Is nuclear viscosity dependent on temperature ? Clues from systems of intermediate fissility ………An ultra-short journey on dissipation in fission Emanuele Vardaci Dipartimento di Fisica, Università di Napoli “Federico II” Istituto Nazionale Fisica Nucleare, Sezione di Napoli International Workshop on Nuclear Reactions on Nucleons and Nuclei, Messina ,October 25-26, 2017

E. Vardaci, A. Di Nitto, P. Nadtochy, G. La Rana, D. Quero, A E. Vardaci, A. Di Nitto, P. Nadtochy, G. La Rana, D. Quero, A. Pulcini, F. Davide, Md Ashaduzzaman INFN and Dipartimento di Scienze Fisiche dell’Università di Napoli M. Cinausero, G. Prete Laboratori Nazionali di Legnaro N. Gelli INFN and Dipartimento di Fisica dell’Università di Firenze G.N. Knyazheva, E.M. Kozulin, T.A. Loktev, S. Smirnov Flerov Laboratory of Nuclear Reactions, JINR,141980, Dubna

Fusion-Fission Reactions @10MeVA Light particles and g emission can provide a moving picture of the time evolution Multiplicity is the most sensible observable for time scales

Prologue Pre-scission neutron multiplicity in nuclear fission 16O + 197Au 4 Prologue Statistical Model 3 a / a f n Pre-Scission Neutron Multiplicity Pre-scission neutron multiplicity in nuclear fission 2 1.00 1 1.06 40 60 80 Excitation Energy (MeV) D. J. Hinde et al.,PRC45 (1992)

Effect of Viscosity on light particle emission in fission 0 tpre tssc time Equilibrium Saddle-Point Scission-Point pre-scission emission Excess of pre-scission n, p, a with respect to statistical model predictions Dynamical effect: path from equilibrium to scission slowed-down by the nuclear viscosity

td= (35 ± 15) x 10-21 s Statistical Model 16O + 197Au 4 Gf Gn Ga Gp 3 Statistical Model a / a f n Pre-Scission Neutron Multiplicity 2 1.00 t < td Gf = 0 t > td Gf = GBW 1 td= (35 ± 15) x 10-21 s D. J. Hinde et al. 1.06 40 60 80 Hyp: Particle evaporation is believed to be correctly treated! Excitation Energy (MeV) D. J. Hinde et al.,PRC45 (1992)

Modified Statistical Model Gf t GfBW Fission as a dissipative diffusion process (Kramer, 1940): the presence of nuclear viscosity reduces the fission rate GBW the full BW fission rate is never attained. g  nuclear viscosity parameter g < 1 underdamped g > 1 overdamped b  reduced dissipation coefficient tf  transient buildup time of the flux over the barrier

Time Scales from Statistical Mod. Dynamical fission time scale: tf = tpre + tssc n tf = (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, a tpre = 10 x 10-21 s tssc = 50 x 10-21 s J. P. Lestone et al. A. Saxena et al. p, a tpre  0 H. Ikezoe et al. GDR tpre = 5-500 x 10-21 s Hofman et al, Shaw et al., Thoennessen et al. The determination of the fission time scale and of the average deformation relies on Statistical Model calculations.

Collective Transport Models Energy in collective degrees of freedom Energy in single-particle degrees of freedom Heath Bath Dissipation 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 “heat bath” The time evolution of these collective variables (interaction with the “heat bath” ) describes the fission dynamics. Lagrange equation (deterministic) Transport equations (stochastic): Fokker-Planck and Langevin equations

Prescriptions for Nuclear Dissipation Interaction between individual nucleons and the mean field (gas like behavior) strong dependence on the nuclear shape weak dependence T One-body dissipation (large mean free path) Blocki et al., Ann.Phys.113 (1978)330 Hydrodynamical model, collision between nucleons (liquid like behavior) weak dependence on the nuclear shape strong dependence on T (≈T2) Two-body dissipation (short mean free path) Davies et al., PRC 13 (1976)2385 Both reproduce well the experimental M-TKE Wada et al., PRL 70 , 3358 (1993)

