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Microscopic description of the fission process
Witold Nazarewicz
University of Tennessee
1
Problem
 Need capability to:
 Predict fission probabilities

Neutron-induced cross section


Ground state
Excited states
 Predict prompt fission fragment
products



Mass distribution
Kinetic energy
Excitation energy
 Predict emission from fission
fragments
 Neutron reactions with prompt
fission fragments
Why Focus on a Microscopic Nuclear Theories?
 The nuclear problem is very complex, computationally difficult
 Much of the progress in the past 50 years has been based on
empirical models (most with microscopic degrees of freedom) tuned
to experimental data
• This highly limits our predictive capability
• And it is difficult to estimate the uncertainties
 How can we do Quantification of Margins and Uncertainties?
 The physics of nuclei impacts the programs because nuclei are the
source of the energy and they are important diagnostics
• Fission
• Thermonuclear reactions
• Neutron-induced reactions
With a fundamental picture of nuclei based on the correct microphysics,
we can remove the empiricism inherent today, thereby giving us greater
confidence in the science we deliver to the programs
Powerful phenomenology exists…
… but no satisfactory microscopic understanding of:
•Barriers
•Fission half-lives and mass/energy splits
•Fission dynamics
•Cross sections
•…
What is needed?
•Expertise in nuclear theory
•Collaborative efforts focused on programmatic needs
•Microscopic many-body techniques
•Computational algorithms
•Hardware
Our SSAA Fission Program
http://www.phys.utk.edu/witek/fission/fission.html
Funded 2002
People
Witold Nazarewicz
Arthur Kerman
Jordan McDonnell
Nikolai Nikolov
Nicolas Schunck
University of Tennessee Team
UT/ORNL
UT/MIT
Graduate Student, UT, Krell I. Fellow
Graduate Student, UT
UT/ORNL
poster
poster
External Collaborators
, Team Members
Andrzej Baran
Maria Sklodowska-Curie University, Lublin, Poland
Andrzej Staszczak
Maria Sklodowska-Curie University, Lublin, Poland
Jacek Dobaczewski
University of Warsaw, Warsaw, Poland
Javid Sheikh
University of Kashmir, Srinagar, India
Janusz Skalski
Soltan Institute for Nuclear Studies, Warsaw, Poland
Walid Younes
Daniel Gogny
Erich Ormand
Patrick Talou
Yaron Danon
Other External Collaborators
LLNL
LLNL
LLNL
LANL
Rensselaer Polytechnic Institute
Annual LACM/Fission Workshops
2004 Annual Workshop
Theoretical Description of the Nuclear Large Amplitude Collective Motion (with a focus on fission)
March 17-19, 2004, Joint Institute for Heavy Ion Research, Oak Ridge
Attended by 25 participants
2005 Annual Workshop
The Second International Workshop on the Theoretical Description of the Nuclear Large Amplitude
Collective Motion
March 30 - 31, 2005, Joint Institute for Heavy Ion Research, Oak Ridge.
Attended by 21 participants
2007 Annual Workshop
The Joint JUSTIPEN-LACM Meeting
March 5-8, 2007, Joint Institute for Heavy Ion Research, Oak Ridge
Attended by 60 participants
2008 Annual Workshop
Joint LACM-EFES-JUSTIPEN Meeting
January 23-25, 2008, Joint Institute for Heavy Ion Research, Oak Ridge
Attended by 70 participants
2009 Annual Workshop
The 3rd LACM-EFES-JUSTIPEN Meeting
February 23-25, 2009, Joint Institute for Heavy Ion Research, Oak Ridge
Attended by 90 participants
All meetings involved participants from NNSA/DP Laboratories (LANL, LANL, NNSA), as well as many
students and post-docs.
Recent Scientific Activities
Microscopic description of complex
nuclear decay: Multimodal fission
A. Staszczak, A.Baran, J. Dobaczewski, W.N.,
Phys. Rev. C 80, 014309 (2009)
Microscopic description of spontaneous fission
Two-dimensional total energy
surface for 258Fm in the plane
of two collective coordinates:
elongation, Q20, and reflectionasymmetry, Q30. Dashed lines
show the fission pathways:
symmetric compact fragments
(sCFs) and asymmetric
elongated fragments (aEFs).
Nuclear shapes are shown as
three-dimensional images that
correspond to calculated
nucleon densities.
Two-dimensional total energy
surface for 258Fm in the plane of
two collective coordinates:
elongation, Q20, and necking, Q40.
Summary of fission pathway results
obtained in this study. Nuclei around
252Cf are predicted to fission along the
asymmetric path aEF; those around
262No along the symmetric pathway
sCF. These two regions are separated
by the bimodal symmetric fission (sCF
+ sEF) around 258Fm. In a number of
the Rf, Sg, and Hs nuclei, all three
fission modes are likely (aEF + sCF +
sEF; trimodal fission). In some cases,
labeled by two-tone shading with one
tone dominant, calculations predict
coexistence of two decay scenarios
with a preference for one. Typical
nuclear shapes corresponding to the
calculated nucleon densities are
marked.
Calculated fission half lives of even-even fermium
isotopes, with 242 ≤ A ≤ 260, compared with
experimental data.
A. Staszczak et al. Phys. Rev. C 80, 014309 (2009)
Fission barriers of compound nuclei
•J. Pei, J. Sheikh, WN, A. Kerman, Phys. Rev. Lett. 102, 192501 (2009)
•J. Sheikh, WN, J. Pei, Phys. Rev. C 80, 011302(R) (2009)
•J.D. McDonnell, WN, and J.A. Sheikh, Proc. Fourth International Workshop
On Nuclear Fission And Fission Product Spectroscopy, Cadarache, France,
May, 13-16, 2009. AIP Conference Proceedings 1175, 371, (2009).
Unique HFB solvers made this work possible:
