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ab initio no core shell model status and prospects James P. Vary Iowa State University Computational Forefront in Nuclear Theory: Preparing for FRIB Argonne National Laboratory March 26, 2010

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Ab initio nuclear physics - fundamental questions What controls nuclear saturation? How does the nuclear shell model emerge from the underlying theory? What are the properties of nuclei with extreme neutron/proton ratios? Can nuclei provide precision tests of the fundamental laws of nature? JaguarFranklin Blue Gene/p Atlas

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Nuclear Structure QCD Applications in astrophysics, defense, energy, and medicine Bridging the nuclear physics scales - D. Dean, JUSTIPEN Meeting, February 2009

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List of Priority Research Directions Physics of extreme neutron-rich nuclei and matter Microscopic description of nuclear fission Nuclei as neutrino physics laboratories Reactions that made us - triple process and 12 C( ) 16 O 2 ( 12 C 12 C( 16 O DOE Workshop on Forefront Questions in Nuclear Science and the Role of High Performance Computing, Gaithersburg, MD, January 26-28, 2009 Nuclear Structure and Nuclear Reactions

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http://extremecomputing.labworks.org/nuclearphysics/report.stm

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ab initio nuclear theory - building bridges Standard Model (QCD + Electroweak) NN + NNN interactions & effective EW operators quantum many-body theory describe/predict experimental data UPDATEUPDATE

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Thus, even the Standard Model, incorporating QCD, is an effective theory valid below the Planck scale < 10 19 GeV/c The “bare” NN interaction, usually with derived quantities, is thus an effective interaction valid up to some scale, typically the scale of the known NN phase shifts and Deuteron gs properties ~ 600 MeV/c (3.0 fm -1 ) Effective NN interactions can be further renormalized to lower scales and this can enhance convergence of the many-body applications ~ 300 MeV/c (1.5 fm -1 ) “Consistent” NNN and higher-body forces are those valid to the same scale as their corresponding NN partner, and obtained in the same renormalization scheme. All interactions are “effective” until the ultimate theory unifying all forces in nature is attained.

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Realistic NN & NNN interactions High quality fits to 2- & 3- body data Meson-exchange NN: AV18, CD-Bonn, Nijmegen,... NNN: Tucson-Melbourne, UIX, IL7,... Chiral EFT (Idaho) NN: N3LO NNN: N2LO 4N: predicted & needed for consistent N3LO Inverse Scattering NN: JISP16 Need Improved NNN Need Fully derived/coded N3LO Need JISP40 Consistent NNN Need Consistent EW operators

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Effective Nucleon Interaction (Chiral Perturbation Theory) R. Machleidt, D. R. Entem, nucl-th/0503025 Chiral perturbation theory ( PT) allows for controlled power series expansion Within PT 2 -NNN Low Energy Constants (LEC) are related to the NN-interaction LECs {c i }. Terms suggested within the Chiral Perturbation Theory Regularization is essential, which is obvious within the Harmonic Oscillator wave function basis. CDCD CECE

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The Nuclear Many-Body Problem The many-body Schroedinger equation for bound states consists of 2( ) coupled second-order differential equations in 3A coordinates using strong (NN & NNN) and electromagnetic interactions. Successful ab initio quantum many-body approaches (A > 6) Stochastic approach in coordinate space Greens Function Monte Carlo (GFMC) Hamiltonian matrix in basis function space No Core Shell Model (NCSM) No Core Full Configuration (NCFC) Cluster hierarchy in basis function space Coupled Cluster (CC) Comments All work to preserve and exploit symmetries Extensions of each to scattering/reactions are well-underway They have different advantages and limitations

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NCSM NCFC RGM SpNCS M QFT BLFQ J-matrix NCSM with Core Structure Reactions

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Adopt realistic NN (and NNN) interaction(s) & renormalize as needed - retain induced many-body interactions: Chiral EFT interactions and JISP16 Adopt the 3-D Harmonic Oscillator (HO) for the single-nucleon basis states, , ,… Evaluate the nuclear Hamiltonian, H, in basis space of HO (Slater) determinants (manages the bookkeepping of anti-symmetrization) Diagonalize this sparse many-body H in its “m-scheme” basis where [ =(n,l,j,m j, z )] Evaluate observables and compare with experiment Comments Straightforward but computationally demanding => new algorithms/computers Requires convergence assessments and extrapolation tools Achievable for nuclei up to A=16 (40) today with largest computers available No Core Shell Model A large sparse matrix eigenvalue problem

