Technology to calculate observables Global properties Spectroscopy DFT Solvers Functional form Functional optimization Estimation of theoretical errors DFT Applications, Work Plan Summary Witold Nazarewicz (Tennessee) UNEDF Annual Meeting, June 2009

Year 3 Accomplishments Performance optimization of DFT solvers Augmented Lagrangian Method for constrained calculations adopted. Benchmarking derivative-free algorithms HFODD/HFBTHO benchmarked for odd-A nuclei with LN DFT mass tables with e-e, odd-A, and o-o nuclei on Jaguar 837,220 configurations, 9,060 processors, in a single 12 CPU hour run Odd-even mass staggering benchmarked rms deviation ~250 keV Comparing various ways of calculating odd-A nuclei Simple blocking (EFA) is sufficient for comparison with experiment Effect of odd-T fields small, <100 keV Atomic condensate extension First applications of MADNESS(++) to nuclear physics Single-particle potential with spin-orbit. Very high accuracy and scalability demonstrated HFB extension tested. SLDA calculations on the way

EDF for asymmetric unitary gas Prediction of the Larkin-Ovchinnikov phase Demonstration and validation of 2D SLDA for diluted fermions Extension to asymmetric systems Optimized HFODD Temperature-dependent fission barriers; 2D fission surfaces Isospin mixing Data analysis and visualization MassExplorer package MTEX improved Visualization package for odd-A spectra Output for Visualization in MADNESS in place for nuclear physics

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Unitary Fermi supersolid Phase separation for polarized atomic condensate in a deformed trap

Publications Large-Scale Surveys "Large-Scale Mass Table Calculations," M. Stoitsov, W. Nazarewicz, and N. Schunck, Journal of Modern Physics E 18, 816 (2009). "Odd-even mass differences from self-consistent mean-field theory," G.F. Bertsch, C.A. Bertulani, W. Nazarewicz, N. Schunck, M.V. Stoitsov, Phys. Rev. C 79, (2009). "One-quasiparticle States in the Nuclear Energy Density Functional Theory," N. Schunck, J. Dobaczewski, J. McDonnell, J. More, W. Nazarewicz, J. Sarich, and M. V. Stoitsov, Phys. Rev. C, to be submitted "Structure of even-even nuclei using a mapped collective Hamiltonian and the Gogny interaction," J.-P. Delaroche, M. Girod, J. Libert, H. Goutte, S. Hilaire, S. Peru, N. Pillet, and G.F. Bertsch, in preparation. "Odd-even mass difference and isospin dependent pairing interaction," C.A. Bertulani, Hongfeng Lu, and H. Sagawa, arXiv: Code development "Solution of the Skyrme-Hartree-Fock-Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis. (VI) HFODD (v2.38j): a new version of the program," J. Dobaczewski, W. Satula, B.G. Carlsson, J. Engel, P. Olbratowski, P. Powalowski, M. Sadziak, J. Sarich, N. Schunck, A. Staszczak, M. Stoitsov, M. Zalewski, H. Zdunczuk, Comput. Phys. Comm.; arXiv: "Deformed Coordinate-Space Hartree-Fock-Bogoliubov Approach to Weakly Bound Nuclei and Large Deformations," J.C. Pei, M.V. Stoitsov, G.I. Fann, W. Nazarewicz, N. Schunck and F.R. Xu, Phys. Rev. C 78, (2008).

Concepts "Unitary Fermi Supersolid: The Larkin-Ovchinnikov Phase," A. Bulgac and M.M. Forbes, Phys. Rev. Lett. 101, (2008) "Hartree-Fock-Bogoliubov Theory of Polarized Fermi Systems," G. Bertsch, J. Dobaczewski, W. Nazarewicz, and J. Pei, Phys. Rev. A 79, (2009). "Coordinate-Space Hartree-Fock-Bogoliubov Description of Superfluid Fermi Systems," J.C. Pei, W. Nazarewicz, and M. Stoitsov, EPJA, in press; arXiv: "Isospin mixing in nuclei within the nuclear density functional theory," W. Satula, J. Dobaczewski, W. Nazarewicz, and M. Rafalski, Phys. Rev. Lett., (2009). "Whence the odd-even staggering in nuclear binding?," W.A. Friedman and G.F. Bertsch, Eur. Phys. J. A 41, 109 (2009). Fission "Fission barriers of compound superheavy nuclei," J.C. Pei, W. Nazarewicz, J.A. Sheikh and A.K. Kerman, Phys. Rev. Lett. 102, (2009). "Microscopic description of complex nuclear decay: multimodal fission," A. Staszczak, A. Baran, J. Dobaczewski, and W. Nazarewicz, Phys. Rev. C, in press "Systematic study of fission barriers of excited superheavy nuclei", J.A. Sheikh, W. Nazarewicz, and J.C. Pei, Phys. Rev. C (Rapid Communications), in press. SciDAC-2009 “Towards The Universal Nuclear Energy Density Functional,” M. Stoitsov, J. More, W. Nazarewicz, J. C. Pei, J. Sarich, N. Schunck, A. Staszczak, S. Wild, SciDAC2009 Proceedings, Journal of Physics: Conference Series (JPCS) "Fast Multiresolution Methods for Density Functional Theory in Nuclear Physics", G.I. Fann, J. Pei, R.J. Harrison, J. Jia, J. Hill, M. Ou, W. Nazarewicz, W. A. Shelton, and N. Schunck, SciDAC 2009 Proceedings, Journal of Physics: Conference Series (JPCS)

