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Zong-Chao Yan University of New Brunswick Canada

Computational methods for Coulomb four-body systems. Zong-Chao Yan University of New Brunswick Canada. Collaborators: G. W. F. Drake Liming Wang Chun Li. NSERC, SHARCnet, ACEnet, CAS/SAFEA. August 24-27, 2015, Trento. Atomic physics method: Proposed by Drake in 90s for isotope shifts

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Zong-Chao Yan University of New Brunswick Canada

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  1. Computational methods for Coulomb four-body systems Zong-Chao Yan University of New Brunswick Canada Collaborators: G. W. F. Drake Liming Wang Chun Li NSERC, SHARCnet, ACEnet, CAS/SAFEA August 24-27, 2015, Trento

  2. Atomic physics method: Proposed by Drake in 90s for isotope shifts Shiner et al 3,4He Riis,..,Drake, 6,7Li+ Extended to radioactive isotopes: in the past 10 years 6He, 8He, 11Li, 11Be (Argonne, GSI, Drake, Pachucki et al.) Currently: 8B, one-proton halo (Argonne, GSI)

  3. b b a a A A’ No experiment can separate MS and FS so that we have to reply on theory to determine MS accurately.

  4. Isotope shift MS FS 1 Z

  5. Why isotope shifts? Finally, nuclear polarizability: Several nuclides have a halo in the excited state not in the ground state (Pachucki et al)

  6. Absolute measurement

  7. Theoretical background For low-Z systems, we use perturbation theory: Variational principle: then

  8. Rayleigh-Ritz Method: Choose a basis set Then Now Letting we have a generalized eigenvalue equation

  9. Hylleraas basis set: The basis is generated according to The nonlinear parameters are optimized by

  10. Perkins expansion: are odd, then the integral becomes an infinite series: If all In terms of W integrals:

  11. Ground state of lithium

  12. Li 2s-2p oscillator strength

  13. Relativistic and QED corrections The Bethe logarithm is very difficult to calculate.

  14. Drake-Goldman Method: Can. J. Phys. 77, 835 (1999) Works for atoms: H, He, Li Molecule: H2+ (converged to 9-10 digits)

  15. Puchalski, Kedziera, Pachucki PRA 87, 032503 (2013)

  16. Slow convergence when: Li, Wang, Yan, Int. J. Quantum Chem.113,1307(2013)

  17. Singular integral: type I • Expand etc. into infinite series • Perform multiple summation with convergence accelerators • Absolutely numerically stable • Recursion relations with quadrature Our approach: Pachucki’s approach:

  18. Singular integral: type II

  19. Other methods • Explicitly correlated Gaussian • Extensively used by Adamowicz et al and Pachucki et al • (sometimes mixed use with Hylleraas) up to Be • b) Hylleraas-CI • Sims and Hagstrom, He, Li, Be, but for nonrelativistic case

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