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R. Machleidt, University of Idaho

Recent advances in the theory of nuclear forces and its relevance for the microscopic approach to dense matter. R. Machleidt, University of Idaho. Outline. Introduction Historical perspective – The many-body problem and the nuclear force problem: two very different histories

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R. Machleidt, University of Idaho

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  1. Recent advances in the theory of nuclear forces and its relevance for the microscopic approach to dense matter R. Machleidt, University of Idaho

  2. Outline • Introduction • Historical perspective – The many-body problem and the nuclear force problem: two very different histories • The link between nuclear forces and QCD: chiral effective field theory (EFT) • EFT based nuclear forces and results • The limitations of chiral EFT and the lasting significance of meson theory • Conclusions Theory of Nuclear Forces ... IWND09, Shanghai, 8-24-09

  3. One of the most fundamental goals of theoretical nuclear physics: Explain the properties of nuclear matter and finite nuclei in terms of the basic forces between the constituents. Theory of Nuclear Forces ... IWND09, Shanghai, 8-24-09

  4. This microscopic approach to nuclear structure and reactions, a.k.a. the ab initio approach, has two ingredients • Many-body theory/methods • “Bare” nuclear forces But note: The history of each ingredient is very different. Theory of Nuclear Forces ... IWND09, Shanghai, 8-24-09

  5. Some many-body history Theory of Nuclear Forces ... IWND09, Shanghai, 8-24-09

  6. “Brueckner Theory” ≈1955 R. Machleidt Theory of Nuclear Forces ... IWND09, Shanghai, 8-24-09 6

  7. Coupled Cluster Theory ≈1958 R. Machleidt Theory of Nuclear Forces ... IWND09, Shanghai, 8-24-09 7

  8. The fundamental basis for today’s many-body methods was provided already 50 years ago. • “The nuclear force” 50 years ago: Gammel-Thaler potential • Only since ≈ A.D. 2000 quantitative nuclear forces derived on fundamental grounds have been developed. Theory of Nuclear Forces ... IWND09, Shanghai, 8-24-09

  9. The CRUX of NN potential development up to about 2000 • There are many quantitative NN potentials which are, however, not fundamental (the latest are the “high-precision potentials” developed in the 1990s). • Fundamental approaches were either not fundamental or not quantitative. • In short: • The more quantitative, the less fundamental. • The more fundamental, the less quantitative. Theory of Nuclear Forces ... IWND09, Shanghai, 8-24-09

  10. Therefore, we need … • a fundamental approach that produces a quantitative description of the nuclear force. • A fundamental approach must necessarily be based upon QCD. Theory of Nuclear Forces ... IWND09, Shanghai, 8-24-09

  11. The chiral effective field theory approach to nuclear forces • Clear connection to QCD: via symmetries • Degrees of freedom relevant to (low-energy) nuclear physics: pions and nucleons • Systematic expansion: Q/Λ • Controlled error, predictive power. • Explains the empirically known hierarchy of nuclear forces Theory of Nuclear Forces ... IWND09, Shanghai, 8-24-09

  12. 3N forces 4N forces 2N forces Leading Order The Hierarchy of Nuclear Forces Next-to Leading Order Next-to-Next-to Leading Order Next-to-Next-to-Next-to Leading Order R. Machleidt Theory of Nuclear Forces ... IWND09, Shanghai, 8-24-09 12

  13. 2N forces Leading Order The Hierarchy of Nuclear Forces The Hierarchy of Nuclear Forces Next-to Leading Order Next-to-Next-to Leading Order Next-to-Next-to-Next-to Leading Order Theory of Nuclear Forces ... IWND09, Shanghai, 8-24-09

  14. Phase shifts up to 300 MeV Red Line: N3LO Potential by Entem & Machleidt, PRC 68, 041001 (2003). Green dashed line: NNLO Potential, and blue dotted line: NLO Potential by Epelbaum et al., Eur. Phys. J. A19, 401 (2004). Theory of Nuclear Forces ... IWND09, Shanghai, 8-24-09

  15. N3LO Potential by Entem & Machleidt, PRC 68, 041001 (2003). NNLO and NLO Potentials by Epelbaum et al., Eur. Phys. J. A19, 401 (2004). R. Machleidt Theory of Nuclear Forces ... IWND09, Shanghai, 8-24-09 15

  16. 4N forces 2N forces Leading Order The Hierarchy of Nuclear Forces The Hierarchy of Nuclear Forces Next-to Leading Order Next-to-Next-to Leading Order Next-to-Next-to-Next-to Leading Order Theory of Nuclear Forces ... IWND09, Shanghai, 8-24-09

  17. 4NF at N3LO (leading order) Essentially negligible, as to be expected. R. Machleidt Theory of Nuclear Forces ... IWND09, Shanghai, 8-24-09 17

  18. Interim summary • 2NF o.k. • 4NF (negligibly) small … Theory of Nuclear Forces ... IWND09, Shanghai, 8-24-09

  19. 3N forces 4N forces 3NF 2N forces Leading Order The Hierarchy of Nuclear Forces The Hierarchy of Nuclear Forces Next-to Leading Order The focus: The 3NF Next-to-Next-to Leading Order Next-to-Next-to-Next-to Leading Order Theory of Nuclear Forces ... IWND09, Shanghai, 8-24-09

