1 Technology to calculate observables Global properties Spectroscopy DFT Solvers Functional form Functional optimization Estimation of theoretical errors Using the Functionals Towards Spectroscopic-Quality NEDF DFT Applications Witold Nazarewicz (Tennessee) DOE UNEDF Review, April 2008

UTK/ORNL (Nazarewicz, Schunck, Stoitsov) MSU (Brown), UW (Bertsch), Texas Commerce (Bertulani) ANL (Moré, Sarich) Warsaw, Jyväskylä (Dobaczewski) UTK/ORNL (Nazarewicz, Schunck, Stoitsov) UW (Bulgac) ANL (Moré, Norris, Sarich) ORNL (Fann, Shelton, Roche) Warsaw (Dobaczewski, Magierski) UTK (Pei) UTK/ORNL (Nazarewicz) ANL (Moré, Norris, Sarich) Bruyeres (Goutte) Lublin (Baran, Staszczak) UNEDF Physics UNEDF CS/AM UNEDF Foreign Collaborator Outside UNEDF

Constrained by microscopic theory: ab-initio functionals (cf. talks by Carlson and Furnstahl) Not all terms are equally important. Usually ~12 terms considered Some terms probe specific experimental data Pairing functional poorly determined. Usually 1-2 terms active. Becomes very simple in limiting cases (e.g., unitary limit) pairing functional Construction of the functional Perlinska et al., Phys. Rev. C 69, (2004) Most general second order expansion in densities and their derivatives (cf. talk by Bertsch for definitions of densities and currents) p-h densityp-p density

Nuclear DFT: works well for differences Global DFT mass calculations: HFB mass formula:  m~700keV Stoitsov et al., PRL 98, (2007)

Bimodal fission in nuclear DFT

41 participants see

7 Example: Large Scale Mass Table Calculations Science scales with processors  The SkM* mass table contains 2525 even-even nuclei  A single processor calculates each nucleus 3 times (prolate, oblate, spherical) and records all nuclear characteristics and candidates for blocked calculations in the neighbors  Using 2,525 processors - about 4 CPU hours (1 CPU hour/configuration)  9,210 nuclei  599,265 configurations  Using 3,000 processors - about 25 CPU hours Even-Even Nuclei All Nuclei M. Stoitsov HFB+LN mass table, HFBTHO Number of processors > number of nuclei! Jaguar Cray XT4 at ORNL INCITE award Dean et al. 17.5M hours INCITE award Dean et al. 17.5M hours

Example: Broyden Mixing Collaborative effort: UTK/ORNL, UW, ANL

9 Example: Mass Table eXplorer ( Example: Mass Table eXplorer ( (tools for data analysis/processing)

Solid microscopic foundation  link to ab-initio approaches  limits obeyed (e.g., unitary regime) Unique opportunities provided by coupling to CS/AM Comprehensive phenomenology probing crucial parts of the functional  different observables probing different physics Stringent optimization protocol providing not only the coupling constants but also their uncertainties (theoretical errors) Unprecedented international effort Unique experimental data available (in particular: far from stability; link to FRIB science) Conclusion: we can deliver a well theoretically founded EDF, of spectroscopic quality, for structure and reactions, based on as much as possible ab initio input at this point in time Why us? There is a zoo of nuclear functionals on the market. What makes us believe we can make a breakthrough?

Backup

Building blocks: Nuclear Local Densities and Currents isoscalar (T=0) density isovector (T=1) density isovector spin density isoscalar spin density current density spin-current tensor density kinetic density kinetic spin density + analogous p-p densities and currents

Can dynamics be incorporated directly into the functional? Example: Local Density Functional Theory for Superfluid Fermionic Systems: The Unitary Gas, Aurel Bulgac, Phys. Rev. A 76, (2007) See also: Density-functional theory for fermions in the unitary regime T. Papenbrock Phys. Rev. A72, (2005) Density functional theory for fermions close to the unitary regime A. Bhattacharyya and T. Papenbrock Phys. Rev. A 74, (R) (2006)

One-quasiparticle States

Deformed States Collaborative effort: UTK/ORNL, UW, ANL E SD (the.)-E SD (exp.) [MeV]

Physics/Computer Science Partnerships Fann+, More+, Roche+ Examples: Optimization techniques for petascale nuclear structure DFT codes Solving large-scale systems of nonlinear equations Evaluation of performance and scalability in DFT calculations Evaluation of derivative-free methods for noisy, nonlinear problems 3-D adaptive multi-resolution method for atomic nuclei (Madness)