What do we need ? …exit strategy 1 Work-out a realistic model Limit the overlap of presaddle – postsaddle and reaction mechanisms 2 Use as many observables as possible to constraint the relevant model parameters 3 GOAL: To reproduce many observables with one set of input parameters

3D Langevin approach + Statistical Model 1 Work-out a realistic model 3D Langevin approach + Statistical Model LILITA_N11 for light particle evaporation along trajectories Karpov, Nadtochy et al. Phys.Rev. C63, 2001 PS: it is very important to calculate as many observables as possible that are directly comparable to experimental data

3D-Langevin Eq. q1 = deformation q2 = neck size q3 = mass asymmetry Inertia Tensor Friction Tensor Karpov, Nadtochy et al. PRC63, 2001 Neutron, protons and alpha particle can be evaporated along the whole decay path

Dynamical vs. Statistical

Statistical gin < gout gin Viscosity g is treated as a free parameter (adjusted on exp. data) gin < gout Light particle/GDR are emitted mostly in the post-saddle region Viscosity increases as T or T2 Data can be equally well reproduced with g (T) or g (R) Artificial change of g at small and large deformations mimics a temperature dependence Compound Nucleus gin < gout Saddle point gout Energy Fission barrier Scission Ground state Deformation τf τSaddle-Scission Back et al., PRC 60 (1999) 044602 Hofman et al., PRC 51 (1995) 2597 Diószegi et al., PRC 61 (2000)024613 Shaw et al., PRC 61 (2000)044612 Diószegi et al., PRC 63 (2000)014611

Dynamical Compound system can pass the saddle point several times Dissipation is driven by the changing shape No free parameter in the dissipation model Viscosity is higher in the pre-saddle than in the post-saddle Light particle/GDR are emitted mostly in the pre-saddle region DEFORMATION Karpov et al. Phys.Rev. C63 (2001) 054610 Nadtochy et al., PRC 65 (2002) 064615

Dynamical vs. Statistical: opposite views Light particle/GDR are emitted mostly in the post-saddle region Viscosity is higher in the post-saddle than in the pre-saddle region Light particle/GDR are emitted mostly in the pre-saddle region Viscosity is smaller in the post-saddle than in the pre-saddle region Who is right?

Open Questions How long is the fission time scale ? (tf = 5 -500x10-21s) one-body or two-body like? dependent on the shape ? dependent on the temperature ? Is dissipation

Limit the overlap of presaddle – postsaddle and reaction mechanisms 2 Use as many observables as possible to constraint the relevant model parameters 3

Systems of Intermediate Fissility c~0.60 c>0.60 deformation ssc pre t >> More constraint on the model’s parameters (sER, L. p. multiplicities in ER channel) deformation effects on lcp emission sharing of internal and collective energy different than in heavier systems no much data on these systems

Systems Studied System CN Ex (MeV) 32S + 109Ag 141Eu 90 18O + 150Sm 168Yb 93 32S + 100Mo 132Ce 122 32S + 126Te 158Er 121Sb + 27Al 149Gd 135 40Ar + natAg 147,9Tb 128 194 E. Vardaci et al., PRC 92, 034610 (2015) G. La Rana et al., EPJ A16 (2003) 199 E. Vardaci et al., Phys.Atomic Nuclei 66, (2003) 1182 E. Vardaci et al., EPJ A43 (2010) 127 A. Di Nitto et al., EPJ A 47 (2011) 83 E. Vardaci et al., JNPMSRA, 1 (2013) 1-12.

8pLP @ LNL – LCP - FF - ER WALL BEAM ER-trigger BALL

200 MeV 32S + 100Mo: Multiplicity Analysis with Statistical Model A/6 OM RS A/12 OM LDM A/6 OM LDM No delay necessary to reproduce multiplicities and cross sections E. Vardaci et al., EPJ A43 (2010) 127 A. Di Nitto et al., EPJ A 47 (2011) 83

What if we adds more observables ?

