arXiv subjects

Ch. Elster

Publications and source records attributed to Ch. Elster.

At least 73 records · Page 4Linked to original sources

arXiv2007

Three-body scattering in Poincaré invariant quantum mechanics

The relativistic three-nucleon problem is formulated by constructing a dynamical unitary representation of the Poincaré group on the three-nucleon Hilbert space. Two-body interactions are included that preserve the Poincaré symmetry, lead to the same invariant two-body S-matrix as the corresponding non-relativistic problem, and result in a three-body S-matrix satisfying cluster properties. The resulting Faddeev equations are solved by direct integration, without partial waves for both elastic and breakup reactions at laboratory energies up to 2 Gev.

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arXiv2007

Relativistic Effects in Exclusive pd Breakup Scattering at Intermediate Energies

The relativistic Faddeev equation for three-nucleon scattering is formulated in momentum space and directly solved in terms of momentum vectors without employing a partial wave decomposition. Relativistic invariance is achieved by constructing a dynamical unitary representation of the Poincaré group on the three-nucleon Hilbert space. The exclusive breakup reaction at 508 MeV is calculated based on a Malfliet-Tjon type of two-body interaction and the cross sections are compared to measured cross sections at this energy. We find that the magnitude of the relativistic effects can be quite large and depends on the configurations considered. In spite of the simple nature of the model interaction, the experimental cross sections are in surprisingly good agreement with the predictions of the relativistic calculations. We also find that although for specific configurations the multiple scattering series converges rapidly, this is in general not the case.

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arXiv2007

Relativistic Three-Body Scattering in a First Order Faddeev Formulation

Relativistic Faddeev equations for three-body scattering at arbitrary energies are solved in first order in the two-body transition operator in terms of momentum vectors without employing a partial wave decomposition. Relativistic invariance is incorporated within the framework of Poincar{é} invariant quantum mechanics. Based on a Malfliet-Tjon type interaction, observables for elastic and breakup scattering are calculated and compared to the nonrelativistic ones.

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arXiv2007

Influence of the N(1440) and N(1535) Resonances in Intermediate Energy pp and np Scattering

Motivated by a recent measurement of proton-proton elastic scattering observables up to 3.0 GeV, we investigate the description of those data within models of the nucleon-nucleon (NN) interaction valid above the pion production threshold. In addition to including the well known Delta resonance we incorporate two low-lying N* resonances, the N*(1440) and the N*(1535), and study their influence on pp and np observables for projectile laboratory kinetic energies up to 1.5 GeV.

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arXiv2007

Three-Nucleon Scattering at Intermediate Energies

By means of a technique, which does not employ partial wave (PW) decompositions, the nucleon-deuteron break-up process is evaluated in the Faddeev scheme, where only the leading order term of the amplitude is considered. This technique is then applied to calculate the semi-exclusive proton-deuteron break-up reaction d(p,n)pp for proton laboratory energies Elab of a few hundred MeV. A comparison with PW calculations is performed at 197 MeV projectile energy. At the same energy rescattering processes, which are not included in the 3D calculations yet, are shown to be still important in the full Faddeev PW calculations, especially for the cross section and the analyzing power Ay. Next, kinematical relativistic effects are investigated for projectile energies up to about 500 MeV. At the higher energies, those relativistic effects start not to be negligible, especially in the peak of the cross section.

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arXiv2007

First Order Relativistic Three-Body Scattering

Relativistic Faddeev equations for three-body scattering at arbitrary energies are formulated in momentum space and in first order in the two-body transition-operator directly solved in terms of momentum vectors without employing a partial wave decomposition. Relativistic invariance is incorporated within the framework of Poincare invariant quantum mechanics, and presented in some detail. Based on a Malfliet-Tjon type interaction, observables for elastic and break-up scattering are calculated up to projectile energies of 1 GeV. The influence of kinematic and dynamic relativistic effects on those observables is systematically studied. Approximations to the two-body interaction embedded in the three-particle space are compared to the exact treatment.

