22 th winter workshop on nuclear dynamics la jolla, 2006 1 new clues on fission dynamics from...
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22th Winter Workshop on Nuclear DynamicsLa Jolla, 2006
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New Clues on Fission Dynamics from Systems of Intermediate
FissilityE.V., A. Brondi, G. La Rana, R. Moro, M.Trotta, A. Ordine, A. Boiano
Istituto Nazionale di Fisica Nucleareand Dipartimento di Scienze Fisiche dell’Università di Napoli, I-80125 Napoli, Italy
M. Cinausero, E. Fioretto, G. Prete, V. Rizzi, D. ShettyIstituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Legnaro
I-36020 Legnaro (Padova), Italy
M. Barbui, D. Fabris, M. Lunardon, S. Moretto, G. ViestiIstituto Nazionale di Fisica Nucleare
and Dipartimento di Fisica dell’Università di Padova, I-35131 Padova, Italy
F. Lucarelli, N. GelliIstituto 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
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Fusion-Fission Reactions @10MeVA
Light particles and emission can provide a moving picture of the time evolution Multiplicity is a sensible
observable for time scales
Multiplicity is a sensible observable for time scales
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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
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16O + 197Au
Excitation Energy (MeV)
40 60 80
4
3
2
1
1.06
1.00
af /an
Neutr
on
Mult
iplic
ity Statistical Model
= (35 ± 15) x 10-21 s
D. J. Hinde et al.
p
n
f
Statistical Model
< d f = 0
> d f = BW
/
D. J. Hinde et al.,PRC45 (1992)
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- Inclusion of d (step function)
< d f = 0
> d f = BW
- Fission Barriers from A. J. Sierk Phys. Rev. C33 (1986)
- an from Toke and Swiatecki, Nucl. Phys. A372 (1981)
Calculations performed for different values of af / a and d:
0.94 < af / a < 1.12
0 < d < 40 x 10-21 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)
- an from Toke and Swiatecki, Nucl. Phys. A372 (1981)
Calculations performed for different values of af / a and d:
0.94 < af / a < 1.12
0 < d < 40 x 10-21 s
-Different sets of transmission coefficients: default, OM, IWBCM
Multiplicity Analysis with SM
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Modified Statistical Model
TE ff /10ln2/ 20
2
121BW
fKramersf f
Kramersff tt /exp1
202/
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 underdamped > 1 overdamped
reduced dissipation coefficient
f transient buildup time of the flux over the barrier
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Time Scales
n f = (35 ± 15) x 10-21 s D. J. Hinde et al.
f = (120 ± 10) x 10-21 s L. M. Pant et al.
n, p, d = 10 x 10-21 s ssc = 50 x 10-21 s J. P. Lestone et al.
p, d 0 H. Ikezoe et al.
GDR d = 30-200 x 10-21 s Shaw et al., Thoennessen et al.
Dynamical fission time scale: f = d + ssc
Dynamical fission time scale: f = d + ssc
The determination of the fission time scale and of the average deformation relies on Statistical Model calculations.
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
Use as many observables as possible to constraint the
relevant model parametersGOAL: To reproduce many observables with one set of input parameters
GOAL: To reproduce many observables with one set of input parameters
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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.
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…but..
Nucleus E* (MeV) s Exp. Observ. ref.200Pb 60-100 3 Mn(pre) Pf L + K178W – 251Es 40-100 2neck 30sci
Mn(pre) Pf L + K
181,185,187Ir 164 5-8 Mn(pre) FP181,185,187Ir 164 22 Mn(pre) WF158Er 70-140 6 Mn(pre) KG + SM158Er 70-140 14 Mn(pre) SML224Th 64 20 ± 6 MGDR KG + SM175Ta 123 20 MGDR KG + SM90Sr - 278110 70-160 0.5 TKE KG + SM141Eu 90 20 Mn(pre), Mp(pre) M(pre)
Mn(ER), Mp(ER) M(ER) fiss
KG + SM
L+K: Langevin and Kramer; FP: Fokker-Plank; KG: Kramers-Grangé; SM: Statistical Model; WF: wall formula.
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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 ( > 2x1021 s-1)
…but..
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The role of isospin in the dissipation
W. Ye, Eur. Phys. J. A18 (2003) 571
N/Z
1.25
1.40
1.52
N/Z
1.49
1.40
1.32
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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.
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FRE More constraint on the model’s parameters(ER, lp multiplicities in ER channel)
~~0.600.60 >0.60>0.60
Systems of Intermediate Fissility 0.5 - 0.6)
sscpre
deformation effects on lcp emission
no much data on these systems
deformation effects on lcp emission
no much data on these systems
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Target
8LP layout
34.0°
116 Si- CsI Telescopes
(E-DE & TOF)126 Si- C
sI Telescopes
(E-DE & PSD)
4 PPACs
ring G
4.7°60cm15cm
FF
ring A
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The 8LP 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 12C
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What observables ?
particle – FF coincidences
particle – ER coincidences
particle – FF coincidences
particle – ER coincidences
8LP + Trigger for ER and FF
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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
Fast Fission
R. Lacey et al., Phys. Rev. C37 (1988) 2540
W. Parker et al., Nucl. Phys. A568 (1994) 633
System CN Ex (MeV) d (10-21 s)
32S + 109Ag 141Eu 90 2718O + 150Sm 168Yb 93 ?32S + 100Mo 132Ce 122 ?121Sb + 27Al 149Gd 135 840Ar + natAg 147,9Tb 128 440Ar + natAg 147,9Tb 194 532S + 100Mo 132Ce 152 0
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200 MeV 32S + 100Mo132Ce: Fragment-Fragment
Correlations
Ring F-G
Ring G-G
E1
E2 E2
E1
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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.
