Calvin Johnson

Dick Furnstahl

Erich Ormand

Bira van Kolck

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Laura Lee
(206) 685-3509

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Effective Field Theories and the Many-Body Problem

March 23 - June 5, 2009

The goal of this workshop is to tie together and build on the recent success stories in the nuclear many-body problem at different nucleon number A, which involve three broad communities:
  • Effective field theories (EFTs) and few-body systems. Nuclear EFTs, both pionful and pionless, incorporate QCD symmetries and allow systematic expansions of nuclear observables in powers of momenta. A related approach uses the renormalization group to generate low-momentum potentials.
  • General many-body theories (MBTs) for light and medium nuclei. Computational approaches include Green's Function and Auxiliary Field Monte Carlo, shell model (no-core, full configuration interaction, Monte Carlo, etc.), and coupled cluster methods. For light nuclides one has nearly exact calculations of bound states starting from good quality internucleon interactions.
  • Density functional theory (DFT) for medium and heavy nuclei. Computational limits preclude using MBTs to systematically address heavy nuclides, so one turns to density functional theory and its extensions. There are different phenomenological approaches, such as Skyrme, Gogny, and the relativistic meson-exchange models, and new microscopic approaches are under development.

There have been a few preliminary attempts to marry the elegance of EFTs to the power of recent many-body calculations, but significant conceptual and language barriers exist. We will provide a forum where these obstacles can be breached and cross-pollination pushed much farther. A goal is for EFT experts to go away with a good idea of what MBT and DFT practitioners need and can or cannot use, and for MBT and DFT practitioners to understand what EFTs can (currently) provide.

We note that all three communities restrict the many-body degrees of freedom--cutoffs in momentum or position space for EFTs, cutoffs in cluster correlations (for example) in MBTs, and placing the weight of correlations in the energy functional for DFTs. Can we have a unified framework for systematic and controlled reduction of the degrees of freedom for these disparate disciplines? How do we transplant information about reduced degrees of freedom from one community to another?

The workshop program will address three Big Questions, given here with some representative sub-questions:

  1. How do EFTs evolve with A, and can we at some point extrapolate smoothly?
    • How far in A (and density) can one push the pionless EFT?
    • How can we calculate with EFT for A > 3?
  2. How can we put the many-body dependence of EFTs in a tractable form into MBTs?
    • MBT methods have used EFT potentials as input in the same manner as phenomenological ones. Is there a more efficient/correct way to marry EFT and MBTs?
    • How can we improve the many-body methods? How does one derive simultaneous effective operators (for electron scattering, beta decay, etc.) along with the interaction itself? Can we justify approximations or selection of certain contributions with an EFT power counting?
    • Can we develop EFTs specifically for many-nucleon systems?
    • Can the choice of EFT fields be exploited to either minimize, or put into a form convenient for MBT and DFT, the three/many-body interaction?
  3. How can we use EFTs to constrain DFTs?
    • How can EFT help to provide much-needed controlled extrapolations and theoretical error bars?
    • Since DFT can be cast in the form of an effective action approach, it is immediately compatible with EFT in principle. How do we implement this in practice?
    • What are the possible EFTs for nuclear matter? Can we write an EFT around the Fermi surface? Does Pauli blocking make the EFT (more?) perturbative, as suggested by work with low-momentum potentials? Is there a covariant EFT that can explain and improve the successes of ``relativistic mean field'' phenomenology?