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Ab initio many-body calculations of light-ion reactions

Ab initio many-body calculations of light-ion reactions. Petr Navratil Collaborators: Sofia Quaglioni (LLNL), R. Roth (TU Darmstadt), E. Jurgenson (LLNL) 6th ANL/MSU/JINA/INT FRIB Theory Workshop, Argonne National Laboratory, March 23 - 26, 2010.

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Ab initio many-body calculations of light-ion reactions

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  1. Ab initio many-body calculations of light-ion reactions Petr Navratil Collaborators: Sofia Quaglioni (LLNL), R. Roth (TU Darmstadt), E. Jurgenson (LLNL) 6th ANL/MSU/JINA/INT FRIB Theory Workshop, Argonne National Laboratory, March 23 - 26, 2010 Lawrence Livermore National Laboratory, P. O. Box 808, Livermore, CA 94551 This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 LLNL-PRES-425682

  2. Outline • Motivation • Ab initio no-core shell model (NCSM) • Extension of the no-core shell model by resonating group method (ab initio NCSM/RGM) • Nucleon-alpha scattering • n-3H, p-3He cross sections • 11Be parity-inverted ground state • n-7Li, N-12C, n-16O scattering • Calculations with wave functions from importance-truncated NCSM • d-T fusion • Outlook

  3. Our goal is to develop an ab initio theory to understand nuclear structure and reactions of light nuclei The Hoyle state missing • Nuclei are quantum many-body systems with bound states, resonances, scattering states • Bound-state techniques not sufficient • Our approach - combining the ab initio no-core shell model (NCSM) with the resonating group method (RGM)  ab initioNCSM/RGM • NCSM - single-particle degrees of freedom • RGM - clusters and their relative motion NCSM PRL99, 042501(2007) RGM Preserves Pauli principle and translational invariance  Important as nucleons are fermions and nuclei self-bound

  4. The ab initio no-core shell model (NCSM) in brief • The NCSM is a technique for the solution of the A-nucleon bound-state problem • Realistic nuclear Hamiltonian • High-precision nucleon-nucleon potentials • Three-nucleon interactions • Finite harmonic oscillator (HO) basis • A-nucleon HO basis states • Jacobi relative coordinates • Cartesian single-particle coordinates • complete Nmaxh model space • Translational invariance preserved even with single-particle coordinate Slater-determinant (SD) basis • Effective interaction tailored to model-space truncation for NN(+NNN) potentials • Lee-Suzuki-Okamoto unitary transformation in n-body cluster approximation (n=2,3) • Or a sequence of unitary transformations in momentum space: • Similarity-Renormalization-Group evolved NN(+NNN) potential • Soft: No further model-space dependent effective interaction needed • Variational calculation Convergence to exact solution with increasing Nmax for bound states. No coupling to continuum.

  5. NCSM Convergence: 4He • Chiral N3LO NN plus N2LO NNN potential • Bare interaction (black line) • Variational calculation • Strong short-range correlations • Large basis needed • Similarity-renormalization group evolved effective interaction (red line) • Unitary transformation • Two- plus three-body components, four-body omitted • Softens the interaction • Variational calculation • Smaller basis sufficient

  6. Hamiltonian kernel Norm kernel The ab initio NCSM/RGM in a snapshot eigenstates of H(A-a) and H(a) in the ab initio NCSM basis • Ansatz: • Many-body Schrödinger equation:  either bare interaction or NCSM effective interaction • Non-local integro-differential coupled-channel equations: NCSM/RGM: NCSM microscopic wave functions for the clusters involved, and realistic (bare or derived NCSM effective) interactions among nucleons. Proper boundary conditions for scattering and/or bound states

  7. (A-1) (1) (1,…,A-1) (1,…,A-1) (A) (A)  (A-1)  (1) (A-1) Single-nucleon projectile: the norm kernel Localized parts of kernels expanded in the HO basis

  8. (A-1) (1) (A-1) “direct potential”  +(A-1) “exchange potential” (A-1)(A-2) The RGM kernels in the single-nucleon projectile basis In the A=5 system the 1/2+ (2S1/2) is a Pauli-forbidden state, therefore g.s. in P wave

