Emission of Scission Neutrons: Testing the Sudden Approximation

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Emission of Scission NeutronsTesting the Sudden
Approximation
N. Carjan Centre d'Etudes Nucléaires de
Bordeaux-Gradignan,CNRS/IN2P3 Université
Bordeaux I, B.P. 120, 33175 Gradignan Cedex,
France
M. Rizea National Institute of Physics and
Nuclear Engineering, P.O.Box MG-6, Bucharest,
Romania
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I. Halpern's sudden approximation and our
mathematical formulation of it a short
reminder. More details plus numerical results for
symmetric fission in N. Carjan,P. Talou,O.
Serot Nucl. Phys. A792 (2007)
102 II. Dependence on the mass asymmetry of the
fission fragments N. Carjan,M. Rizea
Nucl. Phys. A805 (2008) 437 III.Beyond
the sudden approximation in reality the
transition takes place in a short but finite time
interval. We need to follow the time evolution of
each neutron state by solving numerically the
two-dimensional time-dependent Schrodinger
equation M. Rizea,N Carjan in Exotic Nuclei and
Nuclear Astrophysics , AIP Conference Proceedings
972 (2008) 526.
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sudden approximation
Halperns cartoon
Equipotentials V0/2 for the two scission
configurations studied in this work
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The formalism of the sudden approximation (1/3)?
The single-particle wave functions for an
axially-symmetric fissioning nucleus have the
general form Where u(?,z) and d(?,z) contain
the spatial dependence of the two components,
spin up and down respectively. ? is the
projection of the total angular momentum along
the symmetry axis and is a good quantum number.
Since we are dealing with symmetric fission, the
parity ? is also a constant of motion. If the
scission is characterized by a sudden change of
nuclear deformation, an eigenstate of the just
before scission hamiltonian will be distributed
over the eigenstates of the immediately after
scission hamiltonian One can notice that
only ?fgt states the same (?,?) values as ?igt
will have non-zero contributions. These states
are mainly bound states but contain also a few
discrete states in the continuum that will
spontaneously decay.
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The formalism of the sudden approximation (2/3)?
Therefore the emission probability of a neutron
that had occupied the state ?igt is In this
way we do not need to use the states in the
continuum that are less precise in the numerical
diagonalization. The Pemis will be referred as
partial probabilities since they only consider
one occupied state. The limit between bound and
unbound states is the barrier for neutron
emission, which is zero if the centrifugal
potential and the energy needed to break a pair
are not taken into account. Summing over all
occupied states one obtains the total number of
scission neutrons per fission event where
vi2 is the ground-state occupation probability of
?igt.
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The formalism of the sudden approximation (3/3)?
We have also calculated the part of the initial
wave function that was emitted Since it gives
access to the spatial distribution of the
emission points Of course, we
have Finally, the occupation probabilities
after the sudden transition are of interest
since they show the degree of excitation in which
the fragments are left
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Typical neutron state favored for emission
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Typical neutron state hindered for emission
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Low density high-? statesthe emitted part
contains only one state (the next to the initial
state)?
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Scission neutron multiplicity calculated with
different assumptions concerning the scission
shapes and the emission barrier heights

• Emission strongly depends on the quantum numbers
  (????) of the state which the neutron occupies
  just before scission
• We predict, on the average, one neutron emitted
  for every 3 fission events

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Distribution of the emission points

• The distribution of the emission points are
  strongly peaked in the region between the nascent
  fragments
• Very few scission neutrons are emitted in the
  direction of the fission fragments

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Fission fragments residual excitation energies
After the sudden transition, the primary
fragments are left in an excited state neutron
states below the Fermi level (-5 MeV) are
depopulated at the expense of neutron states
above.
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Scission Neutron Multiplicity as a function of
Heavy Fragment Mass Case of 235U(nth,f)?
Calculations performed with only ?1/2 states
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Scission Neutron Multiplicity as a function of
Isospin Case of Pu Isotopes
Calculations performed with only symmetric
configurations
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????? Contributions to the Total Scission Neutron
Multiplicity Cases of 236Pu and 256Pu
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Conclusions

• We have presented a dynamical model for the
  emission of scission neutrons that may lead to
  quantities characterising the nuclear
  configuration at scission (minimum neck radius,
  excitation energy of primary fission fragments,
  number of emitted neutrons and their angular
  distribution, etc) that are not available from
  other sources.
• In the sudden approximation the model is
  relatively simple and produces results that are
  easy to interpret microscopically in terms of the
  quantum numbers of the states involved.
• Calculations including the mass asymmetry and
  for a long series of isotopes open new
  perspectives calling for new improved
  measurements of neutrons emitted during nuclear
  fission.
• More realistic calculations using the 2 dim TDSE
  have shown that the sudden approximation is a
  good approximation (20 error) and also gave time
  scales for adiabatic and extreme diabatic
  processes.

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Possible extensions

• Using scission configurations predicted by
  theory Hartree Fock or liquid drop estimates
• Calculating the scission neutron spectrum and
  the final angular distribution
• Study the influence of scission neutrons on the
  emission of prompt neutrons (chronology).