Transcript Structure of Fission Potential

Fission potential energy surfaces in
ten-dimensional deformation space.
Vitaly Pashkevich
Yuri Pyatkov
Anna Unzhakova
Joint Institute for Nuclear Research.
Dubna, Russia
Moscow Engineering Physics Institute.
Moscow, Russia
St. Petersburg State University.
St. Petersburg, Russia
Introduction
•Fission Potential Energy Surfaces (PES)
Strutinsky shell correction model developed in Dubna was
designed to make high dimensional calculations possible.
•Accurate Shape Families in Ten-Dimensional
Deformation Spaces
Theoretical description of multimodality, exotic and rare fission
processes requires more then five nuclear shape degrees of
freedom.
•No Projection to the Three-Dimensional PES has
been applied
In non-restricted deformation space the influence of magic shellbounded structures leads to the potential energy minima related
to the different fission valleys.
24-28 Sep, 2008
Kazimierz Dolny, Poland
15th Nuclear Physics Workshop "Marie and Pierre Curie“
70 Years of Nuclear Fission
2
Shape Parameterization
Potential energy surfaces are calculated as a liquid drop component with the
shell correction by using the single-particle potential of Woods-Saxon type.
Nuclear shape is parameterized in the coordinate system associated with
Cassini ovaloids with parameters (, n).
Cassini ovaloids – the one-parameter set of curves effective for
approximation of nuclear shapes in fission process.
The value of basic parameter  = 0 corresponds to sphere,  = 1.1 and 1.2
corresponds to the separated fission fragments after the scission point.
R(x) = R0(1 + n n Pn(x))
24-28 Sep, 2008
Kazimierz Dolny, Poland
15th Nuclear Physics Workshop "Marie and Pierre Curie“
70 Years of Nuclear Fission
3
Discussion
P. Möller, D.G. Madland, A.J. Sierk, A. Iwamoto, Nature 409 785 (2001)
24-28 Sep, 2008
Kazimierz Dolny, Poland
15th Nuclear Physics Workshop "Marie and Pierre Curie“
70 Years of Nuclear Fission
4
Fission barriers vs. elongation and asymmetry
PES calculation: symmetrical and two asymmetrical fission valleys
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Kazimierz Dolny, Poland
15th Nuclear Physics Workshop "Marie and Pierre Curie“
70 Years of Nuclear Fission
5
Calculated Binary Fission Valleys (252Cf)
Fission valleys 1 – 5 are
connected with different
dicluster configurations.
1. Cluster radioactivity.
2. Cold binary fission, for
which no neck has yet
developed.
3. and 4. Two different
asymmetrical valleys (B, A).
5. Symmetrical valley.
(Qadrupole moment)
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Kazimierz Dolny, Poland
15th Nuclear Physics Workshop "Marie and Pierre Curie“
70 Years of Nuclear Fission
6
Manifestation of Clustering
The contour map of the conditional distribution P(M | E*). The panels
depict the shapes of the fissioning system following from the PES
calculations ascribed to the two dominant structures.
24-28 Sep, 2008
Kazimierz Dolny, Poland
15th Nuclear Physics Workshop "Marie and Pierre Curie“
70 Years of Nuclear Fission
7
252Cf
Potential Energy Surfaces
Calculation results in
deformation space with
ten parameters.
Cross-sections of the PES
for different values of
asymmetry.
 = (AH - AL)/(AH + AL)
Different curves correspond
to the bottoms of the
potential valleys as a
function of quadrupole
moment Q.
24-28 Sep, 2008
Kazimierz Dolny, Poland
15th Nuclear Physics Workshop "Marie and Pierre Curie“
70 Years of Nuclear Fission
8
Cluster Radioactivity Valley
Potential energy of the ground state
and of the possible configurations at
early stages of elongation was
calculated in the same ten-dimensional
deformation space.
Two valleys starting near the ground
state differ in the main magic cluster
formed inside.
24-28 Sep, 2008
Kazimierz Dolny, Poland
15th Nuclear Physics Workshop "Marie and Pierre Curie“
70 Years of Nuclear Fission
9
Calculated Binary Fission Valleys (246Cm)
The calculation gives us the
bottom points of possible fission
paths with the parameters of
their fine shapes and the
corresponding
deformation
energies.
