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Title: Dominant 2{pi}{gamma}-exchange nucleon-nucleon interaction: Spin-spin and tensor potentials

Abstract

We calculate at two-loop order in chiral perturbation theory the electromagnetic corrections to the two-pion exchange nucleon-nucleon interaction that is generated by the isovector spin-flip {pi}{pi}NN contact-vertex proportional to the large low-energy constant c{sub 4}{approx_equal}3.4 GeV{sup -1}. We find that the respective 2{pi}{gamma}-exchange potentials contain sizable isospin-breaking components which reach up to -4% of corresponding isovector 2{pi}-exchange potentials. The typical values of these novel charge-independence breaking spin-spin and tensor potentials are -0.11 and 0.09 MeV, at a nucleon distance of r=m{sub {pi}}{sup -1}=1.4 fm. The charge-symmetry breaking spin-spin and tensor potentials come out a factor of 2.4 smaller. Our analytical results for these presumably dominant isospin-violating spin-spin and tensor NN-forces are in a form such that they can be easily implemented into phase-shift analyses and few-body calculations.

Authors:
 [1]
  1. Physik Department T39, Technische Universitaet Muenchen, D-85747 Garching (Germany)
Publication Date:
OSTI Identifier:
20864247
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. C, Nuclear Physics; Journal Volume: 74; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevC.74.067001; (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; CHARGE INDEPENDENCE; CHIRALITY; CORRECTIONS; DISTANCE; ISOSPIN; ISOVECTORS; MEV RANGE; NUCLEON-NUCLEON INTERACTIONS; NUCLEONS; PERTURBATION THEORY; PHASE SHIFT; PIONS; POTENTIALS; SPIN; SPIN FLIP; SYMMETRY BREAKING

