Non-adiabatic transition of the fissioning nucleus at scission: - - PowerPoint PPT Presentation

Non-adiabatic transition of the fissioning nucleus at scission: stationary and time- dependent approaches

• N. Carjan

Centre d'Etudes Nucléaires de Bordeaux-Gradignan,CNRS/IN2P3 – Université Bordeaux I, B.P. 120, 33175 Gradignan Cedex, France and National Institute of Physics and Nuclear Engineering, P. O. Box MG-6, Bucharest, Romania

• M. Rizea

National Institute of Physics and Nuclear Engineering, P.O.Box MG-6, Bucharest, Romania

Why emission of prompt neutrons and -rays is an important research topic Reflecting the properties of the primary fission fragments, they contribute to the the fundamental understanding of the fission dynamics around scission. In addition they play a major role in applications: development of nuclear reactors and transmutation of used fuel. These applications require a very accurate knowledge of the neutron multiplicity  and of the neutron spectrum N(). To estimate the total energy release the -rays are also needed. For instance, the computer codes (deterministic or stochastic) that simulate the transport of neutrons and gammas in reactors use this information as input to calculate the reactor properties: reactivity, power distribution, heating, etc. Evaluation files (JEFF, ENDF, JENDL,etc) present discrepancies, are incomplete and have no predictive power. To compensate, a big effort has been done to make better fits or better simulations of the fragments’ de-excitation but relatively little was done on a more fundamental level i.e., to understand the emission mechanisms and identify the various energy sources responsible for this emission. My talk is a step into this direction.

1)A microscopic dynamical model of the transition that a fissioning nucleus undergoes at scission will be presented: a) for an infinitely fast transition (the sudden approximation) b) for a diabatic change of the potential at scission (in a short but finite time interval) using the 2-dim time-dependent Schrodinger equation with time-dependent potential. 2)The model allows to estimate: a) the excitation energy of each primary fission fragment as function of its mass (thus avoiding the arbitrary hypotheses employed so far concerning the partition of the excitation energy among the fragments) b) the number of scission neutrons as function of mass asymmetry c) the extra-deformation energy of each primary fragment at scission. Calculations have been performed for 235U(nth ,f). Plans for the near future: use the results to predict the mass asymmetry dependence of prompt neutron and gamma-ray mutiplicities.

I.Halpern's sudden approximation and our mathematical formulation of it 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

&

• Phys. Rev. C82 (2010) 014617

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.

Halpern’s cartoon

‘sudden approximation’

Equipotential lines V0 /2 for the pre and post scission configurations studied in this work

Z [fm]  [fm]

The formalism of the sudden approximation (1/4)

The single-particle wave functions for an axially-symmetric fissioning nucleus have the general form Where u(,z) and d(ρ,z) contain the spatial dependence of the two components, spin up and down respectively. Ω 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

• f

the “just before scission” hamiltonian will be distributed over the eigenstates

• f the

“immediately after scission” hamiltonian: One can notice that only |f> states with the same (,) values as |i> 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 (assuming no centrifugal barrier).

Therefore the emission probability

• f a neutron that had occupied the state |i> is

In this way we do not need to use the states in the continuum that are less precise in the numerical diagonalization. The Pem

i’s

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 vi

2

is the ground-state occupation probability of |i>.

The formalism of the sudden approximation (2/4)

that can be used to test the numerical accuracy.

.

The second source being the extra deformation energy of the nascent fragments Edef

Equipotential lines V0 /2 that define the sudden transition for 3 mass asymmetries

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

Occupation probabilities of the neutron states

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.

Contribution of each Ω to Esc*

Excitation energies

Total excitation energy

Contribution of each Ω to νsc

Neutron multiplicities

60 70 80 90 100 110 120 130 140 150 160 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Neutron Multiplicity Mass Number

Appelin+Nishio NuTOT

• P. Moller and J. R. Nix, Nucl. Phys. A536 (1992) 20

Pairing gap at scission

Neutron levels at scission

Summary and Conclusions

• We have presented a microscopic dynamical model for the

emission of scission neutrons that may lead to quantities characterising the nuclear configuration at scission (minimum neck radius, excitation energy and deformation 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

• f the quantum numbers of the states involved. It predicts that up to

30% (the sudden approximation giving only an upper limit) of the prompt neutrons are scission neutrons.

• More realistic calculations using the 2 dim TDSE have shown that

the sudden approximation is a good approximation (20% error

• nly). They also give the scales of time for adiabatic and extreme

diabatic processes.

Summary and Conclusions (cont.)

• A strong dependence of the pairing gap at scission ∆sc on the

fragment mass ration AL /AH was found with a pronounced minimum at 1.5 which is the experimental mass division of the main fission

• mode. This proves the reliability of the neutron energies and wave

functions used.

• What we usually call ‘prompt neutrons’

contains 2 distinct components well separated in time and having different origins. They are expected to have different behaviours as function of mass

• asymmetry. This opens new perspectives calling for new improved

measurements of neutrons emitted during nuclear fission.

• Estimate the nuclear re-absorption by the fragments of the

unbound neutrons immediately after scission. This correction has to be taken into account when comparing with experimental data. With Takahiro Wada

• Study the influence of the sudden transition at scission on the

evaporation of neutrons from fully accelerated fragments (chronology). Note that TXE=Esc

*

+ ∆Edef can be calculated for the light and heavy fragment separately thus avoiding arbitrary hypotheses. With Vitaly Pashkevich

Ongoing extensions

Extra-deformation energy of the primary fragments

71Ni/165Gd fragmentation