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U. van Kolck

Publications and source records attributed to U. van Kolck.

At least 109 records · Page 6Linked to original sources
arXiv1999

Charge-Independence Breaking in the Two-Pion-Exchange Nucleon-Nucleon Force

Charge-independence breaking due to the pion-mass difference in the (chiral) two-pion-exchange nucleon-nucleon force is investigated. A general argument based on symmetries is presented that relates the charge-symmetric part of that force to the proton-proton case. The static potential linear in that mass difference is worked out as an explicit example by means of Feynman diagrams, and this confirms the general argument.

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arXiv1999

Compton Scattering on the Deuteron in Baryon Chiral Perturbation Theory

Compton scattering on the deuteron is studied in the framework of baryon chiral perturbation theory to third order in small momenta, for photon energies of order the pion mass. The scattering amplitude is a sum of one- and two-nucleon mechanisms with no undetermined parameters. Our results are in good agreement with existing experimental data, and a prediction is made for higher-energy data being analyzed at SAL.

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arXiv1999

The N N -> NN pi+ Reaction near Threshold in a Chiral Power Counting Approach

Power-counting arguments are used to organize the interactions contributing to the N N -> d pi, p n pi reactions near threshold. We estimate the contributions from the three formally leading mechanisms: the Weinberg-Tomozawa (WT) term, the impulse term, and the $Δ$-excitation mechanism. Sub-leading but potentially large mechanisms, including $S$-wave pion-rescattering, the Galilean correction to the WT term, and short-ranged contributions are also examined. The WT term is shown to be numerically the largest, and the other contributions are found to approximately cancel. Similarly to the reaction p p -> p p pi0, the computed cross sections are considerably smaller than the data. We discuss possible origins of this discrepancy.

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arXiv1999

Effective Field Theory of Nuclear Forces

The application of the effective field theory (EFT) method to nuclear systems is reviewed. The roles of degrees of freedom, QCD symmetries, power counting, renormalization, and potentials are discussed. EFTs are constructed for various energy regimes of relevance in nuclear physics, and are used in systematic expansions to derive nuclear forces in terms of a number of parameters that embody information about QCD dynamics. Two-, three-, and many-nucleon systems, including external probes, are considered.

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arXiv1998

Renormalization of the Three-Body System with Short-Range Interactions

We discuss renormalization of the non-relativistic three-body problem with short-range forces. The problem becomes non-perturbative at momenta of the order of the inverse of the two-body scattering length, and an infinite number of graphs must be summed. This summation leads to a cutoff dependence that does not appear in any order in perturbation theory. We argue that this cutoff dependence can be absorbed in a single three-body counterterm and compute the running of the three-body force with the cutoff. We comment on relevance of this result for the effective field theory program in nuclear and molecular physics.

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arXiv1998

The Three-Boson System with Short-Range Interactions

We discuss renormalization of the non-relativistic three-body problem with short-range forces. The problem is non-perturbative at momenta of the order of the inverse of the two-body scattering length. An infinite number of graphs must be summed, which leads to a cutoff dependence that does not appear in any order in perturbation theory. We argue that this cutoff dependence can be absorbed in one local three-body force counterterm and compute the running of the three-body force with the cutoff. This allows a calculation of the scattering of a particle and the two-particle bound state if the corresponding scattering length is used as input. We also obtain a model-independent relation between binding energy of a shallow three-body bound state and this scattering length. We comment on the power counting that organizes higher-order corrections and on relevance of this result for the effective field theory program in nuclear and molecular physics.

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arXiv1998

Chiral Symmetry and Three-Nucleon Forces

After a brief review of the role three-nucleon forces play in the few-nucleon systems, the chiral-perturbation-theory approach to these forces is discussed. Construction of the (nominal) leading- and subleading-order Born terms and pion-rescattering graphs contributing to two-pion-exchange three-nucleon forces is reviewed, and comparisons are made of the types of such forces that are used today. It is demonstrated that the short-range $c$-term of the Tucson-Melbourne force is unnatural in terms of power counting and should be dropped. The class of two-pion-exchange three-nucleon forces then becomes rather uniform.

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arXiv1998

Effective Field Theory for Short-Range Forces

The method of effective field theories (EFTs) is developed for the scattering of two particles at wavelengths which are large compared to the range of their interaction. It is shown that the renormalized EFT is equivalent to the effective range expansion, to a Schroedinger equation with a pseudo-potential, and to an energy expansion of a generic boundary condition at the origin. The roles of regulators and potentials are also discussed. These ideas are exemplified in a toy model.

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arXiv1997

Nucleon-Nucleon Interaction and Isospin Violation

The application of the chiral effective theory to processes with two or more nucleons is discussed. We gain a qualitative understanding of the gross features of nuclear physics and quantitative, testable postdictions and predictions involving photons and pions.

