Progress in ab-initio calculations. The nuclear A-body problem

Transcription

1 60 50 Progress in ab-initio calculations The nuclear A-body problem A G. Hagen et al., Nature Physics 12, 186 (2016) Year In the early decades, the progress was approximately linear in A because the computing power, which increased exponentially according to Moore s law, was applied to exponentially expensive numerical algorithms. In recent years, newgeneration algorithms, which exhibit polynomial scaling in A, have greatly increased the reach.

2 Green s Function Monte Carlo (imaginary-time method) ψ 0 ψ τ = lime τ ( ) = e ˆ ( H ˆ E 0 )τ ( H E 0 )τ ψ V ψ V ψ( 0) = ψ V, ψ( ) = ψ 0 τ = nδτ ψ τ ( )* ( ) = e ˆ trial wave function ( H E 0 )Δτ Quantum Monte Carlo (GFMC) 12 C No-Core Shell Model 14 F, 14 C Faddeev-Yakubovsky Lattice EFT 12 C (Hoyle) Coupled-Cluster Techniques 17 F, 56 Ni Fermionic Molecular Dynamics +,- n ψv

3 GFMC: S. Pieper, ANL 1-2% calculations of A = 6 12 nuclear energies are possible excited states with the same quantum numbers computed

4 11 C +n 11 B +p Results - Longitudinal form factor 12 C structure: Ground-state and Hoyle-state In 1954, Hoyle postulated that a7.65 MeV carbon state. This state plays a crucial role in the hydrogen burning of stars heavier than our sun and in the production of carbon and other elements necessary for life. 11 C +n 11 B +p 8 Be +α Experimental data are well reproduced by theory over the whole range of momentum transfers; Two-body terms become appreciable only for q > 3 fm 1, where they interfere destructively with the onebody contributions bringing theory into closer agreement with experiment. Monday, June 24, F(q) exp ρ 1b ρ 1b+2b ρ ch (r) r (fm) q (fm -1 ) Lovato et al., Phys. Rev. Lett. 111, (2013). Quantum Monte Carlo 4439 ( ) 8 12 C ~ 0p Epelbaum et al., Phys. Rev. Lett. 109, (2012). Lattice EFT

5 Anthropic Principle hhp://en.wikipedia.org/wiki/anthropic_principle The anthropic principle (from Greek anthropos, meaning "human") is the philosophical considera+on that observa+ons of the physical Universe must be compa+ble with the conscious life that observes it. Some proponents of the anthropic principle reason that it explains why the universe has the age and the fundamental physical constants necessary to accommodate conscious life. Anthropic considera+ons in nuclear physics: U. Meissner. hhp://arxiv.org/abs/ The nucleosynthesis of carbon-12 and Hoyle state Non-anthropic scenario Anthropic scenario (fine-tuned Universe)

6 Dean Lee "Viability of Carbon-Based Life as a Func+on of the Light Quark Mass", Phys. Rev. LeH. 110 (2013) "Dependence of the triple-alpha process on the fundamental constants of nature", Eur. Phys. J. A 49 (2013) 82 "Varying the light quark mass: impact on the nuclear force and Big Bang nucleosynthesis", Phys. Rev. D 87 (2013)

7 Ab ini+o calcula+on of the neutron-proton mass difference Science 347, 1452 (2015) The result of the neutron-proton mass spligng as a func+on of quark-mass difference and electromagne+c coupling. In combina+on with astrophysical and cosmological arguments, this figure can be used to determine how different values of these parameters would change the content of the universe. This in turn provides an indica+on of the extent to which these constants of nature must be fine-tuned to yield a universe that resembles ours.

8 ab-initio alpha-alpha scattering Elhatisari et al., Nature 528, 111 (2015)

9 Anomalous Long Lifetime of 14 C Determine the microscopic origin of the suppressed β-decay rate: 3N force 0.29 Maris et al., PRL 106, (2011) GT matrix element N3LO NN only N3LO + 3NF (c D = -0.2) N3LO + 3NF (c D = -2.0) s p sd pf sdg pfh sdgi pfhj sdgik pfhjl configuration space Dimension of matrix solved for 8 lowest states ~ 10 9 Solution took ~ 6 hours on 215,000 cores on Cray XT5 Jaguar at ORNL

10 The frontier in experiment and theory: neutron-rich calcium isotopes LO NLO N2LO N3LO Quantified input Nuclear Forces from χeft NN derived 2000 derived NNN optimized simultaneously 2014 derived 2003 derived G. Hagen et al., Nature Physics 12, 186 (2016) S 2n (MeV) Unique data Experiment MBPT CC CI (KB3G) CI (GXPF1A) Ca neutron number Neutron num Consistency with known data Prediction (a) Extrapolations are tough 38 E( ) (MeV) proton number 20 NNLO sat postdiction prediction neutron number

11 Fusion of Light Nuclei Computational nuclear physics enables us to reach into regimes where experiments and analytic theory are not possible, such as the cores of fission reactors or hot and dense evolving environments such as those found in inertial confinement fusion environment. Ab ini+o theory reduces uncertainty due to conflic+ng data NIF The n- 3 H elastic cross section for 14 MeV neutrons, important for NIF, was not known precisely enough. Delivered evaluated data with required 5% uncertainty and successfully compared to measurements using an Inertial Confinement Facility First measurements of the differential cross sections for the elastic n- 2 H and n- 3 H scattering at 14.1 MeV using an Inertial Confinement Facility, by J.A. Frenje et al., Phys. Rev. Lett. 107, (2011)

12 Configuration interaction techniques light and heavy nuclei detailed spectroscopy quantum correlations (lab-system description) Input: configura+on space + forces NN+NNN interac+ons Matrix elements fihed to experiment Renormaliza+on Method Diagonaliza+on Trunca+on+diagonaliza+on Monte Carlo Observables Direct comparison with experiment Pseudo-data to inform reaction theory and DFT

13 Average one-body Hamiltonian 120 Sn Unbound states Coulomb barrier Discrete (bound) states ε F ε F 0 Surface region n p A i=1 Flat bottom H ˆ 0 = h i, h i = 2 2M 2 i +V i h i φ k ( i) = ε k φ k i ( )

14 ˆ H = t i i Nuclear shell model v ij = (t i +V i ) i, j i i j + $ & & % ' V ) i ) i ( 1 2 v ij i, j i j One-body Hamiltonian Construct basis states with good (J z, T z ) or (J,T) Compute the Hamiltonian matrix Diagonalize Hamiltonian matrix for lowest eigenstates Number of states increases dramatically with particle number Full fp shell for 60 Zn : J z states 5,053,594 J = 0,T = 0 states 81,804, 784 J = 6,T =1 states Can we get around this problem? Effective interactions in truncated spaces (P-included, finite; Q-excluded, infinite) Residual interaction (G-matrix) depends on the configuration space. Effective charges Breaks down around particle drip lines Residual interactioni P + Q =1

15 Microscopic valence-space Shell Model Hamiltonian Energy (MeV) Coupled Cluster Effective Interaction (valence cluster expansion) CCEI Exp. 22 O 3 + USD G.R. Jansen et al., Phys. Rev. Lett. 113, (2014) Energy (MeV) In-medium SRG Effective Interaction O MBPT IM-SRG NN+3N-ind IM-SRG NN+3N-full 4 + (4 + ) ( ) ( ) Expt. S.K. Bogner et al., Phys. Rev. Lett. 113, (2014)

16 Diagonalization Shell Model (medium-mass nuclei reached;dimensions 10 9!) Honma, Otsuka et al., PRC69, (2004) Martinez-Pinedo ENAM 04

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