Dissipation phenomena in nuclear fission

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Dissipation phenomena in nuclear fission

• Intrinsic and collective degrees of freedom.
• Intrinsic motion states of
  individual nucleons in the nuclear potential,
  heating.
• collective motion coordinated
  motion of great part or all nucleons. e.g.
  rotations and vibrations, also the elongation and
  the necking in of a fissioning nucleus

• viscosity , a basic property of nuclear
  matter,
• describes the coupling between intrinsic and
  collective degrees of
• freedom.
• generated by collisions of individual
  molecules with the walls of the
• container in thin gas.
• In a viscous liquid, collisions between
  molecules are very frequent.
• The mean free path of the molecules is small. The
  viscosity is generated by
• friction inside the liquid. Honey is an example
  of a very viscous liquid. 

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Classical relations for the viscosity
Viscous Force F
FµSwx / z
Distance from the wall
z
wx
Plate velocity
S
Surface area of plate
µ TP 1012 dyn s/cm2 6.24x 10-22
MeV s/fm3
dE/dt d(Fx)/dt µSwx2 / z
Energy dissipation
The velocity of liquid in the moving plate
decreases towards the wall
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Two body dissipation Dissipation due to
collision between nucleons when Mean free path is
smaller compared to nuclear dimension ? 1/T2
for nuclear matter
One body dissipation dissipation is due to the
collision of independent non-interacting
particles with a moving wall
(a) Wall dissipation mono-nucleus regime
(b) Window dissipation di-nucleus regime
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• The nucleons fill the nuclear potential up to a
  certain level, the Fermi energy, as each nucleon
  can only occupy one state.
• In an intrinsic excitation of moderate energy,
  only nucleons near the Fermi surface are
  involved. In both processes, collisions with the
  "container" (the nuclear potential) and
  collisions with other nucleons (friction),
  nucleons in deep-lying states cannot be excited.
  Such collisions are "Pauli blocked". This tends
  to reduce the nuclear viscosity.
• With increasing temperature, more and more
  nucleons are involved in intrinsic excitations
  and consequently the viscosity is expected to
  increase. At very low temperatures, the nucleus
  becomes superfluid due to pairing correlations,
  and the viscosity is expected to decrease
  considerably.

• Since fission corresponds to a typical
  large-scale motion process, it has
• been recognised as one of the most promising
  tools to investigate the
• nuclear viscosity.

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• If the breaking of nucleonic pairs
  the transition from adiabatic to damped
  fission
• then adiabatic fission processes manifest
  themselves also in even-odd effects in the mass
  yields and the kinetic energy distributions.
• Experimental evidence of abundance of even-Z
  products in thermal neutron fission of 235U by
  20-50 relative to the average yield. That fine
  structure in the yields is gradually lost if
  going to heavier nuclei.

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• The experimental fission fragment excitation
  energies provide direct information
• about intrinsic excitations and therefore about
  the energy dissipated during the
• fission process.

• On the other hand, Ex is experimentally given by
  the total energy carried by the neutrons and
  gamma rays emitted from the fragments.

• The experimental confirmation thus supports the
  previously mentioned
• conjecture that fragments with low (high) kinetic
  energy result from a
• damped (adiabatic) fission process.

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Dynamical calculations of fission widths
Kramers (1940) showed using FPE that fission
width is reduced due to dissipation
Bohr Wheeler width
Grangé, Jun-Qing and Weidenmuller
Kramers
Here ?ß/2?o
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Transient Time
Overdamped
Underdamped
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Effects of dissipation at deformations beyond the
saddle point

• Dynamics of fission from the ground-state to the
  saddle-point (Fission probability)

• Dynamics of fission beyond the saddle-point

At large deformations, dissipation damps the
fission motion due to the friction force
H.Hofmann and J.R.Nix, Phys. Lett. B122 (1983)
Dissipation enlarges the
saddle-to-scission time tssc
Undamped
3x10-21s
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Dissipation results in long
saddle-to-scission time and small pre-scission
kinetic energy and more elongated shape at
scission.
K.T.R.Davies,A.J.Sierk, and J.R.Nix, Phys. Rev.
C13,2385 (1976)
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This means that translational kinetic energy at
scission which consists of pre-scission kinetic
energy and Coulomb interaction energy at
scission, decreases with increasing viscosity.
This is pertinent for heavy nuclei.
For light nuclei saddle to scission
distance is short and effect of
viscosity on TKE is not seen.
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Pre-equilibrium fission
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DEEP INELASTIC COLLISION
v rel. vel.

• There is a smooth transition from deep inelastic
  to elastic or quasi-elastic (elastic with
  few-particle exchange and energy losses less than
  about 10 MeV) scattering into an angle which is
  slightly smaller than the grazing angle.

DIC
Peaks at PLF and TLF with complete energy damping
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84Kr 165Ho at Elab 600 MeV
Sharp cut off
bl?
Quasi-elastic
DIC
Fusion
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L G Moretto and R P Schmitt, Rep. Prog. Phys.,
Vol. 44, 1981.
Quasi-elastic
Wilczynski
plot
40Ar232Th.
DIC
average I value leading to deep inelastic
collision,lav
µ reduced mass r0 interaction radius
Hierarchy of relaxation times
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28Si232Th at 340 MeV
A.Saxena et al., Nucl Phys. A730, (2004) 299
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TRANSFER INDUCED FISSION Reactions 28Si232Th at
340 MeV
A.Saxena et al. Phys. Rev. C65, 064601 (2002)
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R. Vandenbosch et al. PRL,52 1964(1984)
This result gives Ex(TLF)Ex(PLF) for small
Eloss reaching roughly the 80 of the thermal
equilibrium condition for Eloss150 MeV.
Dynamical calculations
Equal excitation energy creates temp. Imbalance
driving towards temp. equilibration
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Quasi-Fission
64Ni197Au at 418 MeV
J.Velkovska, C.R. Morton, R.L. McGrath, P. Chung,
I. Dioszegi, preprint
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Forwardbackward symmetry seen
Time period extracted for mass relaxation is
much longer than rotational period
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J. Blocki and J. Wilczynski,ACTA PHYSICA POLONICA
B29 (1998) 333
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These values of µ are much larger than those
deduced from the analysis of the mean kinetic
energies of the fission fragments. This
inconsistency of results for two-body dissipation
can be used as an argument supporting the idea
that at such low energies (below 10 MeV/nucleon)
one-body dissipation still plays a dominating
role.
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Nuclear Clocks

