Ab initio calculations of radiative capture

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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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