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P. Navratil, J.P. Vary and B.R. Barrett, Phys. Rev. Lett. 84, 5728(2000); Phys. Rev. C62, 054311(2000) C. Viazminsky and J.P. Vary, J. Math. Phys. 42, 2055 (2001); K. Suzuki and S.Y. Lee, Progr. Theor. Phys. 64, 2091(1980); K. Suzuki, ibid, 68, 246(1982); K. Suzuki and R. Okamoto, ibid, 70, 439(1983) Preserves the symmetries of the full Hamiltonian: Rotational, translational, parity, etc., invariance ab initio NCSM Effective Hamiltonian for A-Particles Lee-Suzuki-Okamoto Method plus Cluster Decomposition Select a finite oscillator basis space (P-space) and evaluate an - body cluster effective Hamiltonian: Guaranteed to provide exact answers as or as.

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n-body cluster approximation, 2 n A H (n) eff n-body operator Two ways of convergence: – For P 1 H (n) eff H – For n A and fixed P: H (n) eff H eff unitary model space dimension Effective Hamiltonian in the NCSM Lee-Suzuki-Okamoto renormalization scheme

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Key equations to solve at the a-body cluster level Solve a cluster eigenvalue problem in a very large but finite basis and retain all the symmetries of the bare Hamiltonian

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A. Negoita, et al, to be published

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JISP16 results with HH method Lee-Suzuki-Okamoto Veff 6 He 6 Li

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NCSM with Chiral NN (N3LO) + NNN (N2LO, C D =-0.2) P. Maris, P. Navratil, J. P. Vary, to be published

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(C D = -0.2)

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P. Maris, P. Navratil, J. P. Vary, to be published Note additional predicted states! Shown as dashed lines (C D = -0.2)

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ab initio NCSM with EFT Interactions Only method capable to apply the EFT NN+NNN interactions to all p-shell nuclei Importance of NNN interactions for describing nuclear structure and transition rates Better determination of the NNN force itself, feedback to EFT (LLNL, OSU, MSU, TRIUMF) Implement Vlowk & SRG renormalizations (Bogner, Furnstahl, Maris, Perry, Schwenk & Vary, NPA 801, 21(2008); ArXiv 0708.3754) Response to external fields - bridges to DFT/DME/EDF (SciDAC/UNEDF) - Axially symmetric quadratic external fields - in progress - Triaxial and spin-dependent external fields - planning process Cold trapped atoms (Stetcu, Barrett, van Kolck & Vary, PRA 76, 063613(2007); ArXiv 0706.4123) and applications to other fields of physics (e.g. quantum field theory) Effective interactions with a core (Lisetsky, Barrett, Navratil, Stetcu, Vary) Nuclear reactions & scattering (Forssen, Navratil, Quaglioni, Shirokov, Mazur, Vary) Extensions and work in progress P. Navratil, V.G. Gueorguiev, J. P. Vary, W. E. Ormand and A. Nogga, PRL 99, 042501(2007); ArXiV: nucl-th 0701038.

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N max - 12 C cross section and the 0 + -> 1 + Gamow-Teller transition A.C.Hayes, P. Navratil, J.P. Vary, PRL 91, 012502 (2003); nucl-th/0305072 First successful description of the GT data requires 3NF N3LO + 3NF(TM’) N3LO only Exp JISP16 Non-local NN interaction from inverse scattering also successful Will be updated with N max = 8 results

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Inelastic - 12 C scattering 86% Isospin weighting: (1-T)B(E2) 96% J. P. Vary, et al, to be published Good spread of T=0 E2 EWSR but still ~8 MeV too high at N max =8

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Collaboration: T. S. H. Lee, S. Nakamura, C. Cockrell, P. Maris, J. P. Vary Long-baseline neutrino mixing experiments: Need A(, ’)A* cross sections since A* -> A + gamma & gamma -> e production => background for the CC signal Plan: Evaluate NCSM static and transition 1-body density matrices and electroweak amplitudes from the SM and, together, evaluate the cross section Expanding the range of applications “Tests of fundamental symmetries” Preliminary

