Microscopic Nuclear Theory. RIA Summer School

Transcription

1 Microscopic Nuclear Theory RIA Summer School August 1-6, 2005 Lawrence Berkeley National Laboratory Lectures by James P. Vary ISU, LLNL, SLAC No-Core Shell Model (NCSM) Applications Overview of the previous 2 lectures and plan for lecture 3 Phenomenology - Extreme Single Particle Shell Model (ESPSM) Theory of Effective Operators Ab-initio No-Core Shell Model (NCSM) Applications with realistic NN interactions Applications with realistic NN + NNN interactions Reactions and Scattering with extensions of the NCSM Conclusions and Outlook 1

2 Cluster Approximation Assume the model-space A-body effective Hamiltonian is a superposition of a-body cluster effective Hamiltonians H " H (1) + H (a) # H CM " $ A% ' # = H (1) 2 & + " $ A% " ' $ a% ' # a &# 2& A ( V ) H i1i 2i 3...i a CM i 1 <i 2 <i 3 <... i a V a = e " S a H # a,ae S a " h i a $ i Ab-initio no-core shell model (NCSM) results a = 2 for 2 < A < 16, 47, 48, 49 a = 3 for 3 < A < 16 Results in a harmonic oscillator basis space P A characterized by: h! N m = $ (2n i + l i ) % N min + N max i"# P controls length scale of basis functions ( box ) Results compare well with VMC and GFMC results controls momentum scale limit Special thanks to Petr Navratil and Andrey Shirokov for many results shown below 2

3 NN Interactions featured here with NCSM Traditional meson-exchange theory (Nijmegen X, CD Bonn X, AVX, etc.,) Effective field theory with roots in QCD (EFT X, Idaho X, N X LO, etc.,) Renormalization group reduced bare NN interactions (V-lowk X) Off-shell variations of bare NN interactions (INOY-X, etc.,) Inverse scattering theory (ISTP, JISPX, etc.,) NNN Interactions featured here with NCSM Tucson-Melbourne prime (TM ) EFT at order N 2 LO (N 2 LO) Development of high precision nuclear Hamiltonian Nuclear Stand ard Model Major role for RIA experiments and theory Climb the walls of the valley of stability! Test of convergence and comparison with other methods All other methods give same result E gs = MeV N max 3

4 N max =2 N max =14 N max =0 N max =14 E gs = MeV N max =2 E gs = MeV N max =2 4

5 Theory Experiment 5

6 NCSM calculations with the EFT N 3 LO NN interaction Accurate NN potential at fourth order of chiral-perturbation theory (N 3 LO) D. R. Entem and R. Machleidt, Phys. Rev. C 68, (R ) (2003) N 3 LO Exp 3 H 7.85 MeV 8.48 MeV 4 He 25.35(5) MeV MeV 6 Li 28.5(5) MeV MeV Converged 6 Li excitation energies Correct level ordering, level spacing not right NCSM calculations with the EFT N 3 LO NN interaction: 6 Li binding energy convergence 6

7 NCSM calculations with the EFT N 3 LO NN interaction: Convergence of 6 Li excitation energies Difficult convergence of the binding energy Good convergence of the excitation energies 6 Li quadrupole moment EFT N 3 LO NN potential Exp e fm 2 Theory extraploted NCSM: Good convergence with N max 7

8 p-shell nuclei with realistic NN forces Correct level ordering for light p-shell nuclei Old evaluation NPA490,1(1988) No 1/2-2 and 3/2-2, 7/2-2 reversed New evaluation NPA708,3(2002) introduces 1/2-2 and orders the states as in calculation Binding energy 35.5(5) MeV Convergence of excitation energies Realistic NN interactions provide reasonable description of nuclear structure 10 B using N 3 LO NN potential Clearly, ground state is incorrectly predicted In EFT, three-nucleon interaction appears already at N 2 LO Should be included in the Hamiltonian c 1,c 3,c 4 parameters of the two-pion term should be the same as those used in the N 3 LO NN potential c 1 =-0.81, c 3 =-3.2, c 4 = 5.4 Binding energy: 56.3(2.0) MeV from Theory MeV from Experiment 8