  9. 4He n NCSM/RGM ab initio calculation of n-4He phase shifts • Similarity-renormalization-group (SRG) evolved chiral N3LO NN interaction (R. Roth) • Low-momentum Vlowk NN potential • convergence reached with bare interaction n-4He phase shifts: SRG-N3LO, =2.02 fm-1 Vlowk Fully ab initio. No fit. No free parameters. Good convergence with respect to Nmax

  10. 4He n n+4He differential cross section and analyzing power • NCSM/RGM calculations with • N + 4He(g.s., 0+0) • SRG-N3LO NN potential with Λ=2.02 fm-1 • Differential cross section and analyzing power @17 MeV neutron energy • Polarized neutron experiment at Karlsruhe NNN missing: Good agreement only for energies beyond low-lying 3/2- resonance

  11. p+4He differential cross section and analyzing power

  12. Neutron-triton elastic scattering at 14 MeV • Important for the NIF physics • deuteron-triton fusion generates 14 MeV neutrons • Experimental situation confusing • Good data for p+3He elastic scattering Use NCSM/RGM calculation to relate the two reactions and predict n+3H cross section

  13. 11Be 10Be n NCSM 1/2- 1/2+ 3.0 2.5 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 Parity-inverted g.s. of 11Be understood! E [MeV] Expt. NCSM/RGM 11Be bound states and n-10Be phase shifts • Exotic nuclei: vanishing of magic numbers, abnormal spin-parity of ground states, … • The g.s. of 11Be one of the best examples • Observed spin-parity :1/2+ • p-shell expected: 1/2- • Large-scale NCSM calculations, Forssen et al., PRC71, 044312 (2005) • Several realistic NN potentials • Calculated g.s. spin-parity: 1/2- • NCSM/RGM calculation with CD-Bonn • n + 10Be(g.s.,21+,22+,11+) • Calculated g.s. spin-parity : 1/2+ B(E1;1/2+->1/2-)=0.02 e2 fm2 What happens? Substantial drop of the relative kinetic energy due to the rescaling of the relative wave function when the Whittaker tail is recovered

  14. NCSM/RGM with Importance-Truncated (IT-NCSM) • IT-NCSM, Roth & Navratil, PRL99, 092501 (2007) makes possible: • large Nmax fortarget g.s. + excited states • good convergence for integration kernels • 7Li • NCSM up to Nmax=10 (12 possible) • IT-NCSM up to Nmax=18 • 12C, 16O • NCSM up to Nmax= 8 • IT-NCSM up to Nmax= 18(!) • Benchmark with NCSM in smaller model spaces: perfect agreement Combining the NCSM/RGM with the IT-NCSM highly promising. Access to medium mass nuclei.

  15. 7Li n NCSM/RGM ab initio calculation of n+7Li scattering • Nmax = 12 NCSM/RGM calculation with n + 7Li(g.s.,1/2-, 7/2-) • SRG-N3LO NN potential with Λ = 2.02 fm-1 • 8Li bound states: 2+ and 1+ • Calculated broad 1+ resonance • 3+ resonance not seen when the 7/2- state of 7Li is not included 7Li 2+ 0+ Expt: a01= 0.87(7) fm a02= -3.63(5) fm Calc: a01= 1.24 fm a02= -0.61 fm Predicted narrow 0+ and 2+ resonances seen at recent p+7Be experiment at FSU

  16. 12C n 13C bound states and n-12C scattering • Nmax = 16 NCSM/RGM calculation with n + 12C(g.s.,2+1) • SRG-N3LO NN potential with Λ = 2.02 fm-1 • Three 13C bound states: 1/2-, 3/2-, 1/2+ ( 5/2+ still unbound ) • 5/2+ narrow resonance • Excitation energy of the 1/2+ state drops by 4 MeV when n-12C long-range correlations included

