Status report and plans from OSU and MSU

Transcription

1 Status report and plans from OSU and MSU Validated(Nuclear( Interac/ons( +(MSU,(ORNL,UT,ANL,ORNL( fusion( Stellar(burning( Structure(and(Reac/ons:( Light(and(Medium(Nuclei( Ab-ini/o' RGM' CI' Chiral'EFT' Ab-ini/o' Load'balancing' +(MSU,(IU,( Eigensolvers' (((LANL,UT,( Nonlinear'solvers' (((ANL,ORNL( Model'valida/on' Uncertainty'Quan/fica/on' ' ' Op/miza/on' Model'valida/on' Uncertainty'Quan/fica/on' Neutron'drops' ' Medium'nuclei' Nuclear'maHer' Structure(and(Reac/ons:( Heavy(Nuclei( DFT' TDDFT' Load'balancing' Op/miza/on' Model'valida/on' Uncertainty'Quan/fica/on' Eigensolvers' Nonlinear'solvers' Mul/resolu/on'analysis' ' Neutrinos(and( Fundamental(Symmetries( Neutron(Stars( Fission(

2 Role and Goals of the OSU/MSU Groups From the NUCLEI proposal (not exhaustive): Develop low-momentum NN and NNN (and NNNN) interactions and operators as input to ab initio wave function methods and nuclear matter Develop and apply in-medium SRG Develop nuclear matter calculations with controlled theoretical errors as input to microscopic functionals Optimize, validate, and apply next generation EDF s to constrain the form of the functionals based on underlying NN and NNN interactions Develop and test DME-based functionals for neutron drops, validating against ab initio wave function methods

3 Status reports and plans from OSU and MSU k-space evolved SRG 3NF + other 3NF = neutron matter Kai Hebeler (OSU Herzberg Fellow at TU Darmstadt), rjf New hyperspherical harmonics SRG 3NF evolution Kyle Wendt (OSU UT/ORNL) Correcting for a finite oscillator space Andreas Ekström (Oslo/MSU), rjf, Gaute Hagen, Sushant More (OSU), Thomas Papenbrook In-medium SRG progress report + neutron drop next steps Scott Bogner also for Heiko Hergert (OSU Saclay 2nd interview) Towards IM-SRG calculations of infinite matter Titus Morris (MSU)

4 Status reports and plans from OSU and MSU k-space evolved SRG 3NF + other 3NF = neutron matter Kai Hebeler (OSU Herzberg Fellow at TU Darmstadt), rjf New hyperspherical harmonics SRG 3NF evolution Kyle Wendt (OSU UT/ORNL) Correcting for a finite oscillator space Andreas Ekström (Oslo/MSU), rjf, Gaute Hagen, Sushant More (OSU), Thomas Papenbrook In-medium SRG progress report + neutron drop next steps Scott Bogner also for Heiko Hergert (OSU Saclay 2nd interview) Towards IM-SRG calculations of infinite matter Titus Morris (MSU)

5 Current/future directions Motivations for alternative SRG evolution to HO basis -100 n to infinite systems exp. ion of state -130 Independent checks of SRG atic study evolution of induced many-body contributions e initial Address N3LO issues 3N interactions with 3NF (see also next talk!) -120 identified by Roth et al. = exp. ation of evolved Note: 4NF interactions evolution now to oscillator basis O -200 ation to Check finite approximation nuclei, complimentary of to -220 HO evolution -240 e shell induced model, coupled 3NF as modified cluster) c D emax emax and c E coefficients V low k k alternative Calculations generators of uniform k k symmetric/neutron matter Λ nt decoupling patterns (e.g. Vlow k) 2 Alternative generators = k 2 Λ 1 ved efficiency New 3NFof matrix evolution elements Λ 0 ession of many-body forces E [MeV] E [MeV] NN-only NN+3N-ind. 16 O Ω = 20 MeV Ω = 20 MeV Overview RG Summary Extras Flow Results History Eqs. Problem NN+3N-full Two ways to decouple with RG equations emax Similarity RG k 2 k Lower a cutoff Λ i in k, k, e.g., demand dt (k, k ; k 2 )/dλ = 0 λ 0 λ 1 λ 2 Drive the Hamiltonian toward diagonal with flow equation [Wegner; Glazek/Wilson (1990 s)] Anderson et al., PRC 77, (2008)