9 16 O ground and excited and 3-0 states Ground state changes structure 0hΩ less than 50%, large 2hΩ and 4hΩ components Energy consistent with the UMOA result Excited 3-0 state dominated by 1hΩ; follows the ground state Excited state 2hΩ dominated; stable The 4hΩ dominated state still higher in the 8hΩ model space 9

10 Binding Energy of 16 O (MeV( MeV) Experiment CD-Bonn 2000 AV8 N3LO INOY / /- 3 +/- 5 +/- 5 +/- 3 Again - see role for NNN interactions Convergence for 3 H with a real three-body interaction ] V e M [ E E [MeV] Tucson-Melbourne force 3 H AV18 Needed to reproduce experimental binding energy NCSM AV18 +TM'(81) Faddeev AV18 exact calculation AV18+TM'(81) exact N max Paves the way for including the V3b in the NCSM p-shell calculations 10

11 Neutrino scattering on 12 C Exclusive cross section & transistions Extremely sensitive to the spin-orbit interaction strength B(GT) (B(M1)) - στ, No spin-orbit and in different SU(4) irreps no transition 12 C B(M1; > 1 + 1) 12 C ground state 8 nucleons in p 3/2 Transition underestimated by a factor of six N.B. NCSM - no fit, no free parameters V 2b up to 6hΩ - saturation Underestimates by a factor of 2-3 V 2b +V 3b up to 4hΩ Significant improvement Different processes dominated by different Q Correlation with M1 transverse form factor B(M1) Exp AV8'+TM'(99) CD-Bonn AV8' AV8' AV8'+TM (99) Exp B(GT) CD-Bonn AV8'+TM (99) Exp (< ν e,e - ) ±0.3±0.9 (< ν!,! - ) ±0.08±0.1!-capture ±0.4 Nmax V 3b increases the strength of the spin-orbit force EFT N 2 LO three-nucleon interaction Two-pion exchange term Used in standard Three Nucleon Interaction (TNI) models Fujita-Miyazawa Tucson-Melbourne Urbana Illinois Low-energy constants c 1, c 3, c 4 Determined by the corresponding EFT NN interaction Consistent NN & TNI One-pion exchange plus contact term Low-energy constant c D Must be determined from experiment Contact term Low-energy constant c E Must be determined from experiment A regulator appears in all terms Depends on cutoff parameter Λ Taken consistently from that used in the corresponding EFT NN interaction exp["(q 2 /# 2 ) 2 ] 11

12 Determination of the c D and c E low-energy constants Fit the 3 H and 4 He binding energies Suggested and done by A. Nogga Two solutions 3NF-A c D =-1.11 c E = NF-B c D =8.14 c E =-2.02 Regulator depending on Jacobi coordinates Present work: Two-pion term local in coordinate space Change regulator: depending on momentum transfer Need to re-fit c D and c E A=3 done 4 He under way Presented results 3NFA : c D =-1.11, c E = NFB : c D =8.14, c E = NFA and 3NFB dominated by different terms 3NFA two-pion term dominant 3NFB one-pion term dominant Contact term repulsive in both cases Important for saturation properties exp["((p 2 + q 2 ) /# 2 ) 2 ] exp["(q 2 /# 2 ) 2 ] c E c D = "1.09 = "0.07 = 0.25 = "0.69 = "0.88 = B using N 3 LO NN plus consistent N 2 LO TNI N 2 LO TNI 3NF-A dominated by twopion exchange term Results close to the TM Smaller radius Larger binding energy E B =68.36 MeV N 2 LO TNI 3NF-B dominated by onepion exchange plus contact term Visible difference in particular for higher-lying states Both cure the gs spin problem! Reasonable radius No overbinding E B =63.14 MeV 6hΩ needed to check convergence of spectra Calculation to be re-done after proper fitting to 4 He Both 3NF-A and 3NF-B resolve the 10 B ground state spin problem Similarly like TM,, Illinois 3NF, but unlike Urbana IX 12

