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Title: Effective field theory of nucleon-nucleon scattering on large discrete lattices

Abstract

Nuclear effective field theory is applied to the effective-range expansion of S-wave nucleon-nucleon scattering on a discrete lattice. Lattice regularization is demonstrated to yield the effective-range expansion in the same way as in the usual continuous open space. The relation between the effective-range parameters and the potential parameters is presented in the limit of a large lattice.

Authors:
 [1];  [2];  [3]
  1. Department of Physics and Astronomy, California State University, Northridge, Northridge, California 91330 (United States)
  2. (United States)
  3. Department of Physics, University of Arizona, Tucson, Arizona 85721 (United States)
Publication Date:
OSTI Identifier:
20771423
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. C, Nuclear Physics; Journal Volume: 73; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevC.73.044006; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; LATTICE FIELD THEORY; NUCLEAR FORCES; NUCLEAR REACTION YIELD; NUCLEON-NUCLEON INTERACTIONS; POTENTIALS; S WAVES

Citation Formats

Seki, Ryoichi, W.K. Kellogg Radiation Laboratory, California Institute of Technology, Pasadena, California 91125, and Kolck, U. van. Effective field theory of nucleon-nucleon scattering on large discrete lattices. United States: N. p., 2006. Web. doi:10.1103/PhysRevC.73.044006.
Seki, Ryoichi, W.K. Kellogg Radiation Laboratory, California Institute of Technology, Pasadena, California 91125, & Kolck, U. van. Effective field theory of nucleon-nucleon scattering on large discrete lattices. United States. doi:10.1103/PhysRevC.73.044006.
Seki, Ryoichi, W.K. Kellogg Radiation Laboratory, California Institute of Technology, Pasadena, California 91125, and Kolck, U. van. Sat . "Effective field theory of nucleon-nucleon scattering on large discrete lattices". United States. doi:10.1103/PhysRevC.73.044006.
@article{osti_20771423,
title = {Effective field theory of nucleon-nucleon scattering on large discrete lattices},
author = {Seki, Ryoichi and W.K. Kellogg Radiation Laboratory, California Institute of Technology, Pasadena, California 91125 and Kolck, U. van},
abstractNote = {Nuclear effective field theory is applied to the effective-range expansion of S-wave nucleon-nucleon scattering on a discrete lattice. Lattice regularization is demonstrated to yield the effective-range expansion in the same way as in the usual continuous open space. The relation between the effective-range parameters and the potential parameters is presented in the limit of a large lattice.},
doi = {10.1103/PhysRevC.73.044006},
journal = {Physical Review. C, Nuclear Physics},
number = 4,
volume = 73,
place = {United States},
year = {Sat Apr 15 00:00:00 EDT 2006},
month = {Sat Apr 15 00:00:00 EDT 2006}
}
  • We investigate in detail the effect of making the range of the {open_quotes}contact{close_quotes} interaction used in effective field theory (EFT) calculations of NN scattering finite. This is done in both an effective field theory with explicit pions, and one where the pions have been integrated out. In both cases we calculate NN scattering in the {sup 1}S{sub 0} channel using potentials which are second order in the EFT expansion. The contact interactions present in the EFT Lagrangian are made finite by use of a square-well regulator. We find that there is an optimal radius for this regulator, at which second-ordermore » corrections to the EFT are identically zero; for radii near optimal these second-order corrections are small. The cutoff EFT{close_quote}s which result from this procedure appear to be valid for momenta up to about 100{endash}150MeV/c. We also find that the radius of the square well cannot be reduced to zero if the theory is to reproduce both the experimental scattering length and effective range. Indeed, we show that, if the NN potential is the sum of a one-pion-exchange piece and a short-range interaction, then the short-range piece must extend out beyond 1.05 fm, regardless of its particular form. {copyright} {ital 1997} {ital The American Physical Society}« less
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  • We use effective field theory (EFT) to calculate the nucleon-nucleon scattering amplitude up to next-to-next-to-leading order (NNLO), where we include instantaneous pion exchange but ignore retardation effects. The scattering amplitude in the {sup 1}S{sub 0} channel is calculated using the Kaplan-Savage-Wise power counting scheme. An expansion of the amplitude about the pole at low (imaginary) momentum is used to derive matching conditions for the EFT couplings. After imposing constraints from a renormalization group flow analysis, there are no new free parameters in the amplitude at NNLO. We apply the calculation to a toy model in which there is only instantaneousmore » pion exchange by construction, namely, the two-Yukawa model. We find that, through next-to-next-to-leading order, each successive term in the low energy expansion does systematically improve the approximation to the full amplitude. {copyright} {ital 1999} {ital The American Physical Society}« less