6 3N interactions momentum basis Three-body Faddeev basis: pq i p i q i ; [(LS)J(ls i )j] JJ z (Tt i )TT z 3 p 2 pq 1 pq 2 pq 3 q p q q p 1 Faddeev bound state equations: i = G 0 2t i P + (1 + t i G 0 ) V i 3N (1 + 2P ) i i pq P p q i = i pq p q j

7 SRG flow equations for NN and 3N forces in momentum basis dh s ds =[ s,h s ] s =[T rel,h s ] H = T + V 12 + V 13 + V 23 + V 123 spectators correspond to delta functions, matrix representation of solution: explicit separation of NN and 3N flow equations H s ill-defined dv ij ds = [[T ij,v ij ],T ij + V ij ], dv 123 = [[T 12,V 12 ],V 13 + V 23 + V 123 ] ds + [[T 13,V 13 ],V 12 + V 23 + V 123 ] + [[T 23,V 23 ],V 12 + V 13 + V 123 ] + [[T rel,v 123 ],H s ] only connected terms remain in dv 123 ds, dangerous delta functions cancel Bogner, Furnstahl, Perry PRC 75, (R) (2007)

8 SRG evolution of 3N interactions in momentum space: Results for the Triton s [fm 4 ] E gs [MeV] N =42 J 12 max =5 550/600 MeV NN-only 8.5 exp [fm 1 ] Hebeler PRC(R) 85, (2012)

9 SRG evolution of 3N interactions in momentum space: Results for the Triton s [fm 4 ] E gs [MeV] N =42 J 12 max =5 550/600 MeV NN-only NN + 3N-induced 8.5 exp [fm 1 ] Hebeler PRC(R) 85, (2012) It works! Invariance of E 3 H within apple 1eV for consistent chiral interactions at N 2 LO gs

10 SRG evolution of 3N interactions in momentum space: Results for the Triton s [fm 4 ] E gs [MeV] N =42 J 12 max =5 550/600 MeV NN-only NN + 3N-induced NN + 3N-full 8.5 exp [fm 1 ] Hebeler PRC(R) 85, (2012) It works! Invariance of E 3 H within apple 1eV for consistent chiral interactions at N 2 LO gs

11 SRG evolution of 3N interactions in momentum space: Results for the Triton s [fm 4 ] E gs [MeV] N =42 J 12 max =5 550/600 MeV NN-only NN + 3N-induced NN + 3N-full 450/500 MeV 600/500 MeV 450/700 MeV 600/700 MeV exp [fm 1 ] Hebeler PRC(R) 85, (2012) It works! Invariance of E 3 H within apple 1eV for consistent chiral interactions at N 2 LO gs

12 Matrix elements of evolved 3-neutron interactions for pure neutron systems only long-range 3N interactions contribute dominant 3NF channel for J =1/2 and positive total parity (EM 500 MeV NN) = 20 = 6 tan = 2 p 3 q 2 = p q2 KH and Furnstahl, PRC 87, (R) (2013) strong renormalization effects of long-range two-pion exchange at very small resolution scales

13 VNN Hartree-Fock Equation of state: Many-body perturbation theory central quantity of interest: energy per particle E/N H( )=T + V NN ( )+V 3N ( )+... E = kinetic energy + + V3N Hartree-Fock VNN V3N VNN V3N V3N 2nd-order VNN VNN V3N V3N V3N rd-order and beyond hard interactions require non-perturbative summation of diagrams with low-momentum interactions much more perturbative inclusion of 3N interaction contributions crucial!

14 15 Non-perturbative Quantum Monte Carlo validation of perturbative calculations E/N [MeV] 10 5 QMC (2010) AFDMC N 2 LO 0.8 fm (2nd order) 0.8 fm (3rd order) 1.2 fm (2nd order) 1.2 fm (3rd order) Gezerlis, Tews, Epelbaum, Gandolfi, KH, Nogga, Schwenk PRL (in press), arxiv: 1303: n [fm -3 ] first QMC calculations based on chiral EFT forces (regulator ranges: fm) perfect agreement for soft interactions