• Dissipation lengthens the fission time scale,
  thus an additional
• approach to study nuclear dissipation is to
  measure this time.
• Since 80s- 90s suitable nuclear clocks based
  on the measurement of particle
• and ?-ray multiplicities have been developed
  leading to surprising
• new insights into fission dynamics.
• The measurement of neutron multiplicities prior
  to scission (neutron clock)
• and the measurement of GDR (Giant Dipole
  Resonance) ?-ray multiplicities (GDR clock)
• and charged particles prior scission are the
  most applied nuclear clocks.
• The neutron clock and the GDR clock have been
  extensively described in the
• review articles of Hilscher and Rossner Ann de
  Physic Fr 17 (1992) 471
• and Paul and Thoennessen Ann. Rev. 44 (1994)65,

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Neutron Clock
The basic idea of the neutron clock is to measure
the number of neutrons (or other light
particles) evaporated prior to and post scission.
The pre-scission lifetime can be deduced from
the pre-scission neutron multiplicity according
to the expression



where ?n is the mean partial neutron evaporation
time. ?n can be calculated using the statistical
model.
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232Th and heavier systems
Since the neutron emission time ?n decreases
exponentially with the excitation energy, the
emission time of the last neutron before scission
determines the pre-scission lifetime.
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Separation of pre and post scission neutron

• The kinematical focusing is used to disentangle
  between pre-scission and post-scission
• neutrons. This feature relies on the fact that in
  thermal equilibrium, neutrons are
• evaporated isotropically in the rest frame of the
  emitting source. Thus, in the laboratory
• frame, the neutrons emitted by the compound
  nucleus will follow a homogeneous angular
• distribution, while the angular distribution of
  the neutrons emitted after scission will be
• peaked around the velocity vectors of the fission
  fragments. Moving source analysis
• consisting of three sources (CN2FFS) helps
  disentangle pre and post-scission
• Components.

• The measured pre-scission lifetime is given by

?pre ?formation ?f ?ssc ?acceleration
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Effect of Kinematic focusing
Post-scission
Pre-scission
Low energy fission
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Charged particle Clock
The charged-particle clock leads to larger
uncertainties in the determination of reaction
time scales than the neutron clock. The reason
is that the measurement and interpretation of
charged particle multiplicities is hindered by
the low multiplicity in most reactions, the
anisotropic angular distribution, which makes
more difficult to apply the kinematical
focussing, and the sensitivity of the decay
widths to the deformation of the emitting source
and to the not well defined emission barriers.
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GDR clock

• High energetic ?-rays (E? 5-20 MeV) originating
  from the deexcitation of the
• giant dipole resonance (GDR) during the fission
  process.
• Thoennessen et al. established GDR ?-ray
  multiplicities 50 larger
• than expected by the statistical model.

• Two sources the GDR ?-rays emitted from the
  compound nucleus before scission,
• and the ?-rays emitted from the fission
  fragments.
• Due to the dependence of the energy of the GDR
  ?-rays on the deformation
• and the mass of the emitting system, pre-scission
  GDR ?-rays dominate at energies
• from 7 to 15 MeV, the fission fragment
  component is the strongest at
• the lowest energies
• These different contributions cannot be
  disentangled experimentally and
• must be extracted by comparing with model
  calculations.

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224Th at T1.6 MeV
?-ray
Fission delay
neutron
fission
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Pre-scission neutron negligible after 10-17
s whereas fission is quite probable
M. Morjean, GANIL
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Crystal Blocking

• A positively charged particle blocked by the
  atoms in the crystal row or plane.

• The limits of the sensitivity interval depend on
  the beam energy.
• in the current experiments the lower limit
  10-19 s and the upper limit of 10-14 s.

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Formation Time
In general, these analysis neglect ?formation
assuming that the equilibrium is reached very
rapidly and considering only the process until
the scission point is reached. In fusion-fission
reactions ?formation plays a considerable role
and the pre-scission time scale is affected by
the increase of excitation energy that, due to
dissipation, the system experiences on the way
to scission. Therefore, determining the reaction
times for such processes requires the use of
dynamical codes.
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K.Thomas, R. Davies, A.J.Sierk, Phys. Rev.C31,
915(1986)
Abe
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• A.Saxena et al.,Phys. Rev. C49,932(1994)

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altaBG
agtaBG
ß7x1021 s-1
altaBG
?tr 8x10-21 s
agtaBG
?fo 10-15 10-21 s
?ss 5-30 x10-21 s
?1 1x1021 s-1
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K. Wilczynska et al. Acta Physica Polonica 29,
451 (1999)
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HICOL
Dynamical evolution of colliding nuclei
described by a sequence of shapes of two spheres
connected by a conical neck.
Langevin Eqn can be written as
q collective coordinates
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Friction tensor is governed by exchange of nucleon
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