1. Lawrence Livermore National Laboratory Physical and Life Sciences/Physics 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 Performance Measures x.x, x.x, and x.x

2. 2 Option:UCRL# S&T – PLS/Physics Ab initio: from the begining  Start with χEFTs  SRG is well suited to the many- body hierarchy

3. 3 Option:UCRL# S&T – PLS/Physics What is the Similarity Renormalization Group (SRG) ? PRC 75,061001 (2007) [arXiv: nucl-th/0611045]  Unitary Transformations: where  Implement as flow equations  With G s any Hermitian operator

4. 4 Option:UCRL# S&T – PLS/Physics SRG evolves Hamiltonians unitarily

5. 5 Option:UCRL# S&T – PLS/Physics SRG evolves Hamiltonians unitarily

6. 6 Option:UCRL# S&T – PLS/Physics SRG evolves Hamiltonians unitarily

7. 7 Option:UCRL# S&T – PLS/Physics SRG evolves Hamiltonians unitarily

8. 8 Option:UCRL# S&T – PLS/Physics SRG evolves Hamiltonians unitarily

9. 9 Option:UCRL# S&T – PLS/Physics SRG evolves Hamiltonians unitarily

10. 10 Option:UCRL# S&T – PLS/Physics SRG evolves Hamiltonians unitarily

11. 11 Option:UCRL# S&T – PLS/Physics SRG evolves Hamiltonians unitarily

12. 12 Option:UCRL# S&T – PLS/Physics SRG evolves Hamiltonians unitarily

13. 13 Option:UCRL# S&T – PLS/Physics SRG evolves Hamiltonians unitarily

14. 14 Option:UCRL# S&T – PLS/Physics SRG evolves Hamiltonians unitarily

15. 15 Option:UCRL# S&T – PLS/Physics SRG evolves Hamiltonians unitarily

16. 16 Option:UCRL# S&T – PLS/Physics SRG evolves Hamiltonians unitarily

17. 17 Option:UCRL# S&T – PLS/Physics 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. 18 Option:UCRL# S&T – PLS/Physics Triton  SRG improves convergence PRL 103, 82501 (2009) [arXiv: 09005.1873]

19. 19 Option:UCRL# S&T – PLS/Physics Helium  SRG induces many-body forces – how big are they? PRL 103, 82501 (2009) [arXiv: 09005.1873]

20. 20 Option:UCRL# S&T – PLS/Physics Convergence in 6 Li  Increased N A2max to 300 and N A3max to 40  Simple extrapolations show spread in λ  Example here for one ħΩ – need optimal for each λ

21. 21 Option:UCRL# S&T – PLS/Physics Lithium  Optimal ħΩ shifts with evolution  Extrapolations use this info  Error bars are consistent with previous work  λ dependence reduced from 4 to <1 MeV PRC, to appear [arXiv: 1011.4085]

22. 22 Option:UCRL# S&T – PLS/Physics Carbon  Difference is subtle here but trackable -  plot difference of λ=1.5 - 2.2 vs. parameters

23. 23 Option:UCRL# S&T – PLS/Physics N max /ħΩ dependence  Interesting spread behavior in the basis space  Clues to the source of convergence artifacts

24. 24 Option:UCRL# S&T – PLS/Physics New Generators  Scale c 3 and c 4  Plot the effect on the spread  Many choices of G s  HO basis complicates the choice  More to come…

25. 25 Option:UCRL# S&T – PLS/Physics Hierarchy Preservation: A=3  Show hierarchy and suppression of high momentum strength  Expectation values of contributions to evolution PRC, to appear [arXiv: 1011.4085]

26. 26 Option:UCRL# S&T – PLS/Physics Hierarchy Preservation: A=4  Repeat for A=4  Well defined hierarchy  No positive feedback loops

27. 27 Option:UCRL# S&T – PLS/Physics Hierarchy Preservation: induced vs. initial 3NF  Compare Initial with Induced  Similar composition of contributions

28. 28 Option:UCRL# S&T – PLS/Physics 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. 29 Option:UCRL# S&T – PLS/Physics Adding 3NFs to the many-body problem…  Coupled Cluster (CC)  Density Functional Theory (DFT)  NCSM/RGM (reactions)

30. 30 Option:UCRL# S&T – PLS/Physics Conclusion 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 G s