  17. 12C p 13N ground state and p-12C scattering • Experiments with a polarized proton target under way • Nmax = 16 NCSM/RGM calculation with n + 12C(g.s.,2+1) • SRG-N3LO NN potential with Λ = 2.02 fm-1 • 13N 1/2- ground state (bound by 2.9 MeV), other states unbound • 1/2+ and 5/2+ narrow resonance

  18. 16O n 17O bound states and n-16O scattering • Nmax = 12 NCSM/RGM calc. with n+16O(g.s., 3-,1-,2-) • SRG-N3LO NN potential with Λ = 2.02 fm-1 • 17O bound states: 5/2+, 1/2+ ( 1/2-, 5/2- unbound ) • Narrow resonances only when 16O excited states included • Impact of incomplete 16O description • 13C+alpha not taken into account yet ( ) Nmax=12 Nmax=18 ( ) ( )

  19. Deuterium-Tritium fusion: a future energy source • The d+3Hn+4He reaction • The most promising for the production of fusion energy in the near future • Will be used to achieve inertial-confinement (laser-induced) fusion at NIF, and magnetic-confinement fusion at ITER NIF Resonance at Ecm =48 keV (Ed=105 keV) in the J=3/2+ channel Cross section at the peak: 4.88 b 17.64 MeV energy released: 14.1 MeV neutron and 3.5 MeV alpha ITER

  20.    r r r r r’ r’ n 3H Toward the first ab initio calculation of theDeuterium-Tritium fusion d 4He ✔ n n n n r’ r’ 3H 3H 3H 3H d d d d • d+3H d+3H norm kern • Direct and exchange part • S-wave channel: J=3/2+,J=1/2+ • d, 3H spins parallel, anti-parallel

  21.    r r r r r’ r’ n 3H Toward the first ab initio calculation of theDeuterium-Tritium fusion d 4He ✔ n n n n ✔ r’ r’ 3H 3H 3H 3H d d d d • d+3H n+4He norm kernel • S-wave channel: J=1/2+ • d, 3H spins anti-parallel • d+3H S-wave to n+4He D-wave transition: J=3/2+ • Important for fusion 2 x -3 x

  22. n 3H Toward the first ab initio calculation of theDeuterium-Tritium fusion: Phase shifts d 4He Ab initio phase shift calculations of the d+3H elastic scattering show resonance in the 4S3/2 channel No resonance in the 2S1/2 channel: Pauli principle Phase shift of the n+4He elastic scattering show slight impact of the d+3H channels on P-waves Effect of resonance in the 3/2+D-wave just above the d-3H threshold D-T fusion happens through the S-wave d+3H to D-wave n+4He transition

  23. n 3H Toward the first ab initio calculation of theDeuterium-Tritium fusion: Cross section d 4He Still preliminary, incomplete: Nmax=13, SRG-N3LO NN (Λ=2.02 fm-1), no NNN, ground states of d, 3H, 4He only. Incorrect features: Resonances higher than in experiment: 150 keV vs. 50 keV (d-T) 250 keV vs. 200 keV (d-3He) Cross sections way too low, it gets increased by including 4He resonances (2- 0 in particular) Correct features: Resonance just above threshold, lower for d-T S-factor of d+3He flat as E0: Experimental rise due to electron screening First ab initio results of d-T and d-3He fusion: promising, correct physics, more work needs to be done…

  24. 7Li n Conclusions and Outlook • With the NCSM/RGM approach we are extending the ab initio effort to describe low-energy reactions and weakly-bound systems • Recent results for nucleon-nucleus scattering with NN realistic potentials: • n-3H, n-4He, n-10Be and p-3,4He • S. Quaglioni and P. N.,PRL 101, 092501 (2008), PRC 79, 044606 (2009) • New results with SRG-N3LO: • N-4He, n-7Li, N-12C and n-16O • Breakthrough due to the importance- truncated NCSM approach • First results for 3H(d,n)4He • Development for 3H, 3He projectiles • To do: • Heavier projectiles: 4He • NCSM with continuum (NCSMC) • Inclusion of NNN force • Three-cluster NCSM/RGM and treatment of three-body continuum

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