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Ab initio reactions of nucleons on light nuclei

Collaborative research by P. Navratil, S. Quaglioni, and R. Roth delves into nuclear reactions, utilizing ab initio NCSM/RGM methods and advanced computational models to explore nucleon-nucleus interactions. The study focuses on light nuclei, investigating scattering processes, bound states, resonances, and the role of inter-nucleon potentials, achieving significant insights and comparing results to experimental data.

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Ab initio reactions of nucleons on light nuclei

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  1. Ab initio reactions of nucleons on light nuclei Petr Navratil (LLNL) Collaborators: Sofia Quaglioni (LLNL), Robert Roth (TU Darmstadt) UNEDF SCIDAC meeting, Pack Forest, WA, 6/22/2009 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-410642

  2. 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: Fully implemented for nucleon-nucleus basis. Work on deuteron-nucleus basis under way.

  3. 3He 3H p n • EFT N3LO NN potential: convergence reached with two-body effective interaction NCSM/RGM ab initio calculation of n-3H and p-3He phase shifts • NCSM/RGM calculations with n+3H(g.s.) and p+3He(g.s.), respectively. • Benchmark with Alt, Grassberger and Sandhas (AGS) results [PRC75, 014005(2007)] • What is missing? - n+3H(ex), 2n+d, p-3He(ex), 2p+d configurations The omission of three-nucleon partial waves with 1/2 < J ≤ 5/2leads to effects of comparable magnitude on the AGS results. Need to include target excited states!

  4. n-4He & p-4He phase shifts from accurate NN interactions • 4He states: g.s.,  • Reasonable agreement with experiment for 2S1/2 , 2P1/2, 2D3/2 channels • Coulomb under control n-4He and p-4He phase shifts Insufficient spin-orbit strength: 2P3/2 underestimated  NNN needed CD-Bonn the best description of 2S1/2 phase shifts

  5. 4He n n+4He differential cross section and analyzing power • Neutron energy of 17 MeV • beyond low-lying resonances • Polarized neutron experiment at Karlsruhe • NCSM/RGM calculations • n+4He(g.s,0+0) • SRG-evolved N3LONN potential • Good agreement for angular distribution • Differences for analyzing power • Ay puzzle for A=5? First ever ab initio calculation of Ay in for a A=5 system. Strict test of inter-nucleon interactions.

  6. 7Li n NCSM/RGM ab initio calculation of n+7Li scattering • 7Li • Full NCSM up to Nmax=10 (12 possible) • IT-NCSM up to Nmax=18 • Convergence of both ground and excited states • 8Li • NCSM predicts unobserved low-lying 0+ and 2+ states • NCSM/RGM with7Li 3/2- and 1/2- bound states included • Up to Nmax=14 so far (hΩ=20 MeV used) • Moderate changes from Nmax=6 to Nmax=14 • Bound states • 2+ state bound by 1.07 MeV (expt 2.03 MeV) • 1+ state bound by 0.18 MeV (expt 1.05 MeV) PRC73, 065801 (2006)

  7. 7Li n NCSM/RGM ab initio calculation of n+7Li scattering • 7Li 3/2- and 1/2- bound states included • SRG-N3LO NN interaction with Λ=2.02 fm-1 • Up to Nmax=14 so far (hΩ=20 MeV used) • Moderate changes from Nmax=6 to Nmax=14 • 2+ and 1+ states bound • Other states unbound S-wave scattering length Expt: a01=0.87(7) fm a02=-3.63(5) fm Calc: a01=1.31 fm a02=-0.18 fm Qualitative agreement with experiment. Calculated broad 1+ resonance, predicted narrow 0+ resonance. The 3+ resonancenot seen when 7Li 7/2- state not included.

  8. 7Li n NCSM/RGM ab initio calculation of n+7Li scattering • 7Li 3/2-, 1/2- and 7/2- states included • Result for Nmax=8 shown • 2+ and 1+ states bound (slightly more) • 0+ and 1+ resonances not affected • 3+ and 2+ resonances appear • Improvement of S-wave scattering length S-wave scattering length Expt: a01=0.87(7) fm a02=-3.63(5) fm Calc: a01=0.73 fm a02=-1.42 fm Good match of bound states and narrow resonances with the 8Li NCSM result. Predicted narrow 0+ and 2+ resonance. Seen at recent p+7Be FSU experiment.