Year-3 Deliverables Develop Skyrme-DFT multiwavelet code based on MADNESS, portable and scalable on NLCF machines. Implement outgoing boundary conditions. Well on target. A preliminary HFB solver based on the MADNESS has been implemented. Accurate results have been obtained for the bound state eigenvalues and eigenvectors with |E|<|lambda|. For positive energy states, the HFB equation is solved using an energy shift method based on the bound-state scattering kernel. To treat the continuum part of the spectrum, an outgoing boundary condition is being implemented. The prototype HFB- MADNESS code has been implemented on Jaguar Cray XT-5 and Franklin Cray supercomputers, on Macintosh OS X workstation, and on Linux boxes. Threading and message passing optimization in place Benchmark multiwavelet and ASLDA DFT solvers with pairing The 3D solver is practically finished. The spin-orbit, effective mass and Coulomb potential have been incorporated. The most difficult part of the 3D solver involves the treatment of the pairing field and this requires diagonalization of large hermitian matrices. To this end, a parallel diagonalization package capable of running on various has been developed. 2D version of ASLDA (parallelized) for ultracold atomic gas. Interfaced with TDSLDA code Parallelize HFODD and interface HFTHO/HFODD package with optimization codes. Well on target. Parallelization of HFODD is being carried out. HFODD-HFBTHO interface developed by Stoitsov/Schunck for spherical basis. HFBTHO interfaced with optimization codes of ANL-CS group.

Using limited data set, including microscopic input (novel density dependence from DME), perform optimization and error propagation studies of nuclear EDF A  2 function based on the masses and proton radii of 27 spherical nuclei and 36 deformed nuclei has been constructed. The optimization has been carried out using Nelder-Mead (NM) algorithm and a specific algorithm (MFQns). MFQns turned out much more efficient than NM: 85-90% fewer iterations and a lower  2. Optimization requires more than 3000 CPU hours. Preliminary sensitivity analysis shows that most of the parameters of the fit (related to characteristics of the infinite nuclear matter) are independent of one another. Complete survey of odd-even binding energy differences and single-quasiparticle excitations in well-deformed odd-A nuclei The survey of odd-even binding energy differences has been completed and published. The survey of single-quasiproton excitations has been completed. The paper is ready for submission. Develop a B-spline, coordinate space DFT solver for nonlocal functionals The B-spline, coordinate space HFB-AX solver has been extended to high temperatures and condensates. The non-local extension will be finalized by the end of Year-3.

Optimization – HFODD Profiling Broyden routine: storage of N Broyden fields on 3D Gauss-Hermite mesh Temporary array allocation for HFB matrix diagonalization neutronsprotons Safe limit memory/core on Jaguar/Franklin

Plan for Rest of Year 3 HFB-MADNESS developments Finish SLDA tests Boundary conditions for operators (e.g. 1st and 2nd derivatives) for Dirichlet, Neumann and Robin (mixed). Boundary conditions: high order-absorbing boundary layer and layer potential for scattering operator for splitting domain into interior and exterior problems Dynamic load balancing Optimizations on Cray XT-* and finish port IBM BG/L to IBM BG-* HFODD developments Parallelization (PBLAS, ScaLAPACK) Solving issues related to speed, memory and precision Improving Broyden procedure: updating HFB matrix elements instead of fields ALSDA developments Profile current code and investigate stability of results with respect to pairing window Parallelization of the code + proton-neutron extension Finalize the optimization of the standard Skyrme functional. Publish the results including the covariance analysis and error estimates The first optimization of a DME-EDF functional: UNEDF-1 The non-local extension of B-spline solver Developing the full ATDHFB inertia for fission

Plans for Year-4 First applications of DME functional UNEDF-1 Finalizing the implementation of the DME functional including LO, NLO, and N2LO (density and gradient versions of the LDA) in spherical (HFBRAD) and axially deformed (HFBTHO) solvers Pre-optimization of DME functional using regression analysis and genetic algorithm Optimization of DME functional using the MFQns algorithm and “Golden Data Standard” Nuclear-MADNESS-HFB Testing and development Skyrme-MADNESS-HFB Extensions to continuum and resonant states Optimization of high-order boundary conditions for interior and exterior scattering problems in 3-D Optimization on petaflop boxes Implement DME functionals in HFODD (study of time-odd channels) Complete version 1.0 of parallel HFODD core Demonstrate efficiency and scalability of the code First applications: N-dimensional potential energy surface, fission pathways Improve parallel interface to HFODD: Optimistic: it should be a good application of ADLB (“moderately long to long” work units of 1-2 hours, little communication). Realistic: remove the master and have him work like a slave (French revolution spirit) Replace sequential I/O by parallel I/O for HFODD records (used as checkpoints)

DFT Computing Infrastructure Interfacing codes Parallelize solver Load balancing

Analytical Expressions LO, NLO, N2LO VOLUME PART Expressed in terms of Infinite NM IMPLEMENTATION TO FINITE NUCLEI Implemented in HFBRAD fast (seconds per nucleus) fast (seconds per nucleus) spherical nuclei spherical nuclei Implemented in HFBTHO about 10 min per nucleus about 10 min per nucleus spherical & axially deformed spherical & axially deformed + gradients + gradients Optimization DONE: Regression algorithm Using energies (HFBRAD) ADVANCE STAGE: Genetic algorithm Spherical nuclei (HFBRAD) IN PREPARATION: ANL MFQns algorithm HFBTHO) New Mass Table PHYSICS DME FUNCTIONAL OPTIMIZATION roadmap LOLO ANL MFQns algorithm (HFBTHO) Standard Skyrme functional. Limited data set