15 Energy per neutron [MeV] First results for neutron matter equation of state (3NF in HF approximation) Entem/Machleidt 500 MeV n=n s 3N-full 3N-induced NN-only [fm 1 ] Energy per neutron [MeV] n=n s N2LO 450/500 MeV 3N-full 3N-induced NN-only [fm 1 ] KH and Furnstahl, PRC 87, (R) (2013) significantly reduced -dependence with induced 3NF contributions variations for 3N-full case consistent with size of neglected higher-order many-body contributions (orange bands)

16 E 3N / E NN Scaling of three-body contributions n=n s, no with initial 3NF 3NF n=n s /2, no with initial 3NF 3NF n=n s, no initial 3NF n=n s /2, no initial 3NF λ [fm 1 ] Hebeler and Furnstahl, PRC 87, (R) (2013) relative size of 3N contribution grows systematically towards smaller no obvious trend with density (may be obscured by cancellations among individual 3NF contributions)

17 First results for neutron matter equation of state Energy per neutron [MeV] λ=2.8 fm -1 λ=2.4 fm -1 λ=2.0 fm -1 λ=1.8 fm -1 3N-induced 3N-full EM 500 MeV NN-only n [fm 3 ] Hebeler and Furnstahl, PRC 87, (R) (2013) significantly reduced -dependence with induced 3NF contributions variations for 3N-full case consistent with size of neglected higher-order many-body contributions

18 Complete N3LO calculation of neutron matter E/N [MeV] EM 500 MeV EGM 450/500 MeV EGM 450/700 MeV NLO lattice (2009) QMC (2010) APR (1998) GCR (2012) E/N [MeV] N 2 LO N 3 LO (only EGM) n [fm -3 ] Tews, Krueger, Hebeler, Schwenk PRL 110, (2013) n [fm -3 ] complete neutron matter calculation at N3LO including NN, 3N and 4N forces includes uncertainties from bare interactions

19 Contributions of many-body forces at N 3 LO NN 3N 4N study chiral power counting in nuclear systems first calculations of N 3 LO 3NF and 4NF contributions to EOS of neutron matter found unnaturally large 3NF contributions, comparable to size of N 2 LO contributions Tews, Krueger, KH, Schwenk PRL 110, (2013) Two-pion-exchange 3N Two-pion one-pion-exchange 3N Pion-ring 3N Two-pion-exchange contact 3N E/N [MeV] EM 500 MeV EGM 450/700 MeV EGM 450/500 MeV n [fm -3 ] n [fm -3 ] n [fm -3 ] n [fm -3 ]

20 Current/future directions application to infinite systems equation of state systematic study of induced many-body contributions, scaling behavior include initial N3LO 3N interactions transformation of evolved interactions to oscillator basis application to finite nuclei, complimentary to HO evolution (no core shell model, coupled cluster) study of various generators different decoupling patterns (e.g. Vlow k) improved efficiency of evolution suppression of many-body forces? k k Λ 2 V low k Λ 1 Λ 0 k 2 k 2 Anderson et al., PRC 77, (2008) explicit calculation of unitary 3N transformation RG evolution of operators study of correlations in nuclear systems factorization

21 Calculation of many-body forces at N 3 LO Low Energy Nuclear Physics International Collaboration J. Golak, R. Skibinski, K. Tolponicki, H. Witala E. Epelbaum, H. Krebs A. Nogga R. Furnstahl S. Binder, A. Calci, K. Hebeler, J. Langhammer, R. Roth P. Maris, J. Vary H. Kamada Goal Calculate matrix elements of 3NF in a partialwave decomposed form which is suitable for different few- and many-body frameworks Challenge Due to the large number of matrix elements, the calculation is extremely expensive. Strategy Develop an efficient code which allows to treat arbitrary local 3N interactions. (Krebs and Hebeler)

22 Advertised opportunities Knock-out reactions and variable resolution calculations consistent investigation of knock-out reactions at low resolution, (deuteron electro-disintegration, many-body systems, factorization issues) operators for electro-weak processes, EMC effect, nuclear scaling MBPT with evolved operators, study of many-body terms scheme dependence of spect. factors, ESPE, SRC,... NPLQCD nuclei at very large pion masses plan: match to an effective field theory compare LQCD to ab initio many-body methods HOBET (pronouned like Hobbit ) Haxton et al., Harmonic-Oscillator-Based Effective Theory key element of SciDAC-3 CalLat project (match to LQCD) natural synergy with IR/UV oscillator basis studies