  9. Nucleon-12C scattering with SRG-N3LO NN potential • 12C • Full NCSM up to Nmax=8 • IT NCSM up to Nmax=18(!) • Perfect agreement for both the 0+ ground- and 2+ excited state up to Nmax=8 • Convergence of the IT-NCSM • h=24 MeV used • 13N, 13C within the NCSM • 1/2+ state too high by ~ 6 MeV • 13N, 13C within the NCSM/RGM • up Nmax=16 with 12C g.s. and 2+ included • 13C: • 1/2- bound by 5.34 MeV (expt 4.95 MeV) • 3/2- bound by 2.23 MeV (expt 1.27 MeV) • 1/2+ bound by 0.03 MeV (expt 1.86 MeV) • Excitation energy 5.31 MeV (expt 3.09 MeV) • Excitation energy of the 1/2+ state drops by 4 MeV when n-12C long-range correlations included

  10. p-12C scattering with SRG-N3LO NN potential • Experiments with a polarized proton target under way • NCSM/RGM up Nmax=16 • 12C g.s. and 2+ included • 1/2- state bound by 2.9 MeV • 13N ground state • Other states unbound • 1/2+ resonance at ~1.2 MeV • 5/2+ resonance • Good stability: Moderate changes from Nmax=6 to Nmax=16 • Minimal difference between Nmax=14 and Nmax=16 • Qualitative agreement with experiment

  11. (A-2) (2) (1,…,A-2) (1,…,A-2) (A-1,A) (A-1,A) (2) (A-2) The deuteron projectile: Norm kernel  2(A-2)  + (A-2)(A-3)/2 

  12. (A-2) (2) (1,…,A-2) (1,…,A-2) (A-1,A) (A-1,A) The deuteron projectile: Hamiltonian kernel

  13. d- scattering: Progress so far • Norm kernel coded • Hamiltonian kernel partially coded • Term with three-body density in progress • Convergence reached for d- norm kernel (physics - Pauli principle) 2+ D-wave dominated 1+ S-wave dominated 1- P-wave dominated

  14.                           D D D D n D D D D n D D D n D n D n D n n n n D D D r r r r r r r r r’ r’ r’ r’ r’ r’ r’ r r’ D   r’ r’ r’ r’ r r r r r The n-4He differential cross section (left) and analyzing power (right) for 17 MeV neutrons obtained within the ab initio NCSM/RGM (red solid line) compared to experimental data and ENDF/B-VI evaluations. Toward the first ab initio description of the Deuterium-Tritium fusion • Solve the many-body Schrödinger equation in the Hilbert space spanned by the RGM basis states: • Progress so far: Norm kernels calculated • Introduction: • – A fundamental theory of light-ion fusion reactions is the basis to • enhance the predictive capabilities of astrophysics modeling, and • provide precision diagnostics for prospective fusion-power plants • – Presently there is no realistic theoretical model able to describe • important processes such as the Deuterium-Tritium (D-T) fusion • – Our approach combines the ab initio no-core shell model (NCSM) • and the resonating-group method (RGM)  ab initio NCSM/RGM • NCSM: single-particle degrees of freedom • RGM: clusters and their relative motion • Method: • To calculate the reaction D + T  n +  within the ab initio NCSM/RGM • – Using the ab initio NCSM calculate eigenstates: • – Solve the many-body Schrödinger equation in the Hilbert space • spanned by the RGM basis states: • – From the Scattering matrix calculate total and angular cross sections, • polarization observables Results: – Promising results using the NCSM/RGM nucleon-nucleus formalism D(g.s.)+T(g.s.) D(g.s.)+T(g.s.) D(g.s.)+T(g.s.) D(g.s.)+T(g.s.) D(g.s.)+T(g.s.) (b) (b) (b) (b) (c) (c) (c) (c) (b) (c) r D (a) (a) (a) (a) (a) – Approach applied also to n-T, n-10Be, n-12C, n-16O, p-3,4He • The D+T norm kernel: • diagrammatic representation of the • “direct” and “exchange” components; exchange • components for the spin-parity-isospin (b) 1/2+1/2 and (c) 3/2+1/2 channels • The D+T norm kernel: • diagrammatic representation of the • “direct” and “exchange” components; exchange • components for the spin-parity-isospin (b) 1/2+1/2 and (c) 3/2+1/2 channels • The D+T norm kernel: • diagrammatic representation of the • “direct” and “exchange” components; exchange • components for the spin-parity-isospin (b) 1/2+1/2 and (c) 3/2+1/2 channels • The D+T norm kernel: • diagrammatic representation of the • “direct” and “exchange” components; exchange • components for the spin-parity-isospin (b) 1/2+1/2 and (c) 3/2+1/2 channels • The D+T norm kernel: • diagrammatic representation of the • “direct” and “exchange” components; exchange • components for the spin-parity-isospin (b) 1/2+1/2 and (c) 3/2+1/2 channels More on many-body ab initio calculations of nucleon-nucleus scattering in S. Quaglioni and P. Navratil, PRL 101, 092501 (2008); PRC 79, 044606 (2009)

