Technology to calculate observables Global properties Spectroscopy DFT Solvers Functional form Functional optimization E

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

2. 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) UNEDF Physics UNEDF CS/AM UNEDF Foreign Collaborator Outside UNEDF UTK/ORNL (Nazarewicz) ANL (Moré, Norris, Sarich) Bruyeres (Goutte) Lublin (Baran, Staszczak)

3. Construction of the functional Perlinska et al., Phys. Rev. C 69, 014316 (2004) p-h density p-p density Most general second order expansion in densities and their derivatives (cf. talk by Bertsch for definitions of densities and currents) pairing functional • 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)

4. Nuclear DFT: works well for differences Stoitsov et al., PRL 98, 132502 (2007) • Global DFT mass calculations: HFB mass formula: m~700keV

5. Bimodal fission in nuclear DFT

6. 41 participants http://orph02.phy.ornl.gov/workshops/lacm08/unedf.html see http://orph02.phy.ornl.gov/workshops/lacm08/UNEDF/database.html

7. Example: Large Scale Mass Table Calculations Science scales with processors M. Stoitsov HFB+LN mass table, HFBTHO INCITE award Dean et al. 17.5M hours Even-Even Nuclei • 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) Jaguar Cray XT4 at ORNL All Nuclei • 9,210 nuclei • 599,265 configurations • Using 3,000 processors - about 25 CPU hours Number of processors > number of nuclei!

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

9. Example: Mass Table eXplorer (http://mtex.110mb.com/) (tools for data analysis/processing)

10. Why us? There is a zoo of nuclear functionals on the market. What makes us believe we can make a breakthrough? • 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

11. Backup

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

13. 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, 040502 (2007) See also: Density-functional theory for fermions in the unitary regime T. Papenbrock Phys. Rev. A72, 041603 (2005) Density functional theory for fermions close to the unitary regime A. Bhattacharyya and T. Papenbrock Phys. Rev. A 74, 041602(R) (2006)

14. One-quasiparticle States

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

16. 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)