Halo nuclei are a promising new arena for studies based on effective field theory (EFT). We develop an EFT for shallow p-wave states and discuss the application to elastic nα scattering. In contrast to the s-wave case, both the scattering length and effective range enter at leading order. We also discuss the prospects of using EFT in the description of other halos, such as the three-body halo nucleus 6 He.

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Efimov states are a sequence of shallow 3-body bound states that arise when the 2-body scattering length is large. Efimov showed that the binding energies of these states can be calculated in terms of the scattering length and a 3-body parameter by solving a transcendental equation involving a universal function of one variable. We calculate this universal function using effective field theory and use it to describe the three-body system of 4 He atoms. We also extend Efimov's theory to include the effects of deep 2-body bound states, which give widths to the Efimov states.

The virtues of an effective field theory (EFT) approach to many-body problems are illustrated by deriving the expansion for the energy of an homogeneous, interacting Fermi gas at low density and zero temperature. A renormalization scheme based on dimensional regularization with minimal subtraction leads to a more transparent power-counting procedure and diagrammatic expansion than conventional many-body approaches. Coefficients of terms in the expansion with logarithms of the Fermi momentum are determined by the renormalization properties of the EFT that describes few-body scattering. Lessons for an EFT treatment of nuclear matter are discussed.

An effective field theory for the three-body system with large two-body scattering length a is applied to three-body recombination into deep bound states in a Bose gas. The recombination constant alpha is calculated to first order in the short-distance interactions that allow the recombination. For a < 0, the dimensionless combination m alpha/(Planck's constant a(4)) is a periodic function of ln (absolute value a) that exhibits resonances at values of a that differ by multiplicative factors of 22.7. This dramatic behavior should be observable near a Feshbach resonance when a becomes large and negative.