  15. FY09 accomplishments • Development of ab initio many-body reaction theory by merging the NCSM and the RGM (P. Navratil and S. Quaglioni) • Results with NN potentials used by UNEDF collaboration • n-7Li with SRG-N3LO using the importance-truncated NCSM • p-12C with SRG-N3LO using the importance-truncated NCSM • n-16O with SRG-N3LO using the importance-truncated NCSM • Collaboration with R. Roth (TU Darmstadt) • Deuteron-nucleus scattering under development • Development of the TRDENS transition density code • Distribution of two-body density structure over groups of processors • Similarity-renormalization-group evolution of NN+NNN interactions • Collaboration with D. Furnstahl (OSU) and E. Jurgenson (OSU) • A=14 nuclei with chiral EFT NN+NNN up to Nmax=8 • Transformation of NNN to SD basis up to Nmax=8 • Collaboration with J. Vary, P. Maris, H. Nam, E. Ormand and D. Dean

  16. Publications relevant to UNEDF in 2008/2009 • E. D. Jurgenson, P. Navratil, and R. J. Furnstahl, Evolution of nuclear many-body forces with the similarity renormalization group, arXiv:0905.1873 [nucl-th], submitted to Phys. Rev. Lett. • I. Stetcu, S. Quaglioni, J.L. Friar, A.C. Hayes, and P. Navratil, Electric Dipole Polarizabilities of Hydrogen and Helium Isotopes, Phys. Rev. C 79, 064001 (2009) • P. Navratil, S. Quaglioni, I. Stetcu and B. R. Barrett, Recent developments in no-core shell-model calculations, J. of Phys. G 36 (2009) 083101, invited topical review. • S. Quaglioni, P. Navratil, Ab initio many-body calculations of nucleon-nucleus scattering, Phys. Rev. C 79, 044606 (2009) • C. Forssen, E. Caurier, P. Navratil, Charge radii and electromagnetic moments of Li and Be isotopes from the ab initio no-core shell model, arXiv:0901.0453 [nucl-th], Phys. Rev. C 79, 021303(R) (2009) • D. Gazit, S. Quaglioni, P. Navratil, Three-Nucleon Low-Energy Constants from the Consistency of Interactions and Currents in Chiral Effective Field Theory, arXiv:0812.4444 [nucl-th], submitted to Phys. Rev. Lett. • S. Quaglioni, P. Navratil, Ab initio many-body calculations of n-3H, n-4He, p-3He,4He, and n-10Be scattering, PHYSICAL REVIEW LETTERS 101, 092501 (2008) • R. Roth, P. Navratil, Comment on "Ab initio Study of Ca-40 with an Importance-Truncated No-Core Shell Model'' – Reply, PHYSICAL REVIEW LETTERS 101, 119202 (2008)

  17. Future plan • The rest of Year 3 • Complete n-7Li calculations • Begin n-8He investigation • Continue work on deuteron-nucleus formalism (supported by LDRD) • Year 4 • n-8He, n-9Li calculations • Development of 3H and 3He – nucleus formalism (supported by LDRD) • Development of the coupling of NCSM/RGM and NCSM  NCSMC • Similarity-renormalization-group evolution of NN+NNN interactions • Application to p-shell nuclei (supported by DOE/SC/NP) • Further development of importance-truncation NCSM scheme • Year 5 • High profile science: Capture reactions - 3He(,)7Be • Computational challenges: • n-body density (n>2) calculations • Distribution of structure allocation, parallelization

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