Citation Formats

Kaiser, N. Dominant 2{pi}{gamma}-exchange nucleon-nucleon interaction: Spin-spin and tensor potentials. United States: N. p., 2006. Web. doi:10.1103/PHYSREVC.74.067001.
Kaiser, N. Dominant 2{pi}{gamma}-exchange nucleon-nucleon interaction: Spin-spin and tensor potentials. United States. doi:10.1103/PHYSREVC.74.067001.
Kaiser, N. Fri . "Dominant 2{pi}{gamma}-exchange nucleon-nucleon interaction: Spin-spin and tensor potentials". United States. doi:10.1103/PHYSREVC.74.067001.
@article{osti_20864247,
title = {Dominant 2{pi}{gamma}-exchange nucleon-nucleon interaction: Spin-spin and tensor potentials},
author = {Kaiser, N.},
abstractNote = {We calculate at two-loop order in chiral perturbation theory the electromagnetic corrections to the two-pion exchange nucleon-nucleon interaction that is generated by the isovector spin-flip {pi}{pi}NN contact-vertex proportional to the large low-energy constant c{sub 4}{approx_equal}3.4 GeV{sup -1}. We find that the respective 2{pi}{gamma}-exchange potentials contain sizable isospin-breaking components which reach up to -4% of corresponding isovector 2{pi}-exchange potentials. The typical values of these novel charge-independence breaking spin-spin and tensor potentials are -0.11 and 0.09 MeV, at a nucleon distance of r=m{sub {pi}}{sup -1}=1.4 fm. The charge-symmetry breaking spin-spin and tensor potentials come out a factor of 2.4 smaller. Our analytical results for these presumably dominant isospin-violating spin-spin and tensor NN-forces are in a form such that they can be easily implemented into phase-shift analyses and few-body calculations.},
doi = {10.1103/PHYSREVC.74.067001},
journal = {Physical Review. C, Nuclear Physics},
number = 6,
volume = 74,
place = {United States},
year = {Fri Dec 15 00:00:00 EST 2006},
month = {Fri Dec 15 00:00:00 EST 2006}
}
  • Two-pion-exchange (TPE) nucleon-nucleon potentials are derived for one or two {Delta} isobars in the intermediate states. Strong dynamical pair suppression is assumed. At the {ital NN}{pi} and the {ital N}{Delta}{pi} vertices Gaussian form factors are incorporated into the relativistic two-body framework by using a dispersion representation for the one-pion-exchange amplitudes. The Fourier transformations are performed using factorization techniques for the energy denominators, taking into account the mass difference between the nucleon and the {Delta} isobar. Analytic expressions for the TPE potentials are obtained, which contain at most one-dimensional integrals. The TPE potentials are first calculated up to orders ({ital f}{submore » {ital N}{ital N}{pi}} f{sub {ital N}{Delta}{pi}}){sup 2} and {ital f}{sub {ital N}{Delta}{pi}}{sup 4}. These come from the adiabatic contributions of all planar and crossed three-dimensional momentum-space TPE diagrams. We also give the contributions of the OPE iteration, which can be subtracted or not, depending on whether one performs a coupled-channel calculation for, e.g., the {ital NN}, {ital N}{Delta} system, or a single {ital NN}-channel calculation. Next, we calculate the ({ital m}{sub {pi}}/{ital M}) corrections. These are due to the 1/{ital M} terms in the pion-nucleon vertices, and the 1/{ital M} terms in the nonadiabatic expansion of the nucleon energies in the intermediate states.« less
  • The authors compare the {pi}N scattering amplitudes which underlie 2{pi}-exchange three-nucleon forces (TBFs) with the experimental {pi}N amplitudes. The amplitudes of the Tucson-Melbourne and Brazil TBFs when taken on-pion-mass-shell predict scattering lengths at threshold and phase shifts (slightly) above threshold which are in good agreement with the experimental amplitudes, except for the S-waves. Partial wave amplitudes from separable potentials, recently employed in a 2{pi}-TBF calculation, were continued below threshold, summed into invariant amplitudes, and compared with the experimental amplitudes in this kinematic region which is most relevant to the kinematics of TBFs. The separable potential invariant amplitudes, in contrast tomore » those of TM and Brazil TBFs, do not compare well quantitatively with the experimental amplitudes in this region but have a similar qualitative behavior. The very small TBF effect in the triton of the separable potential amplitude appears to be due to the {pi}NN vertex function rather than the {pi}N amplitude self.« less
  • Pion-rho-exchange nucleon-nucleon potentials are derived for one or two {Delta} isobars in the intermediate states. As in the companion work on two-pion exchange, strong dynamical pair suppression is assumed. At the {ital NN}{pi}, {rho} and {ital N}{Delta}{pi}, {rho} vertices Gaussian form factors are incorporated into the relativistic two-body framework by using a dispersion representation for the {pi}- and {rho}-exchange amplitudes. The Fourier transformations are performed using factorization techniques for the energy denominators, taking into account the mass difference between the nucleon and the {Delta} isobar. The potentials are calculated in the adiabatic approximation of all planar and crossed three-dimensional momentum-spacemore » {pi}{rho} diagrams. We also give the contributions of the {pi}{rho} iteration, which can be subtracted or not, depending on whether one performs a coupled-channel calculation for, e.g., the {ital NN}, {ital N}{Delta} system, or a single {ital NN}-channel calculation.« less
  • >The total cross sections for processes yielding only neutral particles from 300 to 1600 Mev were determined. For this, the number of incident n- was counted, which interact in a liquid-hydrogen target without giving charged particles in a 4 x counter surrounding the target. The reactions pi -+ p yields pi /sup -/ no + n between 300 and 1100 Mev were separated. By supposing that only these two reactions were realized by placing lead absorbers between the target and 4 pi counter and by comparing the counting rate for neutral events with and without lead. The transmission raeasured ismore » a function of the average number of photons produced and therefore of the ratio between the two neutral channels, pi /sup 0/ + n and pi /sup 0/ + pi /sup 0/ + n. The experimental results are dis cussed and compared to those obtained in the study of photoproduction and the pi /sup -/ nucleon interaction. (auth)« less