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 Option:UCRL# S&T – PLS/Physics Ab initio: from the begining Start with χEFTs SRG is well suited to the many- body hierarchy
3 Option:UCRL# S&T – PLS/Physics What is the Similarity Renormalization Group (SRG) ? PRC 75, (2007) [arXiv: nucl-th/ ] Unitary Transformations: where Implement as flow equations With G s any Hermitian operator
4 Option:UCRL# S&T – PLS/Physics SRG evolves Hamiltonians unitarily
5 Option:UCRL# S&T – PLS/Physics SRG evolves Hamiltonians unitarily
6 Option:UCRL# S&T – PLS/Physics SRG evolves Hamiltonians unitarily
7 Option:UCRL# S&T – PLS/Physics SRG evolves Hamiltonians unitarily
8 Option:UCRL# S&T – PLS/Physics SRG evolves Hamiltonians unitarily
9 Option:UCRL# S&T – PLS/Physics SRG evolves Hamiltonians unitarily
10 Option:UCRL# S&T – PLS/Physics SRG evolves Hamiltonians unitarily
11 Option:UCRL# S&T – PLS/Physics SRG evolves Hamiltonians unitarily
12 Option:UCRL# S&T – PLS/Physics SRG evolves Hamiltonians unitarily
13 Option:UCRL# S&T – PLS/Physics SRG evolves Hamiltonians unitarily
14 Option:UCRL# S&T – PLS/Physics SRG evolves Hamiltonians unitarily
15 Option:UCRL# S&T – PLS/Physics SRG evolves Hamiltonians unitarily
16 Option:UCRL# S&T – PLS/Physics SRG evolves Hamiltonians unitarily
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 Option:UCRL# S&T – PLS/Physics Triton SRG improves convergence PRL 103, (2009) [arXiv: ]
19 Option:UCRL# S&T – PLS/Physics Helium SRG induces many-body forces – how big are they? PRL 103, (2009) [arXiv: ]
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 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: ]
22 Option:UCRL# S&T – PLS/Physics Carbon Difference is subtle here but trackable - plot difference of λ= vs. parameters
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 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 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: ]
26 Option:UCRL# S&T – PLS/Physics Hierarchy Preservation: A=4 Repeat for A=4 Well defined hierarchy No positive feedback loops
27 Option:UCRL# S&T – PLS/Physics Hierarchy Preservation: induced vs. initial 3NF Compare Initial with Induced Similar composition of contributions
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 Option:UCRL# S&T – PLS/Physics Adding 3NFs to the many-body problem… Coupled Cluster (CC) Density Functional Theory (DFT) NCSM/RGM (reactions)
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