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arXiv2006

Three-Body Elastic and Inelastic Scattering at Intermediate Energies

The Faddeev equation for three-body scattering at arbitrary energies is formulated in momentum space and directly solved in terms of momentum vectors without employing a partial wave decomposition. For identical bosons this results in a three-dimensional integral equation in five variables, magnitudes of relative momenta and angles. The cross sections for both elastic and breakup processes in the intermediate energy range up to about 1 GeV are calculated based on a Malfliet-Tjon type potential, and the convergence of the multiple scattering series is investigated.

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arXiv2005

The near threshold N N -> d pi reaction in chiral perturbation theory

The near-threshold n p -> d pi0 cross section is calculated in chiral perturbation theory to next-to-leading order in the expansion parameter sqrt{M m_pi}/Lambda_chi. At this order irreducible pion loops contribute to the relevant pion-production operator. While their contribution to this operator is finite, considering initial-and final-state distortions produces a linear divergence in its matrix elements. We renormalize this divergence by introducing a counterterm, whose value we choose in order to reproduce the threshold n p -> d pi0 cross section measured at TRIUMF. The energy-dependence of this cross section is then predicted in chiral perturbation theory, being determined by the production of p-wave pions, and also by energy dependence in the amplitude for the production of s-wave pions. With an appropriate choice of the counterterm, the chiral prediction for this energy dependence converges well.

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arXiv2005

Charged and neutral pion production in the S-matrix approach

The S-matrix approach is used to calculate charged as well as neutral pion production reactions from NN scattering, with the same set of underlying processes and interactions. The chiral perturbation theory piN scattering amplitude is used. For the nucleon-nucleon distortions a newly developed realistic potential within the Bonn family of potentials, valid well above the pion production threshold, is considered. In the pi+ production case, the NN potential, the piN relative p-waves and the treatment of the exchanged pion energy build up the observed cross-section strength.

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arXiv2005

Three-Body Scattering at Intermediate Energies

The Faddeev equation for three-body scattering at arbitrary energies is formulated in momentum space and directly solved in terms of momentum vectors without employing a partial wave decomposition. In its simplest form the Faddeev equation for identical bosons, which we are using, is a three-dimensional integral equation in five variables, magnitudes of relative momenta and angles. This equation is solved through Pade summation. Based on a Malfliet-Tjon-type potential, the numerical feasibility and stability of the algorithm for solving the Faddeev equation is demonstrated. Special attention is given to the selection of independent variables and the treatment of three-body break-up singularities with a spline based method. The elastic differential cross section, semi-exclusive d(N,N') cross sections and total cross sections of both elastic and breakup processes in the intermediate energy range up to about 1 GeV are calculated and the convergence of the multiple scattering series is investigated in every case. In general a truncation in the first or second order in the two-body t-matrix is quite insufficient.

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arXiv2004

Three-Body Scattering without Partial Waves

The Faddeev equation for three-body scattering at arbitrary energies is formulated in momentum space and directly solved in terms of momentum vectors without employing a partial wave decomposition. In its simplest form the Faddeev equation for identical bosons is a three-dimensional integral equation in five variables, magnitudes of relative momenta and angles. The elastic differential cross section, semi-exclusive d(N,N') cross sections and total cross sections of both elastic and breakup processes in the intermediate energy range up to about 1 GeV are calculated based on a Malfliet-Tjon type potential, and the convergence of the multiple scattering series is investigated in every case. In general a truncation in the first or second order in the two-body t-matrix is quite insufficient.

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arXiv2004

The Operator form of 3H (3He) and its Spin Structure

An operator form of the 3N bound state is proposed. It consists of eight operators formed out of scalar products in relative momentum and spin vectors, which are applied on a pure 3N spin 1/2 state. Each of the operators is associated with a scalar function depending only on the magnitudes of the two relative momenta and the angle between them. The connection between the standard partial wave decomposition of the 3N bound state and the operator form is established, and the decomposition of these scalar function in terms of partial wave components and analytically known auxiliary functions is given. That newly established operator form of the 3N bound state exhibits the dominant angular and spin dependence analytically. The scalar functions are tabulated and can be downloaded. As an application the spin dependent nucleon momentum distribution in a polarized 3N bound state is calculated to illustrate the use of the new form of the 3N bound state.

