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Many-Nucleon Interactions via the SRG Trento, Italy July 13, 2011

Performance Measures x.x, x.x, and x.x. Many-Nucleon Interactions via the SRG Trento, Italy July 13, 2011. Eric Jurgenson Collaborators: P. Maris, R. Furnstahl, P. Navratil, E. Ormand, J. Vary. Prepared by LLNL under Contract DE-AC52-07NA27344. Ab initio: from the begining. Start with χEFTs

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Many-Nucleon Interactions via the SRG Trento, Italy July 13, 2011

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  1. Performance Measures x.x, x.x, and x.x Many-Nucleon Interactions via the SRGTrento, ItalyJuly 13, 2011 Eric Jurgenson Collaborators: P. Maris, R. Furnstahl, P. Navratil, E. Ormand, J. Vary Physical and Life Sciences/Physics Prepared by LLNL under Contract DE-AC52-07NA27344

  2. Ab initio: from the begining • Start with χEFTs • SRG is well suited to the many-body hierarchy

  3. What is the Similarity Renormalization Group (SRG) ? • Unitary Transformations: where • Implement as flow equations PRC 75,061001 (2007) [arXiv: nucl-th/0611045] • With Gs any Hermitian operator

  4. SRG evolves Hamiltonians unitarily

  5. SRG evolves Hamiltonians unitarily

  6. SRG evolves Hamiltonians unitarily

  7. SRG evolves Hamiltonians unitarily

  8. SRG evolves Hamiltonians unitarily

  9. SRG evolves Hamiltonians unitarily

  10. SRG evolves Hamiltonians unitarily

  11. SRG evolves Hamiltonians unitarily

  12. SRG evolves Hamiltonians unitarily

  13. SRG evolves Hamiltonians unitarily

  14. SRG evolves Hamiltonians unitarily

  15. SRG evolves Hamiltonians unitarily

  16. SRG evolves Hamiltonians unitarily

  17. Many-Body Forces (ANFs) • ANFs arise from eliminating DoF’s • Omitting them leads to model dependence (Tjon line) • 3NF help saturate nuclear matter • All many-body methods must deal with them • SRG induces ANFs! : • RG flows extend consistently to many-body spaces • State of the art now includes evolved 3NFs!

  18. Triton • SRG improves convergence PRL 103, 82501 (2009) [arXiv: 09005.1873]

  19. Helium • SRG induces many-body forces – how big are they? PRL 103, 82501 (2009) [arXiv: 09005.1873]

  20. Convergence in 6Li • Increased NA2max to 300 and NA3max to 40 • Simple extrapolations show spread in λ • Example here for one ħΩ – need optimal for each λ

  21. Lithium PRC, to appear [arXiv: 1011.4085] • Optimal ħΩ shifts with evolution • Extrapolations use this info • Error bars are consistent with previous work • λ dependence reduced from 4 to <1 MeV

  22. Carbon • Difference is subtle here but trackable -  plot difference of λ=1.5 - 2.2 vs. parameters

  23. Nmax/ħΩ dependence • Interesting spread behavior in the basis space • Clues to the source of convergence artifacts

  24. New Generators • Scale c3 and c4 • Plot the effect on the spread • Many choices of Gs • HO basis complicates the choice • More to come…

  25. Hierarchy Preservation: A=3 PRC, to appear [arXiv: 1011.4085] • Show hierarchy and suppression of high momentum strength • Expectation values of contributions to evolution

  26. Hierarchy Preservation: A=4 • Repeat for A=4 • Well defined hierarchy • No positive feedback loops

  27. Hierarchy Preservation: induced vs. initial 3NF • Compare Initial with Induced • Similar composition of contributions

  28. Carbon Revisited • Induced ANFs are as expected from existing work • Extrapolation in ħΩ should show reduction in spread • Larger systems are needed to determine 3/4NF needs…

  29. Adding 3NFs to the many-body problem… • Coupled Cluster (CC) • Density Functional Theory (DFT) • NCSM/RGM (reactions)

  30. Recap SRG improves convergence Variational and model space independent Truncations are well understood/controlled Induced forces are of natural size, though details still to be investigated Great freedom in SRG form for such work Outlook Monitor hierarchy of induced higher-body forces (MFDn, Bigstick, IT-NCSM) Coupled cluster results with SRG evolved 3NF inputs Apply these 3NFs to reactions (NCSM+RGM) Explore various ideas about the choice of Gs Conclusion

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