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arXiv1997

Nucleon-Deuteron Scattering from an Effective Field Theory

We use an effective field theory to compute low-energy nucleon-deuteron scattering. We obtain the quartet scattering length using low energy constants entirely determined from low-energy nucleon-nucleon scattering. We find $a_{th}=6.33$ fm, to be compared to $a_{exp}=6.35\pm 0.02$ fm.

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arXiv1997

Electromagnetic Corrections to the One-Pion-Exchange Potential

Leading-order electromagnetic loop corrections to the one-pion-exchange potential are computed within the framework of chiral perturbation theory. These corrections generate an effective nucleon-nucleon potential, $V_{πγ}$, which supplements the sum of OPEP and the nucleon-nucleon Coulomb potential. This potential is charge dependent and its construction is demonstrated to be gauge invariant. The potential $V_{πγ}$ has been included in the Nijmegen partial-wave analysis of np data. A particular renormalization scheme is chosen that leads to a negligible change in the charged-piNN coupling constant and in the np 1S0 scattering length and effective range.

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arXiv1997

Chiral Perturbation Theory in Few-Nucleon Systems

The low-energy effective theory of nuclear physics based on chiral symmetry is reviewed. Topics discussed include the nucleon-nucleon force, few-body potentials, isospin violation, pion-deuteron scattering, proton-neutron radiative capture, pion photoproduction on the deuteron, and pion production in proton-proton collisions.

hep-ph↗
arXiv1997

Neutral pion photoproduction on deuterium in baryon chiral perturbation theory to order q^4

Threshold neutral pion photoproduction on the deuteron is studied in the framework of baryon chiral perturbation theory beyond next-to--leading order in the chiral expansion. To fourth order in small momenta, the amplitude is finite and a sum of two- and three-body interactions with no undetermined parameters. With accurate theoretical and experimental input from the single nucleon sector for the proton amplitude, we investigate the sensitivity of the threshold cross section to the elementary $γn \to π^0 n$ amplitude. A precise measurement of the threshold cross section for $γd \to π^0 d$ is called for.

hep-ph↗
arXiv1996

Meson Exchange and Pion Rescattering Contributions to the Cross Section for $pp\to ppπ^0$

Short range meson-exchange mechanisms such as $ρ\toωπ^0$ contribute significantly to the amplitude for $pp\rightarrow ppπ^0$ near threshold in addition to pion rescattering. The uncertainty of the latter contribution, which depends on poorly determined parameters, is estimated. Allowing for this uncertainty and taking the short range meson-exchange contributions into account makes it possible to reproduce the measured cross section.

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arXiv1996

The $p p \to p pπ^0$ Reaction near Threshold: A Chiral Power Counting Approach

We use power-counting arguments as an organizing principle to apply chiral perturbation theory, including an explicit $Δ$, to the $p p \rightarrow p p π^0$ reaction near threshold. There are two lowest-order leading mechanisms expected to contribute to the amplitude with similar magnitudes: an impulse term, and a $Δ$-excitation mechanism. We examine formally sub-leading but potentially large mechanisms, including pion-rescattering and short-ranged contributions. We show that the pion-rescattering contribution is enhanced by off-shell effects and has a sign opposite to that of a recent estimate based on a PCAC pion interpolating field. Our result is that the impulse term interferes destructively with the pion rescattering and $Δ$-excitation terms. In addition, we have modeled the short-ranged interaction using $σ$ and $ω$ exchange mechanisms. A recoil correction to the impulse approximation is small. The total amplitude obtained including all of these processes is found to yield cross sections substantially smaller than the measured ones.

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arXiv1996

Phenomenological Aspects of Isospin Violation in the Nuclear Force

Phenomenological Lagrangians and dimensional power counting are used to assess isospin violation in the nucleon-nucleon force. The $πNN$ coupling constants (including the Goldberger-Treiman discrepancy), charge-symmetry breaking, and meson-mixing models are examined. A one-loop analysis of the isospin-violating $πNN$ coupling constants is performed using chiral perturbation theory. Meson-mixing models and the $^3$He - $^3$H mass difference are also discussed in the context of naturalness.

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arXiv1995

Neutral Pion Photoproduction on Nuclei in Baryon Chiral Perturbation Theory

Threshold neutral pion photoproduction on light nuclei is studied in the framework of baryon chiral perturbation theory. We obtain a general formula for the electric dipole amplitude in the special case of neutral pion photoproduction on a nucleus. To third order in small momenta, the amplitude is a sum of 2- and 3-body interactions with no undetermined parameters. With reasonable input from the single nucleon sector, our result for neutral pion photoproduction on the deuteron is in agreement with experiment.

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