200 MeV 32S + 100Mo132Ce A/6 OM RS A/12 OM LDM A/6 OM LDM Protons and alpha particles energy spectra well reproduced in the ER channel A. Di Nitto et al., EPJ A 47 (2011) 83

200 MeV 32S + 100Mo132Ce ER channel Prescission pER aER pPRE aPRE sFF mb sER mb sM a.m.u sTKE MeV TKE MeV Ks=1, a=A/6 1.2 0.56 0.052 0.030 143 793 14.9 7.3 82.0 Exp. 0,90 (0.14) 0,56 (0.09) 0,055 (0,007) 0,038 (0,005) 130 (13) 828 (50) 15.4 (1.1) 11.4 90.9 Reasonable overall good agreement with full one-body dissipation. Statistical model not able to reproduce the whole set of observables E. Vardaci et al., PRC 92, 034610 (2015)

…and now, let’s dig into the details of the model calculations…

Viscosity coefficient is dependent on the shape b assumed independent from temperature.

Fission time distribution Dynamics explains the large time scale found in the statistical model approach

Fission time distribution:multichance Yields as function of time for neutrons The emission of every next neutron requires a time larger than the fission delay.

Fission time distribution:multichance Yields as function of time for different particles at first chance

More work is needed to reproduce the multiplicities in the ER channel. 180 MeV 32S + 126Te158Er pER aER nPRE pPRE aPRE sFF(mb) Ks=1, a=A/9 0.26 0.34 1.77 0.032 0.021 186 Exp. 0,375 (0.033) 0,234 (0.08) 1.7 (0.5) 0,034 (0.005) 0,020 (0.003) 195 (20) C.N. td (zs) tfMAX(zs) <tf> (zs) 158Er 9 50 850 Best overall agreement with full one-body dissipation, as in 132Ce nuclei. More work is needed to reproduce the multiplicities in the ER channel. A. Di Nitto, Ph.D. Thesis

Conclusion on dissipation The Statistical Model approach is inadequate; Dissipation is one-body like; Dissipation is dependent on the shape. Importance of the initial conditions for the evaporation calculations during the shape changes What about the dependence of b on the temperature ?

How is b (T) studied ? Excitation function of the light particles and/or GDR-g ray multiplicities. Comparison with models The few known studies are quite controversial: usually an insufficient set of observables is used and the models are not well constrainted.

An example B.B. Back et al., PRC 60 (1999) 044602

In heavy systems the temperature at scission point TSC is roughly constant, regardless of the Temperature of the CN TCN

Does this occur somewhere on the nuclear chart? In heavy systems the detailed dependence of b from T is lost E* Temperature TCN TSC Observables averaged over a large range of T I would be better if E* Temperature TCN TSC Does this occur somewhere on the nuclear chart?

19F + 106Cd: temperature Predictions of our 3-D model

20Ne + 106Cd: temperature Predictions of our 3-D model

…in systems of intermediate fissility… Predictions of our 3-D model

Experiment performed at LNL 19F + 106Cd  125La 7 days of 19F pulsed beam Elab = 135 and 195 MeV ALPI DT = 1-3ns T= 800ns Experiment performed at LNL

Prescission particle multiplicity PROTONS ALPHA A slight dependence on T would be needed. However, the present preliminary analysis does not include yet the data in the evaporation residues channel

Conclusions The Statistical Model approach is inadequate; Dissipation is one-body like; Dissipation is dependent on the shape. Viscosity is slightly dependent on temperature

Thank you for your kind attention

Protons and alpha in the ER channel

Contraddictory SM results on GDR Probe Smaller viscosity required to fit sER compared to Mn or Mg Viscosity increases as T or T2 Data can be equally well reproduced with g (T) or g (R)

3D-Langevin Eq. Light particle multiplicities are the most sensitive observable for the dissipation strength Fission rate and multiplicities dependence on the dimensionality of the model Strong effects isospin related P.N. Nadotchy, E. Vardaci, A. Di Nitto, A. Brondi, G. La Rana, R. Moro, M. Cinausero, G. Prete, N. Gelli, F. Lucarelli Phys.Lett. B 685 (2010) 258

Calculated multiplicities