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Ground state non-local 1-body density matrices 7 Li 12 C Chase Cockrell, et al,to be published Note: These peaks become delta functions in the limit of a local approximation Preliminary

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Innovations underway to improve the NCSM Aim: improve treatment of clusters/intruders Initially, all follow the NCFC approch = extrapolations “Realistic” single-particle basis - Woods-Saxon example Control the spurious CM motion with Lagrange multiplier term A. Negoita, ISU PhD thesis project Symplectic No Core Shell Model Add symmetry-adapted many-body basis states Preserve exactly the CM factorization LSU - OSU - ISU collaboration No Core Monte Carlo Shell Model Invokes single particle basis truncation Separate spurious CM motion in same way as CC approach Scales well to larger nuclei U. Tokyo - ISU collaboration

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A. Negoita, ISU Ph D thesis

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12 C Now underway: Halo nuclei - 6 He,...

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How good is ab initio theory for predicting large scale collective motion? Quantum rotator Dimension = 8x10 9 Theory(N max = 4) = 3.27 Theory WS (N max = 4) = 3.36 12 C ħΩ= 25 MeV E2E2 E4E4

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Novel approach Sp-CI: exploiting symmetries of nuclear dynamics Innovative workload balancing techniques & representations of multiple levels of parallelism for ultra-large realistic problems Impact Applications for nuclear science and astrophysics Goals Ab initio calculations of nuclei with unprecedented accuracy using basis-space expansions Current calculations limited to nuclei with A 16 (up to 20 billion basis states with 2-body forces) Progress Scalable CI code for nuclei Sp(3,R)/SU(3)-symmetry vital Challenges/Promises Constructing hybrid Sp-CI code Publicly available peta-scale software for nuclear science Taming the scale explosion in nuclear calculations NSF PetaApps - Louisiana State, Iowa State, Ohio State collaboration

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Proton-Dripping Fluorine-14 First principles quantum solution for yet-to-be-measured unstable nucleus 14 F Apply ab initio microscopic nuclear theory’s predictive power to major test case Robust predictions important for improved energy sources Providing important guidance for DOE-supported experiments Comparison with new experiment will improve theory of strong interactions Dimension of matrix solved for 14 lowest states ~ 2x10 9 Solution takes ~ 2.5 hours on 30,000 cores (Cray XT4 Jaguar at ORNL) Predictions: Binding energy: 72 ± 4 MeV indicating that Fluorine-14 will emit (drip) one proton to produce more stable Oxygen-13. Predicted spectrum (Extrapolation B) for Fluorine-14 which is nearly identical with predicted spectrum of its “mirror” nucleus Boron-14. Experimental data exist only for Boron-14 (far right column).

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Ab initio Nuclear Structure Ab initio Nuclear Reactions

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J-matrix formalism: scattering in the oscillator basis Forward scattering J-matrix 1. Calculate and with NCSM 2. Solve for S-matrix and obtain phase shifts Inverse scattering J-matrix 1. Obtain phase shifts from scattering data 2. Solve for n(p)+nucleus potential, resonance params A.M. Shirokov, A.I. Mazur, J.P. Vary, and E.A. Mazur, Phys. Rev. C. 79, 014610 (2009), arXiv:0806.4018; and references therein n(p)+nucleus applications

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n scattering A. M. Shirokov, A. I. Mazur, J. P. Vary and E. A. Mazur, Phys. Rev. C. 79, 014610 (2009), arXiv 0806.4018

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Basis Light-Front Quantized (BLFQ) Field Theory J. P. Vary, H. Honkanen, Jun Li, P. Maris, S. J. Brodsky, A. Harindranath, G. F. de Teramond, P. Sternberg, E. G. Ng, C. Yang, “ Hamiltonian light-front field theory in a basis function approach ”, Phys. Rev. C 81, 035205 (2010); arXiv nucl-th 0905.1411 H. Honkanen, P. Maris, J. P. Vary and S. Brodsky, to be published First non-perturbative field theory application: Preliminary

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Observation Ab initio nuclear physics maximizes predictive power & represents a theoretical and computational physics challenge Key issue How to achieve the full physics potential of ab initio theory Conclusions We have entered an era of first principles, high precision, nuclear structure and nuclear reaction theory Linking nuclear physics and the cosmos through the Standard Model is well underway

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