1. 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

2. 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

3. 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

4. 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
Excitation Energy (MeV)
D. J. Hinde et al.,PRC45 (1992)

5. Effect of Viscosity on light particle emission in fission
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

6. 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 = t > td Gf = GBW 1
td= (35 ± 15) x s
D. J. Hinde et al.
1.06
Hyp: Particle evaporation is believed to be correctly treated!
Excitation Energy (MeV)
D. J. Hinde et al.,PRC45 (1992)

7. Modified Statistical ModelGf 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

8. Time Scales from Statistical Mod.
Dynamical fission time scale: tf = tpre + tssc
n tf = (35 ± 15) x s D. J. Hinde et al.
tf = (120 ± 10) x s L. M. Pant et al.
n, p, a tpre = 10 x s tssc = 50 x s J. P. Lestone et al.
A. Saxena et al.
p, a tpre  H. Ikezoe et al.
GDR tpre = x 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.

9. 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

10. 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)

11. What do we need ? …exit strategy1
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

12. 3D Langevin approach + Statistical Model1
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

13. 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

14. Dynamical vs. Statistical

15. 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) Hofman et al., PRC 51 (1995) Diószegi et al., PRC 61 (2000)024613
Shaw et al., PRC 61 (2000)044612
Diószegi et al., PRC 63 (2000)014611

16. 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)
Nadtochy et al., PRC 65 (2002)

17. 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?

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

19. Limit the overlap of presaddle – postsaddle and reaction mechanisms2
Use as many observables as possible to constraint the relevant model parameters 3

20. 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

21. 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, (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.

22. LNL – LCP - FF - ER
WALL
BEAM
ER-trigger
BALL

23. 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

24. What if we adds more observables ?

25. 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

26. 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, (2015)

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

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

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

30. 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.

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

32. 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)
(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

33. 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 ?

34. 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.

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

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

37. 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?

38. 19F + 106Cd: temperature
Predictions of our 3-D model

39. 20Ne + 106Cd: temperature
Predictions of our 3-D model

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

41. 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

43. 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

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

45. Thank you for your kind attention

47. Protons and alpha in the ER channel

48. 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)

49. 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

50. Calculated multiplicities