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Theoretical Description of the Fission Process

This presentation discusses the theoretical understanding of the fission process, focusing on barriers, fission half-lives, fission dynamics, and cross-sections. It explores the need for effective interactions and microscopic many-body techniques. The talk also covers adiabatic approaches to fission, collective inertia, and the various prescriptions for collective inertia and zero-point energy. Additionally, it examines self-consistent static fission paths calculations and related problems such as heavy-ion fusion. The research goals for the next five years are discussed, along with the challenges and potential applications of fission. The presentation concludes by highlighting the importance of coupling modern microscopic theories with high-performance computing.

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Theoretical Description of the Fission Process

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  1. Theoretical Description of the Fission Process Witold Nazarewicz (Tennessee) 2007 Stewardship Science Academic Alliances Program Symposium February 5-7, 2007, Washington, DC Introduction and motivation Accomplishments and recent examples Summary Theoretical Description of the Fission Process NNSA Grant DE-FG03-03NA00083

  2. Powerful phenomenology exists… • … but no satisfactory microscopic understanding of: • Barriers • Fission half-lives • Fission dynamics • Cross sections • … • What is needed? • Effective interaction (UNEDF) • Microscopic many-body technique (SSAA)

  3. http://www.phys.utk.edu/witek/fission/fission.html

  4. V(q) E q Adiabatic Approaches to Fission WKB: collective inertia (mass parameter) multidimensional space of collective parameters The action has to be minimized by, e.g., the dynamic programming method. It consists of calculating actions along short segments between adjacent, regularly spaced hyperplanes, perpendicular to the q-direction [A. Baran et al., Nucl. Phys. A361, 83 (1981)]

  5. Collective potential V(q) • Universal nuclear energy density functional is yet to be developed • Choice of collective parameters • How to define a barrier? • How to connect valleys? • Dynamical corrections going beyond mean field important • Center of mass • Rotational and vibrational • (zero-point quantum • correction) • Particle number

  6. Collective inertia B(q) and ZPE Various prescriptions for collective inertia and ZPE exist: GOA of the GCMRing 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

  7. Self-consistent Static Fission Paths Calculations A. Staszczak, J. Dobaczewski W. Nazarewicz, in preparation See also L. Bonneau, Phys. Rev. C74, 014301 (2006) See also: A. Warda et al., Phys. Rev. C66, 014310 (2002) and IJMP E13, 169 (2004) Gogny A. Staszczak et al., IJMP E14, 395 (2005) Skyrme

  8. A. Baran et al., nucl-th/0610092,

  9. nucl-th/0612017 A. Staszczak, J. Dobaczewski W. Nazarewicz, in preparation

  10. A. Staszczak, J. Dobaczewski W. Nazarewicz, in preparation

  11. Related problem: heavy-ion fusion • nucleus-nucleus potentials • fusion barriers J. Skalski, Phys.Rev. C 74, 051601 (2006) Coordinate-space Skyrme-Hartree-Fock

  12. Research goals for the next five years • Applications of modern adiabatic and time-dependent theories of LACM • Use modern UNEDF optimized for deformation effects • Develop symmetry restoration schemes for DFT • Increase the number of collective coordinates in GCM, including pairing channel • Develop TDHFB theory of fusion; study the effect of neutron skin • Tests of non-adiabatic approaches • Proper quantum treatment of many-body tunneling • Non adiabatic, properly accounts for level crossings and symmetry breaking effects (collective path strongly influenced by level crossings). HF and ATDHF not adequate • TDHF equations in an inverted potential • Evolution in an imaginary time • The lifetime is expressed by the sum of bounces • Difficulty in solving the periodic mean-field equations (fission bounce equations) • Important role of pairing correlations (restore adiabaticity) • Unclear how to restore broken symmetries bounce trajectory governing fission

  13. What is needed? Computing (today) Efficient symmetry-unrestricted HFB (Kohn-Sham) solver UNEDF fitting: optimization/linear regression, distributed computing Action minimization in many dimensions, fission pathways Performance evaluation for existing codes Computing (tomorrow) Beyond-mean-field dynamics (GCM, projections) Real-time evolution for excited states (at and above the barrier) Imaginary-time evolution at subbarier energies Theory Symmetry restoration in DFT Symmetry-conserving formalism of LACM needs to be developed Can imaginary-time propagation be replaced by variational approach?

  14. 2007 Annual workshop: Joint JUSTIPEN-LACM Meeting on March 5-8, 2007 Joint Institute for Heavy-Ion Research, ORNL

  15. Conclusions • Fission is a fundamental many-body phenomenon that possess the ultimate challenge for theory • Understanding crucial for many areas: • Nuclear structure and reactions (superheavies) • Astrophysics (n-rich fission and fusion, neutrino-induced fission) • Numerous applications (energy, AFC, Stockpile Stewardship…) • … • The light in the end of the tunnel: coupling between modern microscopic many-body theory and high-performance computing

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