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Ab initio calculations of radiative capture. CAWONAPS 2010, December 9-10, 2010. Petr Navratil | TRIUMF. Understanding our Sun. Light nuclei from first principles. Goal : Predictive theory of structure and reactions of light nuclei Needed for

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Ab initio calculations of radiative capture CAWONAPS 2010, December 9-10, 2010 Petr Navratil | TRIUMF Understanding our Sun Light nuclei from first principles Goal: Predictive theory of structure and reactions of light nuclei Needed for Physics of exotic nuclei, tests of fundamental symmetries Understanding of nuclear reactions important for astrophysics Understanding of reactions important for energy generation From first principles or ab initio: Nuclei as systems of nucleons interacting by nucleon-nucleon (and three-nucleon) forces that describe accurately nucleon-nucleon (and three-nucleon) systems Our many-body technique: Combinethe ab initio no-core shell model (NCSM) with the resonating group method (RGM) The NCSM: An approach to the solution of the A-nucleon bound-state problem Accurate nuclear Hamiltonian Finite harmonic oscillator (HO) basis Complete Nmaxh model space Effective interaction due to the model space truncation Similarity-Renormalization-Group evolved NN(+NNN) potential Short & medium range correlations No continuum E. Jurgensonet al., PRL 103, 082501 (2009) The RGM: A microscopic approach to the A-nucleon scattering of clusters Nuclear Hamiltonian may be simplistic Cluster wave functions may be simplified and inconsistent with the nuclear Hamiltonian Long range correlations, relative motion of clusters Ab initio NCSM/RGM: Combines the best of both approaches Accurate nuclear Hamiltonian, consistent cluster wave functions Correct asymptotic expansion, Pauli principle and translational invariance 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: realistic nuclear Hamiltonian Non-local integro-differential coupled-channel equations: 4He n The best system to start with: n+4He, p+4He 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 p-p chain Solar neutrinos E < 15 MeV Observed at SNO, Super K - neutrino oscillations Solar p-p chain 7Be(p,g)8B S-factor S17 one of the main inputs in solar neutrino problem Needs to be known with a precision better than 9 % Current evaluation has uncertainty >10% Theory needed for extrapolation to ~ 10 keV Many theoretical calculations in the past… …now something new:Starting from first principles Input: NN interaction, 7Be eigenstates Similarity-Renormalization-Group (SRG) evolved chiral N3LO NN interaction Accurate Soft: Evolution parameter Λ 7Be (7Li) NCSM up to Nmax=10 possible Importance Truncated NCSM up to Nmax=18 R. Roth & P. N., PRL 99, 092501 (2007) large Nmax needed for convergence of Target eigenstates Localized parts of integration kernels 7Be p p-7Be scattering NCSM/RGM coupled channel calculations 7Be states 3/2-,1/2-, 7/2- Soft NN potential (SRG-N3LO with Λ = 1.8 fm-1) 8B 2+ g.s.bound by 126 keV (expt. bound by 137 keV) New 0+, 1+, 2+ resonances predicted Scattering length: Expt: a02= -7(3) fm Calc: a02= -10.2 fm (Λ=2.02 fm-1) P. N., R. Roth, S. Quaglioni, PRC 82, 034609 (2010) 7Be p 7Be(p,γ)8B radiativecapture S-factor NCSM/RGM coupled channel calculations 7Be states 3/2-,1/2-, 7/2- Soft NN potential (SRG-N3LO with Λ = 1.8 fm-1) 8B 2+ g.s.bound by 126 keV (expt. 137 keV) S(0) ~ 21.5 eVb The first ever ab initiocalculations of 7Be(p,γ)8B (still preliminary) Impact of higher excited states of 7Be NCSM/RGM p-7Be calculation with more excited states 1/2-, 7/2-, 5/2-1, 5/2-2 8B 2+g.s. Large P-wave 5/2-2 component 5/2-2 state of 7Be should be included in 7Be(p,γ)8B calculations 8B 2+g.s. 7Be p p-7Be scattering: Impact of 5/2- states NCSM/RGM coupled channel calculations 7Be states 3/2-,1/2-, 7/2-, 5/2-1, 5/2-2 Soft NN potential (SRG-N3LO with Λ = 1.85 fm-1) 8B 2+ g.s.bound by 163 keV (expt. bound by 137 keV) New 0+, 1+,two 2+ resonances predicted s=1 l=1 2+clearly visible in (p,p’) cross sections 7Be p 7Be(p,γ)8B: Impact of 5/2- states NCSM/RGM coupled channel calculations 7Be states 3/2-,1/2-, 7/2-, 5/2-1, 5/2-2 Soft NN potential (SRG-N3LO with Λ = 1.85 fm-1) 8B 2+ g.s.bound by 163 keV (expt. 137 keV) S(0) ~ 20.1 eVb (preliminary) Data evaluation: S(0)=20.8(2.1) eVb The 5/2-2 state improves 7Be(p,γ)8B S-factor energy dependence for E>0.4 MeV Conclusions and Outlook With the NCSM/RGM approach we are extending the ab initio effort to describe low-energy reactions and weakly-bound systems The first 7Be(p,γ)8Bab initio S-factor calculation Both the bound and the scattering states from first principles No fit SRG-N3LO NN potential selected to match closely the experimental threshold (Λ≈1.8~2 fm-1) Prediction of new 8B resonances New results with SRG-N3LO NN potentials: Initial results for 3H(d,n)4He & 3He(d,p)4He fusion and d-4He scattering First steps towards 3He+4He scattering To do: Inclusion of NNN force Alpha clustering: 4He projectile NCSM with continuum (NCSMC) Three-cluster NCSM/RGM and treatment of three-body continuum a-3He Collaborators Sofia Quaglioni, E. Jurgenson (LLNL) Robert Roth (TU Darmstadt) WataruHoriuchi (GSI Darmstadt) n 3H Toward the first ab initio calculation of theDeuterium-Tritium and d-3He fusion d 4He NIF ITER Predictive theory useful Low energy: Electron screening problem. Resonance energy: Shape of the peak P. Navratil et al., arXiv:1009.3965 4He d NCSM/RGM ab initio calculationof d-4He scattering NCSM/RGM calculation with d + 4He(g.s.) up to Nmax = 12 SRG-N3LO potential with Λ = 1.5 fm-1 Deuteron breakup effects included by continuum discretized by pseudo states in 3S1-3D1, 3D2 and 3D3-3G3 channels 6Li The 1+0 ground state bound by 1.9 MeV (expt. 1.47 MeV) Calculated T=0 resonances: 3+, 2+ and 1+ in correct order close to expt. energies

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