We expand the scattering amplitude and the scattering matrix around the zero-range limit, i.e., with point interactions, in the case when the potential has a finite number of wells. The lower-order terms are largely independent of the shape of the potentials.

Journal of Mathematical PhysicsJan 1, 19855 citations

Functional renormalization group for few-nucleon systems: SU(4) symmetry and its breaking

Michael C. Birse, Boris Krippa, Niels R. Walet

arXiv:1207.5735Physical Review CMay 8, 20137 citations

Ядерная физика

Does the Multiple-Scattering Series in the Pion–Deuteron Scattering Actually Converge?

A. E. Kudryavtsev, A. I. Romanov, Vakhid A. Gani

Published Jan 1, 2013• 0 citations

Publisher

Abstract

DOI: 10.7868/s0044002713070106

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Functional renormalization group for few-nucleon systems: SU(4) symmetry and its breaking

Michael C. Birse, Boris Krippa, Niels R. Walet

We apply the functional renormalization group to few-nucleon systems. Our starting point is a local effective action that includes three- and four-nucleon interactions, expressed in terms of nucleon and two-nucleon boson fields. The evolution of the coupling constants in this action is described by a renormalization group flow. We derive these flow equations both in the limit of exact Wigner SU(4) symmetry and in the realistic case of broken symmetry. In the symmetric limit we find that the renormalization flow equations decouple and can be combined into two sets, one of which matches the known results for bosons, and the other result matches the one for a single flavor of spin $1/2$ fermions. The equations show universal features in the unitary limit, which is obtained when the two-body scattering length tends to infinity. We calculate the spin-quartet neutron-deuteron scattering length and the deuteron-deuteron scattering lengths in the spin-singlet and spin-quintet channels.We apply the functional renormalization group to few-nucleon systems. Our starting point is a local effective action that includes three- and four-nucleon interactions, expressed in terms of nucleon and two-nucleon boson fields. The evolution of the coupling constants in this action is described by a renormalization group flow. We derive these flow equations both in the limit of exact Wigner SU(4) symmetry and in the realistic case of broken symmetry. In the symmetric limit we find that the renormalization flow equations decouple and can be combined into two sets, one of which matches the known results for bosons, and the other result matches the one for a single flavor of spin $1/2$ fermions. The equations show universal features in the unitary limit, which is obtained when the two-body scattering length tends to infinity. We calculate the spin-quartet neutron-deuteron scattering length and the deuteron-deuteron scattering lengths in the spin-singlet and spin-quintet channels.

arXiv:1207.5735Physical Review CMay 8, 20137 citations

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fermions. The equations show universal features in the unitary limit, which is obtained when the two-body scattering length tends to infinity. We calculate the spin-quartet neutron-deuteron scattering length and the deuteron-deuteron scattering lengths in the spin-singlet and spin-quintet channels.