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In-Plane Multiplicity Spectra
12 in-plane correlation angles
CS
F1
F2
43o
78o
102o
120o
137o
156o
204o
223o
241o
258o
282o 299o
Elab (MeV)
d2 M/ddE
(
ster
-1 M
eV-1)
=78° =102° =120°=43°
=156° =204° =223°=137°
=258° =241° =282° =299°
200 MeV 32S + 100Mo132Ce
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ring Gring G
= in-plane angle out-of-plane angle
d2 M/ddE
ster
-1 M
eV-1)
Elab (MeV)
= 35.4°
= 24.9°
= 9.2°
= 335.1°
= 324.6°
= 318.9°
= 41.1°
= 350.8°
200 MeV 32S + 100Mo132Ce
CS
F1
F2
Out-Of-Plane Multiplicity Spectra
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ring Ering E
= in-plane angle out-of-plane angle
Elab (MeV)
= 74.2°
= 66.6°
= 38.8°
= 293.4°
= 285.8°
= 77.0°
= 321.2°
d2 M/ddE
(
ster
-1 M
eV-1)
= 283.0°
200 MeV 32S + 100Mo132Ce
CS
F1
F2
Out-Of-Plane Multiplicity Spectra
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d2 M/ddE
(
ster
-1 M
eV-1)
Elab (MeV)
= 113.0°
= 140.8°
= 247.0°
= 254.5°
= 257.3°
= 102.7°
= 219.2°
= 105.5°
200 MeV 32S + 100Mo132Ce
= in-plane angle out-of-plane angle
ring Dring D
CS
F1
F2
Out-Of-Plane Multiplicity Spectra
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MpER M
ER Mppre M
pre ff [mb] ER [mb]
0,90 (0.14)
0,56 (0.09)
0,055
(0,007)
0,038(0,005)
70 ± 7 576 ± 50
200 MeV 32S + 100Mo132Ce:
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Important to measure Mn
200 MeV 32S + 100MoFF
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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 1.8
3. It well reproduces the energy spectra shapes of p and
A B C D E F G
10-
3
10-
2
10-
4
10-
1
0 40 80 120
Lilita_N97exp
alpha
dM
/d
(ste
r-1)
A B C D E F G
expLilita_N97
10-
2
10-
1
10-
3 0 40 80 120
proton
Detector # Detector #
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dM
/d
(ste
r-1)
10-
2
10-
1
A B C D E F G10-
3 0 40 80 120Detector #
expPACE
expPACE
A B C D E F G10-
4 0 40 80 120Detector #
10-
3
10-
2
10-
1
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
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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 ?
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?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?
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......(?)
In principle, if the charged particle multip. are overestimated, the neutron multiplicity should be underestimated......(?)
Excitation Energy (MeV)
40 60 80
4
3
2
1
Neu
tron
Mult
iplic
ity Statistical
Model
1.06
1.00
af
/an
16O + 197AuThis means that the time delay may be overestimated if only neutrons are measured in the FF channel....
This means that the time delay may be overestimated if only neutrons are measured in the FF channel....
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122 MeV 18O + 150Sm168Yb
0
0.5
1
1.5
2
2.5
3
3.5
0 5 10 15 20 25 30 35 40 45
n
p
Newton et al.Nucl.Phys.A483 (1988)
d (x 10-21)
Pre
Sci
ssio
n M
ult
iplic
ity
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What do we do?
By using a more realistic approach we can try to put this picture together!By using a more realistic approach we can try to put this picture together!
3D Langevin approach + Statistical Model
3D Langevin approach + Statistical Model
Karpov, Nadtochy et al.
Phys.Rev. C63, 2001
LILITA_N97 for light particle evaporation along trajectories
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3D 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
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).
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.
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3D Langevin Eq. (2)
)(tFvdt
dvM
)(2
2
tfTdt
dqm
q
V
dt
qdm
)()()( 2 ttDtFtF ijji
TD 22
Inertia Tensor Friction Tensor
q1 = deformation
q2 = neck size
q3 = mass asymmetry
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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
PES
Time Evolution
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fission events Evaporation residue events
- 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.
Samples of Trajectories
scission line
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200 MeV 32S + 100Mo: Fission Rate
t (x 10-21)
Fis
sion
Rat
e L = 60
L = 50
L = 40
L = 0-20
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ER channel Prescission channel
Mp M Mp M
FF
(mb)
ER
(mb)
Exp.0,91 ± 0.15
0,56 ± 0.09
0,055 ± 0,007
0,038 ± 0,005
70 ± 7576 ±
50
Theor. 0.82 0.58 0.050 0.020 61 597
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
Transient time for fission, ranging from 15 to 20 x 10-21 at high angular momentum of the composite system, where fission is relevant
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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