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Heavy Nuclei and Density Functional Theory Witek Nazarewicz (MSU/ORNL)

Heavy Nuclei and Density Functional Theory Witek Nazarewicz (MSU/ORNL) Nuclear Theory Session, 2014 LENP Town Meeting. Mean-Field Theory ⇒ Density Functional Theory. Degrees of freedom: nucleonic densities. Nuclear DFT two fermi liquids self-bound superfluid.

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Heavy Nuclei and Density Functional Theory Witek Nazarewicz (MSU/ORNL)

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  1. Heavy Nuclei and Density Functional Theory WitekNazarewicz (MSU/ORNL) Nuclear Theory Session, 2014 LENP Town Meeting

  2. Mean-Field Theory ⇒ Density Functional Theory Degrees of freedom: nucleonic densities • Nuclear DFT • two fermi liquids • self-bound • superfluid • mean-field ⇒ one-body densities • zero-range ⇒ local densities • finite-range ⇒ gradient terms • particle-hole and pairing channels • Has been extremely successful. A broken-symmetry generalized product state does surprisingly good job for nuclei.

  3. Nuclear Density Functional Theory: Large-Scale Surveys The challenge: Universal Energy Density Functional Asymptotic freedom ? DFT FRIB current from B. Sherrill

  4. Continuum-driven correlations Erler et al. Nature 486, 509 (2012) Phys. Scr. T152, 014022 (2013) See extended discussion in Sec. 6 of arXiv:1206.2600: Hartree-Fock-Bogoliubov solution of the pairing Hamiltonian in finite nuclei J. Dobaczewski, WN J. Meng et al., Phys. Rev. C 65, 041302 (2002) S. Fayans et al., Phys. Lett. 491 B, 245 (2000)

  5. From nuclei to neutron stars (a multiscale problem) Gandolfiet al. PRC85, 032801 (2012) J. Erler et al., PRC 87, 044320 (2013) The covariance ellipsoid for the neutron skin Rskin in 208Pb and the radius of a 1.4M⊙ neutron star. The mean values are: R(1.4M⊙ )=12 km and Rskin= 0.17 fm.

  6. Small and Large-Amplitude Collective Motion • New-generation computational frameworks developed • Time-dependent DFT and its extensions • Adiabatic approaches rooted in Collective Schrödinger Equation • Quasi-particle RPA • Applied to HI fusion, fission, coexistence phenomena, collective strength, superfluid modes Heavy Ion fusion Shape coexistence Spontaneous fission TDSLDA applications

  7. Examples: Nuclear Density Functional Theory Traditional (limited) functionals provide quantitative description BE differences Mass table dm=0.581 MeV Fission barriers N

  8. SF lifetimes Fusion cross section E1 strength Isospin mixing

  9. Proliferation of partial, quasi dynamical symmetries in the triangle (Color coded guide) Expansion in O(6) basis (s,t) O(6) PDS (s quantum number for gsb only) SU(3) PDS: g, ground states are pure SU(3). All others highly mixed. SU(3 )PDS SU(3) QDS Arc of b-g degeneracy, regularity

  10. Connections to Other Fields: Cold Atoms Vortex Dynamics Equation of State Bulgac, Magierski, et al., Science, 332, 1288 (2011) http://www.physicstoday.org/resource/1/phtoad/v64/i8/p19_s1 Exotic pairing phases Gezerlis and Carlson, Phys. Rev. C 77, 032801(R) (2008) Carlson, Gandolfi, Gezerlis, PTEP (2012) J. Pei et al., Phys. Rev. A 82, 021603(R) (2010)

  11. JacekDobaczewski, ARIS 2014

  12. DFT and Heavy Nuclei: Prospects and Needs • Develop predictive and quantified nuclear energy density functional rooted in first-principles theory • Unify the fields of nuclear structure and reactions • Provide the microscopic underpinning of observed, and new, (partial-) dynamical symmetries and simple patterns • Develop predictive microscopic model of fusion and fission that will provide the missing data for astrophysics, nuclear security, and energy research • Carry out predictive and quantified calculations of nuclear matrix elements for fundamental symmetry tests in nuclei and for neutrino physics. Explore the role of correlations and currents. • Develop and utilize tools of uncertainty quantification • Enhance the coupling between theory and experiment • Take the full advantage of high performance computing • Needs: • Workforce (students, physicists, and domain scientists) • Large teams, involving physicists, computer scientists, and applied mathematicians • Capability and capability computing enabling many-dimensional treatment of dynamics

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