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22th Winter Workshop on Nuclear Dynamics

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New Clues on Fission Dynamics from Systems of Intermediate Fissility ... in ring E/F/G Evaporation Residues (4 PPAC- PPAC) CORSET (under construction) ... – PowerPoint PPT presentation

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Title: 22th Winter Workshop on Nuclear Dynamics


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
dellUniversità 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 dellUniversità di Padova, I-35131 Padova,
Italy F. Lucarelli, N. Gelli Istituto Nazionale
di Fisica Nucleare and Dipartimento di Fisica
dellUniversità 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
2
Fusion-Fission Reactions _at_10MeVA
Light particles and g emission can provide a
moving picture of the time evolution
Multiplicity is a sensible observable for time
scales
3
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, a with respect to
statistical model predictions
Equilibrium Saddle-Point
Scission-Point
4
Statistical Model
t lt td Gf 0
t gt td Gf GBW
t (35 15) x 10-21 s
D. J. Hinde et al.
D. J. Hinde et al.,PRC45 (1992)
5
Multiplicity Analysis with SM
  • Inclusion of td (step function)
  • t lt td Gf
    0
  • t gt 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 of af / an and td
  • 0.94 lt af / an lt
    1.12
  • 0 lt td lt
    40 x 10-21 s
  • -Different sets of transmission coefficients
    default, OM, IWBCM

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 lt 1
underdamped g gt 1 overdamped b ? reduced
dissipation coefficient tf ? transient buildup
time of the flux over the barrier
7
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
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
9
but..
LK Langevin and Kramer FP Fokker-Plank KG
Kramers-Grangé SM Statistical Model WF wall
formula.
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 gt 2x1021 s-1)
11
The role of isospin in the dissipation
W. Ye, Eur. Phys. J. A18 (2003) 571
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.

13
Systems of Intermediate Fissility(c ? 0.5 - 0.6)
More constraint on the models parameters (sER,
lp multiplicities in ER channel)
  • deformation effects on lcp emission
  • no much data on these systems

14
8pLP layout
116 Si- CsI Telescopes (E-DE TOF)
126 Si- CsI Telescopes (E-DE PSD)
15
The 8pLP setup
MAX ENERGY Wall up to 64 AMeV Ball up to 34
AMeV
ENERGY THRESHOLDS 0.5 AMeV for p and a
2-3 AMeV for 12C
TRIGGERS Fission Fragments in ring
E/F/G Evaporation Residues (4 PPAC- PPAC) CORSET
(under construction)
16
What observables ?
  • particle FF coincidences
  • particle ER coincidences

8pLP Trigger for ER and FF
17
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
18
200 MeV 32S 100Mo?132Ce Fragment-Fragment
Correlations
E2
E2
E1
E1
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.
20
In-Plane Multiplicity Spectra
12 in-plane correlation angles
21
Out-Of-Plane Multiplicity Spectra
ring G
a in-plane angle b out-of-plane angle
22
Out-Of-Plane Multiplicity Spectra
ring E
a in-plane angle b out-of-plane angle
23
Out-Of-Plane Multiplicity Spectra
ring D
a in-plane angle b out-of-plane angle
24
200 MeV 32S 100Mo?132Ce
25
200 MeV 32S 100Mo?FF
Important to measure Mn
26
particle-ER coincidences
10-1
10-1
exp
exp
Lilita_N97
Lilita_N97
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
40
80
120
0
40
80
120
Detector
Detector
27
particle-ER coincidences PACE (1)
  • The SM code PACE (fission included) reproduces
    the a.d.
  • It overestimates p (by 1.8) and a (by 3.1)
    multiplicities
  • No selection of input parameters improves the
    agreement
  • The energy spectra are generally too hard

28
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?
29
122 MeV 18O 150Sm?168Yb
Newton et al.Nucl.Phys.A483 (1988)
n
PreScission Multiplicity
p
a
td (x 10-21)
30
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
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).
32
3D Langevin Eq. (2)
q1 deformation q2 neck size q3 mass
asymmetry
Friction Tensor
Inertia Tensor
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
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.
35
200 MeV 32S 100Mo Fission Rate
L 60
Fission Rate
L 50
L 40
L 0-20
t (x 10-21)
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
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
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