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ab initio Hamiltonian approach to nuclear physics and to light-front field theory James P. Vary Iowa State University High Energy Physics in the LHC Era HEP-2010 Valparaiso, Chile January 4-8, 2010 Ab initio nuclear physics - fundamental questions Can we develop a predictive theory from QCD to nuclear reactions 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? DOE investments: ~60 cpu-centuries during calendar „09 Jaguar Franklin Blue Gene/p Atlas QCD Theory of strong interactions Big Bang Nucleosynthesis EFT & Stellar Reactions Chiral Effective Field Theory r,s processes & Supernovae www.unedf.org http://extremecomputing.labworks.org/nuclearphysics/report.stm Fundamental Challenges for a Successful Theory What is the Hamiltonian How to renormalize in a Hamiltonian framework How to solve for non-perturbative observables How to take the continuum limit (IR -> 0, UV-> ) Focii of the both the Nuclear Many-Body and Light-Front QCD communities! Realistic NN & NNN interactions High quality fits to 2- & 3- body data Meson-exchange NN: AV18, CD-Bonn, Nijmegen, . . . Need Improved NNN NNN: Tucson-Melbourne, UIX, IL7, . . . Need Chiral EFT (Idaho) Need Fully derived/coded Consistent NN: N3LO N3LO EW operators NNN: N2LO 4N: predicted & needed for consistent N3LO Inverse Scattering Need JISP40 NN: JISP16 Consistent NNN The Nuclear Many-Body Problem The many-body Schroedinger equation for bound states consists A of 2( Z ) coupled second-order differential equations in 3A coordinates using strong (NN & NNN) and electromagnetic interactions. Successful Ab initio quantum many-body approaches Stochastic approach in coordinate space Greens Function Monte Carlo (GFMC) Hamiltonian matrix in basis function space No Core Shell Model (NCSM) 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 No Core Shell Model A large sparse matrix eigenvalue problem H Trel VNN V3N H i E i i i An n i n 0 Diagonalize m H n • 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,mj,z)] n [a a ]n 0 n 1,2,...,1010 or more! • 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 Experiment-Theory comparison RMS(Total E) 0.739 MeV (2%) RMS(Excit‟n E) 0.336 MeV (1%) GTexp 2.161 vs GTthy 2.198(7) (2%) HH+EFT*: Vaintraub, Barnea & Gazit, PRC79,065501(2009);arXiv0903.1048 Solid - JISP16 (bare) Dotted - Extrap. B 1,0 2,1 2,0 0,1 3,0 1,0 P. Maris, A. Shirokov and J.P. Vary, ArXiv 0911.2281 How good is ab initio theory for predicting large scale collective motion? Quantum rotator 12C ˆ J 2 J(J 1) 2 20MeV EJ 2I 2I E4 20 3.33 E2 6 E4 Experiment 3.17 Theory(N max 10) 3.54 E2 Dimension = 8x109 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 P. Navratil, V.G. Gueorguiev, J. P. Vary, W. E. Ormand and A. Nogga, PRL 99, 042501(2007); ArXiV: nucl-th 0701038. Extensions and work in progress • 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) RMS Eabs (45 states) = 1.5 MeV RMS Eex (32 states) = 0.7 MeV P. Maris, J.P. Vary and A. Shirokov, Phys. Rev. C. 79, 014308(2009), ArXiv:0808.3420 Descriptive Science Predictive Science Proton-Dripping Fluorine-14 First principles quantum solution for yet-to-be-measured unstable nucleus 14F 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 ~ 2x109 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). P. Maris, A. M. Shirokov and J. P. Vary, PRC, Rapid Comm., accepted, nucl-th 0911.2281 Ab initio Nuclear Structure Ab initio Quantum Field Theory Light cone coordinates and generators M P P0 P P1 (P P )(P0 P ) P P KE 2 0 1 0 1 1 Equal time x0 H=P0 x1 P1 Discretized Light Cone Quantization (c1985) Basis Light Front Quantization x f x a f * x a where a satisfy usual (anti-) commutation rules. Furthermore, f x are arbitrary except for conditions : Orthonormal: f x f x d x * ' 3 ' Complete: f x f x' x x' * 3 => Wide range of choices for f a x and our initial choice is f x Ne ik x n,m (, ) Ne ik x f n,m () m ( ) Set of transverse 2D HO modes for n=0 m=0 m=1 m=2 m=3 m=4 J.P. Vary, H. Honkanen, J. Li, P. Maris, S.J. Brodsky, A. Harindranath, G.F. de Teramond, P. Sternberg, E.G. Ng and C. Yang, ArXiv:0905:1411 knm k x f nm - x APBC : L x L 1 i kx k x eL 2L k 1 2 , n 1, m 0 J.P. Vary, H. Honkanen, J. Li, P. Maris, S.J. Brodsky, A. Harindranath, G.F. de Teramond, P. Sternberg, E.G. Ng and C. Yang, ArXiv:0905:1411 Symmetries & Constraints bi B i (m i s i ) J z i ki K i Finite basis regulators 2ni | m i | 1 N m ax i Global Color Singlets (QCD) Light Front Gauge Optional - Fock space cutoffs Hamiltonian for “cavity mode” QCD in the chiral limit Why interesting - cavity modes of AdS/QCD H H 0 H int Massless partons in a 2D harmonic trap solved in basis functions commensurate with the trap : 2M 0 1 H 0 2M 0 PC 2ni | m i | 1 K i xi with defining the confining scale as well as the basis function scale. Initially, we study this toy model of harmonically trapped partons in the chiral limit on the light front. Note Kxi k i and BC' s will be specified. Nucleon radial excitations j M EXP j M BLFQ j EXP M 0 M BLFQ 0 1 1.53 2 1.41 2 1.82 3 1.73 Quantum statistical mechanics of trapped systems in BLFQ: Microcanonical Ensemble (MCE) Develop along the following path: Select the trap shape (transverse 2D HO) Select the basis functions (BLFQ) Enumerate the many-parton basis in unperturbed energy order dictated by the trap - obeying all symmetries Count the number of states in each energy interval that corresponds to the experimental resolution = > state density Evaluate Entropy, Temperature, Pressure, Heat Capacity, Gibbs Free Energy, Helmholtz Free Energy, . . . Note: With interactions, we will remove the trap and examine mass spectra and other observables. Microcanonical Ensemble (MCE) for Trapped Partons Solve the finite many- body problem: H i E i i : and form the density matrix (E) i i i E i E Statistical Mechanical Observables: TrO O Tr Tr (E) Total number of states in MCE E at (E) (E) (E) Density of states at E S(E,V ) k ln((E)) 1 S S E ; P T ; CV T E V E T 1 E 2ni | mi | 1 i xi J.P. Vary, H. Honkanen, J. Li, P. Maris, S.J. Brodsky, A. Harindranath, G.F. de Teramond, P. Sternberg, E.G. Ng and C. Yang, ArXiv:0905:1411 Cavity mode QED with no net charge & K = Nmax Distribution of multi-parton states by Fock-space sector K=Nmax 8 10 12 J.P. Vary, H. Honkanen, J. Li, P. Maris, S.J. Brodsky, A. Harindranath, G.F. de Teramond, P. Sternberg, E.G. Ng and C. Yang, ArXiv:0905:1411 Non-interacting QED cavity mode with zero net charge Photon distribution functions Labels: Nmax = Kmax ~ Q “Weak” coupling: “Strong” coupling: Equal weight to low-lying states Equal weight to all states J.P. Vary, H. Honkanen, J. Li, P. Maris, S.J. Brodsky, A. Harindranath, G.F. de Teramond, P. Sternberg, E.G. Ng and C. Yang, ArXiv:0905:1411 J.P. Vary, H. Honkanen, J. Li, P. Maris, S.J. Brodsky, A. Harindranath, G.F. de Teramond, P. Sternberg, E.G. Ng and C. Yang, ArXiv:0905:1411 without color with color but no restriction with color and space-spin degeneracy Jun Li, PhD Thesis 2009, Iowa State University Elementary vertices in LF gauge QED & QCD QCD Renormalization in BLFQ => Analyze divergences Are matrix elements finite - No => counterterms Are eigenstates convergent as regulators removed? Examine behavior of off-diagonal matrix elements of the vertex for the spin-flip case: As a function of the 2D HO principal quantum number, n. Second order perturbation theory gives log divergence if such a matrix element goes as 1/Sqrt(n+1) J.P. Vary, H. Honkanen, J. Li, P. Maris, S.J. Brodsky, A. Harindranath, G.F. de Teramond, P. Sternberg, E.G. Ng and C. Yang, ArXiv:0905:1411 Cavity mode QED H. Honkanen, et al., to be published M0=me=0.511 Mj=1/2 gQED= [4 lepton & lepton-photon Fock space only k photon m e Schwinger perturbative result Preliminary Next steps Increase basis space size Remove cavity Evaluate form factors QFT Application - Status Progress in line with Ken Wilson’s advice = adopt MBT advances Exact treatment of all symmetries is challenging but doable Important progress in managing IR and UV cutoff dependences Connections with results of AdS/QCD assist intuition Advances in algorithms and computer technology crucial First results with interaction terms in QED - anomalous moments Community effort welcome to advance the field dramatically Collaborations - See Individual Slides Collaborators on BLFQ Avaroth Harindranath, Saha Institute, Kolkota Dipankar Chakarbarti, IIT, Kanpur Asmita Mukherjee, IIT, Mumbai Stan Brodsky, SLAC Guy de Teramond, Costa Rica Usha Kulshreshtha, Daya Kulshreshtha, University of Delhi Pieter Maris, Jun Li, Heli Honkanen, Iowa State University Esmond Ng, Chou Yang, Philip Sternberg, Lawrence Berkeley National Laboratory Thank You!

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ab initio, Phys. Rev, J. Chem. Phys, ground state, Coulomb interaction, Iowa State University, P. Maris, matrix elements, potential method, light nuclei

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posted: | 4/1/2011 |

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