Quantitative Relativistic Effects in the Three-Nucleon Problem

The quantitative impact of the requirement of relativistic invariance in the three-nucleon problem is examined within the framework of Poincar\'e invariant quantum mechanics. In the case of the bound state, and for a wide variety of model implementations and reasonable interactions, most of the quantitative effects come from kinematic factors that can easily be incorporated within a non-relativistic momentum-space three-body code.Comment: 15 pages, 15 figure

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.Comment: 26 pages, 13 figure

Relativistic quantum theories and neutrino oscillations

Neutrino oscillations are examined under the broad requirements of Poincar\'e-invariant scattering theory in an S-matrix formulation. This approach can be consistently applied to theories with either field or particle degrees of freedom. The goal of this paper is to use this general framework to identify all of the unique physical properties of this problem that lead to a simple oscillation formula. We discuss what is in principle observable, and how many factors that are important in principle end up being negligible in practice.Comment: 21 pages, no figure

The Balian-Br\'ezin Method in Relativistic Quantum Mechanics

The method suggested by Balian and Br\'ezin for treating angular momentum reduction in the Faddeev equations is shown to be applicable to the relativistic three-body problem.Comment: 14 pages in LaTe

Wavelet Methods in the Relativistic Three-Body Problem

In this paper we discuss the use of wavelet bases to solve the relativistic three-body problem. Wavelet bases can be used to transform momentum-space scattering integral equations into an approximate system of linear equations with a sparse matrix. This has the potential to reduce the size of realistic three-body calculations with minimal loss of accuracy. The wavelet method leads to a clean, interaction independent treatment of the scattering singularities which does not require any subtractions.Comment: 14 pages, 3 figures, corrected referenc

Comparison of Relativistic Nucleon-Nucleon Interactions

We investigate the difference between those relativistic models based on interpreting a realistic nucleon-nucleon interaction as a perturbation of the square of a relativistic mass operator and those models that use the method of Kamada and Gl\"ockle to construct an equivalent interaction to add to the relativistic mass operator. Although both models reproduce the phase shifts and binding energy of the corresponding non-relativistic model, they are not scattering equivalent. The example of elastic electron-deuteron scattering in the one-photon-exchange approximation is used to study the sensitivity of three-body observables to these choices. Our conclusion is that the differences in the predictions of the two models can be understood in terms of the different ways in which the relativistic and non-relativistic $S$-matrices are related. We argue that the mass squared method is consistent with conventional procedures used to fit the Lorentz-invariant cross section as a function of the laboratory energy.Comment: Revtex 13 pages, 5 figures, corrected some typo

Solving the inhomogeneous Bethe-Salpeter equation

We develop an advanced method of solving homogeneous and inhomogeneous Bethe-Salpeter equations by using the expansion over the complete set of 4-dimensional spherical harmonics. We solve Bethe-Salpeter equations for bound and scattering states of scalar and spinor particles for the case of one meson exchange kernels. Phase shifts calculated for the scalar model are in agreement with the previously published results. We discuss possible manifestations of separability for one meson exchange interaction kernels.Comment: 9 pages, 11 eps-figures. Talk presented by S. S. Semikh at XVII International Baldin Seminar on High Energy Physics Problems "Relativistic Nuclear Physics and Quantum Chromodynamics", September 27 - October 2, 2004, Dubna, Russia; to appear in the proceedings of this conferenc

Vacuum Structures in Hamiltonian Light-Front Dynamics

Hamiltonian light-front dynamics of quantum fields may provide a useful approach to systematic non-perturbative approximations to quantum field theories. We investigate inequivalent Hilbert-space representations of the light-front field algebra in which the stability group of the light-front is implemented by unitary transformations. The Hilbert space representation of states is generated by the operator algebra from the vacuum state. There is a large class of vacuum states besides the Fock vacuum which meet all the invariance requirements. The light-front Hamiltonian must annihilate the vacuum and have a positive spectrum. We exhibit relations of the Hamiltonian to the nontrivial vacuum structure.Comment: 16 pages, report \# ANL-PHY-7524-TH-93, (Latex

The AyA_y Puzzle and the Nuclear Force

The nucleon-deuteron analyzing power $A_y$ in elastic nucleon-deuteron scattering poses a longstanding puzzle. At energies $E_{lab}$ below approximately 30 MeV $A_y$ cannot be described by any realistic NN force. The inclusion of existing three-nucleon forces does not improve the situation. Because of recent questions about the $^3P_J$ NN phases, we examine whether reasonable changes in the NN force can resolve the puzzle. In order to do this we investigate the effect on the $^3P_J$ waves produced by changes in different parts of the potential (viz., the central force, tensor force, etc.), as well as on the 2-body observables and on $A_y$. We find that it is not possible with reasonable changes in the NN potential to increase the 3-body $A_y$ and at the same time to keep the 2-body observables unchanged. We therefore conclude that the $A_y$ puzzle is likely to be solved by new three-nucleon forces, such as those of spin-orbit type, which have not yet been taken into account.Comment: 35 pages in REVTeX, 1 figure in postscript and 3 figures in PiCTe

Nucleon electromagnetic form factors

Elastic electromagnetic nucleon form factors have long provided vital information about the structure and composition of these most basic elements of nuclear physics. The form factors are a measurable and physical manifestation of the nature of the nucleons' constituents and the dynamics that binds them together. Accurate form factor data obtained in recent years using modern experimental facilities has spurred a significant reevaluation of the nucleon and pictures of its structure; e.g., the role of quark orbital angular momentum, the scale at which perturbative QCD effects should become evident, the strangeness content, and meson-cloud effects. We provide a succinct survey of the experimental studies and theoretical interpretation of nucleon electromagnetic form factors.Comment: Topical review invited by Journal of Physics G: Nuclear and Particle Physics; 34 pages (contents listed on page 34), 11 figure