2,277 research outputs found
Nuclear Forces and Few-Nucleon Studies Based on Chiral Perturbation Theory
After a brief review on the status of few--nucleon studies based on
conventional nuclear forces, we sketch the concepts of the effective field
theory approach constrained by chiral symmetry and its application to nuclear
forces. Then first results for few--nucleon observables are discussed.Comment: 8 pages, presented by W. Gloeckle at the International Symposium on
"A New Era of Nuclear Structure Physics", Kurokawa Village (Niigata Pref.),
Japan, Nov. 19-22, 200
Few-Nucleon Systems with Two-Nucleon Forces from Chiral Effective Field Theory
Nucleon-nucleon (NN) forces from chiral perturbation theory at
next-to-leading (NLO) and next-to-next-to-leading order (NNLO) are applied to
systems with two, three and four nucleons. At NNLO, we consider two versions of
the chiral potential which differ in the strength of the two-pion-exchange
(TPE) but describe two nucleon observables equally well. The NNLO potential
leads to unphysical deeply bound states in the low partial waves and effects of
the 3N forces, which appear first at this order, are expected to be large. We
provide arguments for a reduction of the TPE potential and introduce the NNLO*
version of the NN forces. We calculate nd scattering observables as well as
various properties of 3H and 4He with the NNLO* potential and find good
agreement with the data and with predictions based upon the standard
high-precision potentials. We find an improved description of the 3H and 4He
binding energies.Comment: 34 pages, 25 figure
Chiral dynamics in few-nucleon systems
We report on recent progress achieved in calculating various few-nucleon
low-energy observables from effective field theory. Our discussion includes
scattering and bound states in the 2N, 3N and 4N systems and isospin violating
effects in the 2N system. We also establish a link between the nucleon-nucleon
potential derived in chiral effective field theory and various modern
high-precision potentials.Comment: 12 pp, uses aipproc style files, 4 figures, contribution to the
conference on "Mesons and Light Nuclei", Prag, July 2001, to appear in the
proceeding
Chiral dynamics in few-nucleon systems
We employ the chiral nucleon-nucleon potential derived using the method of
unitary transformation up to next-to-next-to-leading order (NNLO) to study
bound and scattering states in the two-nucleon system. The predicted partial
wave phase shifts and mixing parameters for higher energies and higher angular
momenta beyond the ones which are fitted are mostly well described for energies
below 300 MeV. Various deuteron properties are discussed. We also apply the
next-to-leading order (NLO) potential to 3N and 4N systems. The resulting 3N
and 4N binding energies are in the same range what is found using standard NN
potentials. Experimental low-energy 3N scattering observables are also very
well reproduced like for standard NN forces. Surprisingly the long standing
Ay-puzzle is resolved at NLO. The cut-off dependence of the scattering
observables is rather mild.Comment: LaTeX2e, 8 pages; invited talk presented at the XVIIth European
Conference on Few-Body Problems in Physics, Evora, Portugal, September 2000;
to be published in the Proceeding
Low-momentum effective theory for nucleons
Starting from a precise two-nucleon potential, we use the method of unitary
transformations to construct an effective potential that involves only momenta
less than a given maximal value. We describe this method for an S-wave
potential of the Malfliet-Tjon type. It is demonstrated that the bound and
scattering state spectrum calculated within the effective theory agrees exactly
with the one based on the original potential. This might open an avenue for the
construction of effective chiral few-nucleon forces and for a systematic
treatment of relativistic effects in few-body systems.Comment: 10 pp, LaTeX file, 4 figures (uses epsf), extended version, accepted
for publiaction in Phys.Lett.
Role of the total isospin 3/2 component in three-nucleon reactions
We discuss the role of the three-nucleon isospin T=3/2 amplitude in elastic
neutron-deuteron scattering and in the deuteron breakup reaction. The
contribution of this amplitude originates from charge-independence breaking of
the nucleon-nucleon potential and is driven by the difference between
neutron-neutron (proton-proton) and neutron-proton forces. We study the
magnitude of that contribution to the elastic scattering and breakup
observables, taking the locally regularized chiral N4LO nucleon-nucleon
potential supplemented by the chiral N2LO three-nucleon force. For comparison
we employ also the Av18 nucleon-nucleon potential combined with the Urbana IX
three-nucleon force. We find that the isospin T=3/2 component is important for
the breakup reaction and the proper treatment of charge-independence breaking
in this case requires the inclusion of the 1S0 state with isospin T=3/2. For
neutron-deuteron elastic scattering the T=3/2 contributions are insignificant
and charge-independence breaking can be accounted for by using the effective
t-matrix generated with the so-called "2/3-1/3" rule.Comment: 24 pages, 8 figures, 3 Table
The Galois Complexity of Graph Drawing: Why Numerical Solutions are Ubiquitous for Force-Directed, Spectral, and Circle Packing Drawings
Many well-known graph drawing techniques, including force directed drawings,
spectral graph layouts, multidimensional scaling, and circle packings, have
algebraic formulations. However, practical methods for producing such drawings
ubiquitously use iterative numerical approximations rather than constructing
and then solving algebraic expressions representing their exact solutions. To
explain this phenomenon, we use Galois theory to show that many variants of
these problems have solutions that cannot be expressed by nested radicals or
nested roots of low-degree polynomials. Hence, such solutions cannot be
computed exactly even in extended computational models that include such
operations.Comment: Graph Drawing 201
The six-nucleon Yakubovsky equations for 6He
The six-nucleon problem for the bound state is formulated in the Yakubovsky
scheme. Hints for a numerical implementation are provided.Comment: 25 pages, 0 figure
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