The three-body problem with short-range forces: renormalized equations and regulator-independent results

Abstract

We discuss effective field theory treatments of the problem of three particles interacting via short-range forces. One case of such a system is neutron-deuteron scattering at low energies. We demonstrate that in attractive channels the renormalization-group evolution of the 1+2 scattering amplitude may be complicated by the presence of eigenvalues greater than unity in the kernel. We also show that these eigenvalues can be removed from the kernel by one subtraction, resulting in an equation which is renormalization-group invariant. A unique solution for 1+2 scattering phase shifts is then obtained. We give an explicit demonstration of our procedure for both the case of three spinless bosons and the case of the doublet channel in nd scattering. After the contribution of the two-body effective range is included in the effective field theory, it gives a good description of the nd doublet phase shifts below deuteron breakup threshold.

35 pages, 7 figures. Physical Review C to be published

References in corpus (18)

• A New Expansion for Nucleon-Nucleon Interactions
• Two-Nucleon Systems from Effective Field Theory
• Renormalization of the Three-Body System with Short-Range Interactions
• Effective Field Theory for Short-Range Forces
• The Three-Boson System with Short-Range Interactions
• Effective Theory of the Triton
• More Effective Field Theory for Nonrelativistic Scattering
• Nucleon-Deuteron Scattering from an Effective Field Theory
• Low Energy Expansion in the Three Body System to All Orders and the Triton Channel
• Improving the Convergence of NN Effective Field Theory
• Range Corrections to Doublet S-Wave Neutron-Deuteron Scattering
• Renormalization of the one-pion-exchange interaction
• Quartet S Wave Neutron Deuteron Scattering in Effective Field Theory
• Universality in the Three-Body Problem for 4He Atoms
• A renormalized equation for the three-body system with short-range interactions
• Efimov States in a Bose-Einstein Condensate near a Feshbach Resonance
• Deuteron electromagnetic properties and the viability of effective field theory methods in the two-nucleon system
• Building light nuclei from neutrons, protons, and pions

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• Universality in Few-body Systems with Large Scattering Length
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• Efimov Physics in Cold Atoms
• Efimov States in Nuclear and Particle Physics
• Improved Convergence in the Three-Nucleon System at Very Low Energies
• Naive Dimensional Analysis for Three-Body Forces Without Pions
• Renormalization of Singular Potentials and Power Counting
• Universality and scaling limit of weakly-bound tetramers
• Implications of a matter-radius measurement for the structure of Carbon-22
• Range Corrections to Three-Body Observables near a Feshbach Resonance
• Subtractive renormalization of the NN scattering amplitude at leading order in chiral effective theory
• Subtractive renormalization of the NN interaction in chiral effective theory up to next-to-next-to-leading order: S waves
• Subtractive renormalization of the chiral potentials up to next-to-next-to-leading order in higher NN partial waves
• Effective theories of scattering with an attractive inverse-square potential and the three-body problem
• Recursive renormalization of the singlet one-pion-exchange plus point-like interactions
• Effective Field Theory Analysis of Three-Boson Systems at Next-To-Next-To-Leading Order
• The Three-Nucleon System at Next-To-Next-To-Leading Order
• Effective density functionals beyond mean field
• Isotropic contact forces in arbitrary representation: heterogeneous few-body problems and low dimensions
• Two and Three Nucleons in a Trap and the Continuum Limit
• Universality in the triton charge form factor
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• Pion-mass dependence of three-nucleon observables
• More on the infrared renormalization group limit cycle in QCD
• The renormalisation group and nuclear forces
• New Calculations of Recombination Rates for Cold ${}^4$He Atoms and Determination of Universal Scaling Functions
• Second-order perturbation theory for 3He and pd scattering in pionless EFT
• Similarity Renormalization Group Evolution of Chiral Effective Nucleon-Nucleon Potentials in the Subtracted Kernel Method Approach
• Three Bosons in One Dimension with Short Range Interactions I: Zero Range Potentials
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• Effective interactions and operators in no-core shell model
• Van der Waals universality in homonuclear atom-dimer elastic collisions
• Toward a systematic strategy for defining power counting in the construction of the energy density functional theory
• P-Wave Two-Particle Bound and Scattering States in a Finite Volume including QED
• Universality in Few-Body Systems
• Effective Range Corrections in Few-Body Systems with large Scattering Length
• Fixed-Point Few-Body Hamiltonians in Quantum Mechanics
• Model-independent mass determination of near-threshold states from short-range production