13 ab initio NCSM wave functions NN only at a=2 level + corrections for long range tails currently being used to investigate problems relevant to nucleosynthesis by Livermore group: 7 Be(p,γ) 8 B S-factor 3 He(α,γ α,γ) 7 Be S-factor n + 4 He elastic scattering phase shifts 10 Be(n,γ) 11 Be cross section Light ion reactions are important for astrophysics Understanding our Sun p-p chain Solar neutrinos E ν < 15 MeV Observed at SNO, Super K - neutrino oscillations 13

14 7 Be(p,γ) 8 B S-factor from ab initio wave functions Sensitivity to NN interaction CD-Bonn 2000 vs. INOY Conclusions and outlook from lecture 3 Ab initio no-core shell model Method for solving the nuclear structure problem for light nuclei Apart from the GFMC the only working method for A>4 at present Advantages applicable for any NN potential Presently the only method capable to apply the QCD χpt NN+NNN interactions to p-shell nuclei Easily extendable to heavier nuclei Calculation of complete spectra at the same time Success - importance of three-nucleon forces for nuclear structure Work in progress - examples shown Better NN interactions whose off-shell properties tuned to nuclei Calculations with realistic three-body forces in the p-shell Better determination of the three-body force itself Coupling of the NCSM to nuclear reactions theories Direct reactions Density from NCSM plus folding approaches Low-energy resonant and nonresonant reactions RGM-like approach Exotic nuclei: RIA Thermonuclear reaction rates: Astrophysics -161 MeV -147 MeV 14

15 Overall Conclusions Phenomenological shell models, such as the Extreme Single Particle Shell Model (ESPM of Lecture 1) provide physical insight and guide our choices of theoretical paths Ab-initio NCSM is founded on this established physical intuition (Lecture 2) High precision comparisons between theory and experiment are emerging Applications up through A = 16 tell us that NNN interactions are needed with realistic local NN interactions New era of interplay between theory and experiment has emerged Outstanding Problems/Challenges (Sample) Role of NNN interactions with non-local NN interactions Converged saturation properties in better agreement with experiment RMS radius of 6-He not understood (discrepancy ~ 9%) Applications with NN + NNN potentials to reactions and scattering Applications to unstable light nuclei and to heavier (stable and unstable) nuclei Acknowledgment of material from many collaborations With thanks to many collaborators K. Joseph Abraham, Oleksiy Atramentov, Peter Peroncik, Bassam Shehadeh, Richard Lloyd, John R. Spence, James P. Vary, Thomas A. Weber, Iowa State University Petr Navratil, W. Erich Ormand, Lawrence Livermore National Laboratory Bruce R. Barrett, U. van Kolck, Hu Zhan, Ionel Stetcu, University of Arizona Andreas Nogga, Institute of Physics, Juelich, Germany E. Caurier, Institute Reserche Subatomique, Strasbourg, France Anna Hayes, Los Alamos National Laboratory M. Slim Fayache, S. Aroua, University of Tunis, Tunisia Cesar Viazminsky, University of Aleppo, Syria Mahmoud A. Hasan, University of Jordan, Jordan Andrey Shirokov, Moscow State University, Russia Alexander Mazur, Sergei Zaytsev, Khabarovsk State Technical University, Russia Alina Negoita, Sorina Popescu, Sabin Stoica, Institute of Atomic Physics, Romania Avaroth Harindranath, Dipankar Chakrabarty, Saha Institute of Nuclear Physics, India Grigorii Pivovarov, Victor Matveev, Institute for Nuclear Research, Moscow, Russia Lubo Martinovic, Institute of Physics Institute, Bratislava, Slovakia Kris Heyde, N. Smirnova, University of Gent, Belgium Larry Zamick, Rutgers University 15