  20. Three-nucleon forces at N2LO TPE-3NF No new parameters! OPE-3NF One new parameter, D. Contact-3NF One new parameter, E. Strategy: Adjust D and E to two few-nucleon observables, e.g., the triton and alpha-particle binding energies. Then predict properties of other light nuclei. Theory of Nuclear Forces ... IWND09, Shanghai, 8-24-09

  21. Results from applications of chiral nuclear forces • Nuclear matter in the Brueckner pair approximation • Ground state of finite nuclei with A≤48 using Coupled Cluster theory • Spectra of light nuclei using the no-core shell model R. Machleidt Theory of Nuclear Forces ... IWND09, Shanghai, 8-24-09 21

  22. Nuclear matter [from Bogner et al. (2009)] Theory of Nuclear Forces ... IWND09, Shanghai, 8-24-09

  23. Chiral NN potential at N3LO underbinds by ~1MeV/nucleon. (Size extensivity at its best.) R. Machleidt Theory of Nuclear Forces ... IWND09, Shanghai, 8-24-09 23

  24. Calculating the properties of light nuclei usingchiral 2N and 3N forces “No-Core Shell Model “ Calculations by P. Navratil et al., LLNL 2N (N3LO) +3N (N2LO) forces 2N (N3LO) force only R. Machleidt Theory of Nuclear Forces ... IWND09, Shanghai, 8-24-09 24

  25. How does the chiral EFT approach To nuclear forces compare To the conventional approach (Meson Theory)? Theory of Nuclear Forces ... IWND09, Shanghai, 8-24-09

  26. ChPT Conventional meson theory OPE TPE Short range R. Machleidt Theory of Nuclear Forces ... IWND09, Shanghai, 8-24-09 26 “Contacts”

  27. What are contact terms? Consider the contribution from the exchange of a heavy meson + + + … Contact terms take care of the short range contributions. Theory of Nuclear Forces ... IWND09, Shanghai, 8-24-09

  28. ChPT Conventional meson theory OPE σ TPE ρ Short range R. Machleidt R. Machleidt Theory of Nuclear Forces ... IWND09, Shanghai, 8-24-09 Theory of Nuclear Forces ... IWND09, Shanghai, 8-24-09 28 28 “Contacts”

  29. Question: When everything is so equivalent to conventional meson theory, why not just use conventional meson theory? Answer: In ChPT, there is an organizational scheme (“power counting”) that allows to estimate the size of the various contributions and the error. This applies also to contributions from many-body forces. In conventional meson theory, we don’t have this. Theory of Nuclear Forces ... IWND09, Shanghai, 8-24-09

  30. However, there is a “However”! Theory of Nuclear Forces ... IWND09, Shanghai, 8-24-09

  31. Phase shifts up to 300 MeV Red Line: N3LO Potential by Entem & Machleidt, PRC 68, 041001 (2003). Green dashed line: NNLO Potential, and blue dotted line: NLO Potential by Epelbaum et al., Eur. Phys. J. A19, 401 (2004). R. Machleidt Theory of Nuclear Forces ... IWND09, Shanghai, 8-24-09 Theory of Nuclear Forces ... IWND09, Shanghai, 8-24-09 31

  32. red = Idaho N3LO, green = Juelich N3LO, black = CD-Bonn Theory of Nuclear Forces ... IWND09, Shanghai, 8-24-09

  33. pp TOTAL CROSS SECTIONS HIGH INTER-MEDIATE LOW pQCD ChPT Meson land Theory of Nuclear Forces ... IWND09, Shanghai, 8-24-09

  34. INTERMEDIATE ENERGIESabove about 0.4 MeV • Too high for ChPT • Too low for perturbative QCD (pQCD) • Lattice QCD • … not very practical • But there is a well-established model – • the relativistic meson model Theory of Nuclear Forces ... IWND09, Shanghai, 8-24-09

  35. Conclusions Theory of Nuclear Forces ... IWND09, Shanghai, 8-24-09

  36. After 70 years of struggle, we have now a proper theory of nuclear forces that is based upon the fundamental theory of strong interactions, QCD. It is chiral effectivefield theory in which the pion plays a fundamental role. Thus, the original Yukawa idea of just ONE MESON which makes the nuclear force is re-instated,but with some refinements (chiral symmetry). The circle of history is closing. • Based upon chiral perturbation theory (ChPT), quantitative NN potentials have been successfully developed and are available for nuclear structure applications. • In ChPT, two- and many-body forces are generated on an equal footing. Many-body forces are predicted to be much smaller than two-body forces, consistent with experience. • The theory is fundamental AND quantitative! • A new era of microscopic nuclear structure has started. Theory of Nuclear Forces ... IWND09, Shanghai, 8-24-09

  37. However .. • Chiral EFT is a LOW-ENERGY theory, restricted to momenta below ≈ 400 MeV/c • O.k. for normal nuclear densities. • Too low for dense matter. • At intermediate energies “meson theory” remains the only valid model. Theory of Nuclear Forces ... IWND09, Shanghai, 8-24-09

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