Neutron Matter: EOS, Spin and Density Response

Transcription

1 Neutron Matter: EOS, Spin and Density Response LANL : A. Gezerlis, M. Dupuis, S. Reddy, J. Carlson ANL: S. Pieper, R.B. Wiringa How can microscopic theories constrain mean-field theories and properties of neutron-rich matter? Neutron Matter EOS 1- and 2-body distribution functions Spin Response Pairing Gap Density Response (Drops) Energies and Saturation Comparing ab-initio energies with Skyrme Single-Particle Energies Outlook

2 Computational Approach: ψ > = exp [ - H τ ] ψt > GFMC: sum over spin/isospin explicitly Diffusion MC: spin-independent (s-wave interactions) AFDMC: Monte-Carlo sums over spin/isospin Mostly calculations on light nuclei Nuclear Structure High-Momentum Pairs

3 H = A ( 2 v(r ij )! k=1 2m k 2 k ) + i<j v(r) [MeV] Argonne v18 Cosh Cold Atoms r [fm] Caveats: Fixed-node (Upper Bound) Finite System Size!! Neutron Matter Diffusion Monte Carlo ~65 particles (scales like N 3 ) Gap from even/odd staggering Need << 1 MeV accuracy Each calculation (fixed ρ,n, k) takes of order 1/2 day on 1 processors approximately 1 Tflop on Franklin 9% parallel efficiency up to 1 processors

4 Neutron Matter EOS Neutron Matter properties less well-known than Nuclear Matter near equilibrium density Ab Initio calculations can provide guidance to the density functional Equation of State at Low Densities k F [fm -1 ] Lenz Neutron Matter Cold Atoms From JILA E / E FG QMC unitarity k F a Gezerlis & Carlson, PRC 28

5 Lattice Results at Unitarity lattice has no fixed-node error Unitarity Limit.44 N = 14, L = odd N = 14, L = even N = /L Good agreement between lattice, continuum

6 1 Low Density Neutron Matter EOS very well determined.8 Neutron Matter Cold Atoms APR GFMC (PRC 3) E / E FG k f (fm -1 ) Skyrmes typically fit at kf = and ~ 1.3 fm -1, but not between

7 Dean Lee, arxiv:84.35

8 Other Quantities: Momentum Distributions.8 VMC GFMC (k / k F ) 2 kf =.54 fm -1

9 2 Pair Distribution Functions 1.5 VMC GFMC 1 all pairs.5 parallel spins r (fm) kf =.54 fm -1

10 Spin Degrees of Freedom Superfluid pairing gap in strong coupling testable in cold atoms Magnetic Fields or different chemical potentials can break superfluidity Polarized Normal State Thermally populated quasiparticles in superfluid Unpolarized Superfluid Figures from Shin, et al, Nature 459, 689-U1, 28

11 Universal Parameters Superfluid State (P=) χ =.4 (2) Superfluid Energy / Fermi Gas Energy Δ =.5 (3) Gap / Fermi Energy Normal State (P=1) Carlson, et al, PRL 23, Giorgini, et al., PRL 24, Carlson and Reddy, PRL 25,... β =.6 (1) Binding Energy of one spin down in Fermi sea of spin up Lobo, et al, PRL, 26

12 ( E - E ) / E(FG) Cold Atom Dispersion QMC BCS k F a=! ( k / k F ) 2 Shin, Ketterle, Carlson and Reddy 25,...

13 Neutron Matter Pairing Gap Polarization !(r)!(r) T =.3 T =.5!=.5, t c =.25!=.38, t c =.25!=.43, t c =.7 (MIT Expt.)!=.46, t c = r/r Analysis of cold atom experiments gives Δ/Ef =.45 (5). Largest Δ/Ef in any system! Carlson and Reddy, PRL 8 Pairing Gap for Atomic Gas Experimentally confirmed to ~1% Calculations also agree; new AFDMC calculation much closer to DMC

14 RF response Increasing T Shin, Ketterle,... 28

15 Neutron Matter Pairing Gap k F [fm -1 ] Δ / E F BCS-atoms QMC Unitarity BCS-neutrons.2.1 Neutron Matter Cold Atoms k F a Gezerlis and Carlson, PRC 8

16 Δ (MeV) Pairing Gap at Low Densities k F [fm -1 ] BCS Chen [26] Wambach [27] Schulze [28] Schwenk [29] Fabrocini [3] AFDMC [3] QMC k F a

17 Δ / E F New Calculations: Dispersion of Single-Particle States GFMC BCS ( k / k F ) 2 kf =.54 fm -1 Can be a constraint to Mean Field models Spin susceptibility - of interest in neutron stars

18 Density Perturbations Static Susceptibility: response to small long-wavelength potential General response to external potentials Relevant to generalized gradient terms in density functional: PREX Inner Crust of Neutron Stars

19 Neutron Drops Woods-Saxon potential (r=3 fm, a=1.1fm) at various depths also initial work on Harmonic Oscillators Binding Energy Potential E V = -25 V = V = AV18 + UIX (closed) AV18 (open) # Neutrons Small dependence upon three-nucleon force

20 -1 Binding Energies: GFMC vs. present Skyrme BSK8 BSK9 SKM* SIII SLY4 SLY5 SLY6 SLY7 AV18 + UIX AV # of neutrons

21 .14 One-body Densities r (fm) Solid points: GFMC w/ various TNI points w/o error bars: Skyrme Models Generic overbinding/small radius

22 Summary and Outlook Simplest properties of neutron matter at T= rapidly becoming well understood: E/A, Δ Similar systems (cold atoms) tested in experiment Will require more advanced density functionals Many more properties will be available shortly: Spin Susceptibility Generalized Static Resonse,... Toward direct studies of neutron-star matter