300 likes | 477 Views
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
E N D
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
Ab initio: from the begining • Start with χEFTs • SRG is well suited to the many-body hierarchy
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
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!
Triton • SRG improves convergence PRL 103, 82501 (2009) [arXiv: 09005.1873]
Helium • SRG induces many-body forces – how big are they? PRL 103, 82501 (2009) [arXiv: 09005.1873]
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
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
Carbon • Difference is subtle here but trackable - plot difference of λ=1.5 - 2.2 vs. parameters
Nmax/ħΩ dependence • Interesting spread behavior in the basis space • Clues to the source of convergence artifacts
New Generators • Scale c3 and c4 • Plot the effect on the spread • Many choices of Gs • HO basis complicates the choice • More to come…
Hierarchy Preservation: A=3 PRC, to appear [arXiv: 1011.4085] • Show hierarchy and suppression of high momentum strength • Expectation values of contributions to evolution
Hierarchy Preservation: A=4 • Repeat for A=4 • Well defined hierarchy • No positive feedback loops
Hierarchy Preservation: induced vs. initial 3NF • Compare Initial with Induced • Similar composition of contributions
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…
Adding 3NFs to the many-body problem… • Coupled Cluster (CC) • Density Functional Theory (DFT) • NCSM/RGM (reactions)
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