The results for different shape
families have been obtained
without any changes in the
model or its parameters.
24-28 Sep, 2008
Kazimierz Dolny, Poland
15th Nuclear Physics Workshop "Marie and Pierre Curie“
70 Years of Nuclear Fission
10
Symmetric Compact Configuration
Andrzej Staszczak1,4), Andrzej Baran1,4),
Jacek Dobaczewski2), Witold Nazarewicz2,3,4)
1)
Institute of Physics, Maria Curie-Sklodowska University, Lublin, Poland
2) Institute of Theoretical Physics, Warsaw University, Warsaw, Poland
3) Department of Physics, University of Tennessee, Knoxville, USA
4) Physics Division, Oak Ridge National Laboratory, Oak Ridge, USA
4th Int. Conf. on Fission and Properties of Neutron-Rich Nuclei,
Sanibel Island, 2007
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Kazimierz Dolny, Poland
15th Nuclear Physics Workshop "Marie and Pierre Curie“
70 Years of Nuclear Fission
11
Conclusions
By accurate fission shape families the transition from the
one-center to two- or multi-center shell structures is
described by Strutinsky Shell Correction Method.
Each magic shell-bound configuration produces and
develops an individual sheet of the potential energy
surface. There is no adiabatic path connecting two different
sheets of PES.
24-28 Sep, 2008
Kazimierz Dolny, Poland
15th Nuclear Physics Workshop "Marie and Pierre Curie“
70 Years of Nuclear Fission
12
Dubna Strutinsky Shell Correction Model
V.M. Strutinsky:
Shell effects in nuclear masses and deformation energies.
1967 Nucl. Phys. A 95, p. 420
‘Shells’ in deformed nuclei.
1968 Nucl. Phys. A 122, p. 1
V.V. Pashkevich:
On the asymmetric deformation of fissioning nuclei.
1971 Nucl. Phys. A 169, p. 275
Precision shapes of symmetrically fissioning very heavy nuclei.
1988 Nucl. Phys. A 447, p. 1
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Kazimierz Dolny, Poland
15th Nuclear Physics Workshop "Marie and Pierre Curie“
70 Years of Nuclear Fission
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Overview
R.V. Jolos, Yu.V. Palchikov, V.V. Pashkevich, A.V. Unzhakova,
Reflection asymmetric deformation and clustering in heavy nuclei
Nuovo Cimento, 110 A, 1997
V.V. Pashkevich, A.V. Unzhakova,
The Fission barriers of the neutron-deficient actinides
Conf. on nuclear spectroscopy and nuclear structure, Obninsk, 1997
V.V. Pashkevich, Yu.V. Pyatkov, A.V. Unzhakova, et al.:
1. Manifestation of clustering in the 252Cf(sf) and 249Cf(nth,f)
reactions
Nuclear Physics A624, 1997
2. Dicluster nuclear configurations in low-energy fission of
actinides
Conf. Nuclear Structure and Related Topics, Dubna, 1997
3. Magic numbers from 2 to 82 in low-energy fission of actinides
Conf. Nuclear Shells – 50 years, St. Petersburg, 1999
24-28 Sep, 2008
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15th Nuclear Physics Workshop "Marie and Pierre Curie“
70 Years of Nuclear Fission
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Overview
4. Collinear cluster tripartition of actinides: mass-energy
correlations of fragments
Conf. Clustering phenomena in nuclear physics, St. Petersburg, 2000
5. New indications of collinear tripartition in
modified FOBOS setup
Physics of Atomic Nuclei 66, 2003
252Cf(sf)
studied at the
6. Cluster-molecular scenario of fission of heavy nuclei at low and
middle excitations
Conf. Nuclear Structure and Related Topics, Dubna, 2003
7. Nontrivial manifestation of clustering in fission of heavy nuclei at
low and middle excitations
Physics of Atomic Nuclei 67, 2004
8. Structure of Fission Potential-Energy Surfaces in Ten-Dimensional
Deformation Spaces
4th Int. Conf. on Fission and Properties of Neutron-Rich Nuclei, Sanibel
Island, 2007
24-28 Sep, 2008
Kazimierz Dolny, Poland
15th Nuclear Physics Workshop "Marie and Pierre Curie“
70 Years of Nuclear Fission
15
Thank you for your attention!