.2° b = 42.1° d2M/dWadEa (ster-1 MeV-1) a = 324.6° b = 25.9° a = 350.8° b = 42.1° a = 335.1° b = 36.1° CS F1 a = 318.9° b = 13.5° F2 Elab (MeV) 200 MeV 32S + 100Mo132Ce Out-Of-Plane Multiplicity Spectra ring G a = in-plane angle b = out-of-plane angle 22th Winter Workshop on Nuclear Dynamics La Jolla, 2006

  22. a = 77.0° b = 19.5° a = 74.2° b = 38.9° a = 66.6° b = 57.8° a = 38.8° b = 74.3° d2M/dWadEa (ster-1 MeV-1) a = 321.2° b = 74.3° a = 293.4° b = 57.8° a = 283.0° b = 19.5° a = 285.8° b = 38.9° CS F1 F2 Elab (MeV) 200 MeV 32S + 100Mo132Ce Out-Of-Plane Multiplicity Spectra ring E a = in-plane angle b = out-of-plane angle 22th Winter Workshop on Nuclear Dynamics La Jolla, 2006

  23. a = 102.7° b = 19.5° a = 105.5° b = 39.0° a = 113.0° b = 57.9° a = 140.8° b = 74.4° d2M/dWadEa (ster-1 MeV-1) a = 219.2° b = 74.4° a = 247.0° b = 57.9° a = 254.5° b = 39.0° a = 257.3° b = 19.5° CS F1 F2 Elab (MeV) 200 MeV 32S + 100Mo132Ce Out-Of-Plane Multiplicity Spectra ring D a = in-plane angle b = out-of-plane angle 22th Winter Workshop on Nuclear Dynamics La Jolla, 2006

  24. 200 MeV 32S + 100Mo132Ce: 22th Winter Workshop on Nuclear Dynamics La Jolla, 2006

  25. 200 MeV 32S + 100MoFF Important to measure Mn 22th Winter Workshop on Nuclear Dynamics La Jolla, 2006

  26. The SM code Lilita_N97 (no fission included) reproduces the angular distribution • It overestimatesp and a multiplicities by the same factor 1.8 • It well reproduces the energy spectra shapes of p and a particle-ER coincidences 10-1 10-1 exp exp Lilita_N97 Lilita_N97 proton alpha 10-2 dM/dW (ster-1) 10-2 10-3 A B C D E F G A B C D E F G 10-4 10-3 0 120 40 80 0 40 80 120 Detector # Detector # 22th Winter Workshop on Nuclear Dynamics La Jolla, 2006

  27. 10-1 10-1 exp exp PACE PACE alpha proton 10-2 dM/dW (ster-1) 10-2 10-3 A B C D E F G A B C D E F G 10-4 10-3 0 120 40 80 0 40 80 120 Detector # Detector # particle-ER coincidences: PACE (1) • The SM code PACE (fission included) reproduces the a.d. • It overestimatesp (by 1.8) and a (by 3.1) multiplicities • No selection of input parameters improves the agreement • The energy spectra are generally too hard 22th Winter Workshop on Nuclear Dynamics La Jolla, 2006

  28. 16O + 197Au 4 Statistical Model 3 a / a n f Neutron Multiplicity 1.00 2 1.06 1 40 60 80 Excitation Energy (MeV) Q & A In principle, if the charged particle multip. are overestimated, the neutron multiplicity should be underestimated......(?) This means that the time delay may be overestimated if only neutrons are measured in the FF channel.... With respect to what baseline number is the excess to be determined? If the model does not work where it is supposed to work, why do we use it in another regime to estimate time scales ? What are the effects of this inability of the model to predict correctly the particle competition in the fission channel? 22th Winter Workshop on Nuclear Dynamics La Jolla, 2006

  29. 122 MeV 18O + 150Sm168Yb Newton et al.Nucl.Phys.A483 (1988) n PreScission Multiplicity p a td(x 10-21) 22th Winter Workshop on Nuclear Dynamics La Jolla, 2006

  30. LILITA_N97 for light particle evaporation along trajectories 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 22th Winter Workshop on Nuclear Dynamics La Jolla, 2006

  31. 3D Langevin Eq. (1) Dynamical approach of fission consists into 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 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). 22th Winter Workshop on Nuclear Dynamics La Jolla, 2006

  32. 3D Langevin Eq. (2) q1 = deformation q2 = neck size q3 = mass asymmetry Friction Tensor Inertia Tensor 22th Winter Workshop on Nuclear Dynamics La Jolla, 2006

  33. Time Evolution PES Ecoll - the energy connected with collective degrees of freedom Eint - the energy connected with internal degrees of freedom Eevap- the energy carried away by the evaporated particles 22th Winter Workshop on Nuclear Dynamics La Jolla, 2006

  34. Samples of Trajectories fission events Evaporation residue events scission line - starting point (sphere) - saddle point For each fissioning trajectory it is possible to calculate masses (M1 and M2) and kinetic energies (EK) of fission fragments, fission time (tf), the number of evaporated light prescission particles. 22th Winter Workshop on Nuclear Dynamics La Jolla, 2006

  35. 200 MeV 32S + 100Mo: Fission Rate L = 60 Fission Rate L = 50 L = 40 L = 0-20 t(x 10-21) 22th Winter Workshop on Nuclear Dynamics La Jolla, 2006

  36. 200 MeV 32S + 100Mo Transient time for fission, ranging from 15 to 20 x 10-21 at high angular momentum of the composite system, where fission is relevant 22th Winter Workshop on Nuclear Dynamics La Jolla, 2006

  37. 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 22th Winter Workshop on Nuclear Dynamics La Jolla, 2006

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