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arXiv2003

Model Study of Three-Body Forces in the Three-Body Bound State

The Faddeev equations for the three-body bound state with two- and three-body forces are solved directly as three-dimensional integral equation. The numerical feasibility and stability of the algorithm, which does not employ partial wave decomposition is demonstrated. The three-body binding energy and the full wave function are calculated with Malfliet-Tjon-type two-body potentials and scalar Fujita-Miyazawa type three-body forces. The influence of the strength and range of the three-body force on the wave function, single particle momentum distributions and the two-body correlation functions are studied in detail. The extreme case of pure three-body forces is investigated as well.

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arXiv2003

The Nd Break-Up Process in Leading Order in a Three-Dimensional Approach

A three-dimensional approach based on momentum vectors as variables for solving the three nucleon Faddeev equation in first order is presented. The nucleon-deuteron break-up amplitude is evaluated in leading order in the NN T-matrix, which is also generated directly in three dimensions avoiding a summation of partial wave contributions. A comparison of semi-exclusive observables in the $d(p,n)pp$ reaction calculated in this scheme with those generated by a traditional partial wave expansion shows perfect agreement at lower energies. At about 200 MeV nucleon laboratory energies deviations in the peak of the cross section appear, which may indicate that special care is required in a partial wave approach for energies at and higher than 200 MeV. The role of higher order rescattering processes beyond the leading order in the NN T-matrix is investigated with the result, that at 200 MeV rescattering still provides important contributions to the cross section and certain spin observables. The influence of a relativistic treatment of the kinematics is investigated. It is found that relativistic effects become important at projectile energies higher than 200 MeV.

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arXiv2003

Photoproduction of eta-prime-mesons from the Proton

The presently available data for the reaction $γp{\to}η^\prime{p}$ are analyzed in terms of a model in which the dominant production mechanism is the exchange of the vector mesons $ω$ and $ρ$. To describe the data at photon energies close to the production threshold we introduce a resonance contribution due to the well established $S_{11}(1535)$ resonance. Finally we study the contributions due to nucleon exchange to the $η^\prime$ photoproduction and find, that those contributions can be seen at large angles in the differential cross section.

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arXiv2002

The Proton-Deuteron Break-Up Process in a Three-Dimensional Approach

The pd break-up amplitude in the Faddeev scheme is calculated by employing a three-dimensional method without partial wave decomposition (PWD). In a first step and in view of higher energies only the leading term is evaluated and this for the process d(p,n)pp. A comparison with the results based on PWD reveals discrepancies in the cross section around 200 MeV. This indicates the onset of a limitation of the partial wave scheme. Also, around 200 MeV relativistic effects are clearly visible and the use of relativistic kinematics shifts the cross section peak to where the experimental peak is located. The theoretical peak height, however, is wrong and calls first of all for the inclusion of rescattering terms, which are shown to be important in a nonrelativistic full Faddeev calculation in PWD.

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arXiv2002

Lorentz Boosted NN Potential for Few-Body Systems: Application to the three-nucleon bound state

A Lorentz boosted two-nucleon potential is introduced in the context of equal time relativistic quantum mechanics. The dynamical input for the boosted nucleon-nucleon (NN) potential is based on realistic NN potentials, which by a suitable scaling of the momenta are transformed into NN potentials belonging to a relativistic two-nucleon Schroedinger equation in the c.m. system. This resulting Lorentz boosted potential is consistent with a previously introduced boosted two-body t-matrix. It is applied in relativistic Faddeev equations for the three-nucleon bound state to calculate the ^3H binding energy. Like in previous calculations the boost effects for the two-body subsystems are repulsive and lower the binding energy.

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arXiv2002

Toy Model for Pion Production II: The role of three-particle singularities

The influence of three-particle breakup singularities on s-wave meson production in nucleon-nucleon collisions is studied within the distorted wave Born approximation. This study is based on a simple scalar model for the two-nucleon interaction and the production mechanism. An algorithm for the exact numerical treatment of the inherent three-body cuts, together with its straightforward implementation is presented. It is also shown that two often-used approximations to avoid the calculation of the three-body breakup are not justified. The possible impact on pion production observables is discussed.

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