HFBAX: J.C. Pei et al., Phys. Rev. C 78, 064306 (2008)
HFODD: J. Dobaczewski and P. Olbratowski, Comput. Phys. Commun. 158,
158 (2004); ibid.167, 214 (2005)
Systematic Study of Fission Barriers of Excited Superheavy Nuclei
J. Sheikh, WN, J. Pei, Phys. Rev. C 80, 011302(R) (2009)
Focus on:
•Mirror asymmetry and triaxiality at high temperatures
•Systematic analysis of barrier damping
J.D. McDonnell, WN, J.A. Sheikh (Poster)
Potential energy surfaces are calculated for the spontaneous fission of light
actinides with (finite-temperature) HF+BCS theory. The fission path favors
more symmetric scission configurations as excitation energy increases.
Surface Symmetry Energy and NEDF
N. Nikolov et al., Poster by N. Schunck
Surface-symmetry term poorly determined in
standard DFT, but crucial role in neutron-rich
nuclei
Leading terms in the
leptodermous expansion
Mass A ~ 190
Deformation properties of LD
driven by surface-symmetry
term in neutron-rich nuclei !
Fission properties of
neutron-rich U isotopes
affected by poorly
known assym
Actinides
Surface
Surface-symmetry
Curvature
Coulomb (HF)
236U
248U
260U
270U
298U
Research goals, mid-term (1)
Applications of modern adiabatic and time-dependent
theories
•
•
•
•
•
Use modern NEDF optimized for deformation effects
Investigate excitation energy dependence
Perform action minimization on many-dimensional meshes
Develop symmetry restoration schemes for DFT
Increase the number of collective coordinates in GCM, including pairing
channel
• Develop time-dependent framework for fission from excited states
(T>0): ATDHFB and TDHFB
Collective inertia B(q) and ZPE
Various prescriptions for collective inertia and ZPE exist:
GOA of the GCM Ring and P. Schuck, The Nuclear Many-Body Problem, 1980
ATDHF+Cranking Giannoni and Quentin, Phys. Rev. C21, 2060 (1980);
Warda et al., Phys. Rev. C66, 014310 (2002)
Goutte et al., Phys. Rev. C71, 024316 (2005)
A.Baran et al., nucl-th/0610092
HFODD+BCS+Skyrme
Recently, a nice
progress with
full ATDHFB
inertia….
Research goals, mid-term (2)
Tests of non-adiabatic approaches
•Non adiabatic tunneling, properly accounts
for level crossings and symmetry breaking
effects (collective path strongly influenced
by level crossings). ATDHF not adequate
•Evolution in an imaginary time
•The lifetime is expressed by the sum of
bounces
•Difficulty in solving the periodic meanfield equations (fission bounce equations)
•Important role of pairing correlations
(restore adiabaticity)
•Unclear how to restore broken symmetries
J. Skalski: Phys. Rev. C 77, 064610 (2008)
Nuclear fission with mean-field instantons
ATDHFB inertia
bounce trajectory
governing fission
Fission was chosen as a principal research directions at workshop for
computing at the extreme scale, see the summary report:
http://extremecomputing.labworks.org/nuclearphysics/PNNL_18739_onlineversion_opt.pdf
Scientific Grand Challenges in National Security:
the Role of Computing at the Extreme Scale
October 6-8, 2009 · Washington, D.C.
Priority Research Direction: Fission Theory
Scientific and computational challenges
Scientific: Tunneling and time-dependent dynamics of
complex heavy nuclei.
Computational: Implementation of highly nonlinear,
nonlocal, multi-dimensional system of time-dependent
integro-differential equations.
Summary of research direction
Develop efficient solvers for the time-dependent (deterministic
and stochastic) nuclear superfluid density functional theory
(DFT). Solve the multi-dimensional optimization problem for
collective action. Develop algorithms to compute bounce
trajectories in imaginary time.
Uncertainty quantification for complex nuclear processes.
Expected Scientific and Computational Outcomes
Scientific: Microscopic description, based on realistic
internucleon interactions, of nuclear fission process.
Explanation of tunneling motion of a many-body system.
Computational: New fast multiresolution methods for the
nuclear DFT. Implementation of new Importance Sampling
Techniques for the time-dependent stochastic evolution
equations.
Potential impact on Nuclear Physics Problems that
arise in NNSA/ASC?
Validate and predict fission cross sections, fragment mass
and energy distributions.
Provide microscopic guidance (extrapolation capability) for
phenomenological models of fission.
Microscopic input to materials damage simulations.
Neutron and photon spectra for stockpile simulation
validation and nonproliferation.
Slide 23
Microscopic description of nuclear fission process
Drivers: Improved understanding, validate and predict fission cross sections ,
fragment mass and energy distributions; neutron and photon spectra
prediction; Uncertainty Quantification for complex nuclear processes
Applications: Advanced Reactors, Stockpile Stewardship,
Nuclear Forensics
Prediction,
Diagnostics
Validation,
Verification
Present
Peta
Exascale
SciDAC Review, submitted
SUMMARY
•There are fundamental problems in fission that cry to be solved
• Basic science (nuclear structure, nuclear astrophysics)
• Programmatic needs
•Fission is a perfect problem for the extreme scale
• Quantum many-body tunneling is tough
•We are developing a microscopic model that will be predictive
• Fission probabilities
• Properties of fission fragments
• Cross sections
•We want to do Quantification of Margins and Uncertainties
•The future is bright!