W. N. Polyzou

Charge Form-Factors of Quark Model Pions

We demonstrate that Poincare invariant quark models of the pion can give charge form factors in agreement with all available data. The quark-antiquark model wave functions are spin-zero eigenfunctions of the four-momentum. The relativistic features of the model are essential for the result. The confinement scale is much smaller than the charge radius.

Three-nucleon force in relativistic three-nucleon Faddeev calculations

We extend our formulation of relativistic three-nucleon Faddeev equations to include both pairwise interactions and a three-nucleon force. Exact Poincare invariance is realized by adding interactions to the mass Casimir operator (rest Hamiltonian) of the non-interacting system without changing the spin Casimir operator. This is achieved by using interactions defined by rotationally invariant kernels that are functions of internal momentum variables and single-particle spins that undergo identical Wigner rotations. To solve the resulting equations one needs matrix elements of the three-nucleon force with these properties in a momentum-space partial-wave basis. We present two methods to calculate matrix elements of three-nucleon forces with these properties. For a number of examples we show that at higher energies, where effects of relativity and of three-nucleon forces are non-negligible, a consistent treatment of both is required to properly analyze the data.

Three-body interactions and on-shell equivalent two-body interactions

The relation between on-shell equivalent two-body interactions and three-body interactions is formulated. Consequences of this relationship are discussed.

Relativistic two-body models

A new method is introduced for constructing relativistic models of two directly interacting particles. This method includes the construction of B. Bakmjian and L. H. Thomas ({ital Phys}. {ital Rev}. {bold 92} (1985), 995) and generalizations (S. N. Sokolov and Shatnii, {ital Teor}. {ital Mat}. {ital Fiz}. {bold 37} (1978), 291; F. Coester and W. N. Polyzou, {ital Phys}. {ital Rev}. {ital D} {bold 26} (1982), 1348), to P. A. M. Diracs forms ({ital Rev}. {ital Mod}. {ital Phys}. {bold 21} (1949), 392) of the dynamics as special cases. The new feature of this method is the way in which the theory of group representations is used to decouple the problem of adding interactions from the problem of ensuring full Poincare invariance. An analytically solvable example is given and discussed. {copyright} 1989 Academic Press, Inc.

Unified connected theory of few-body reaction mechanisms in N-body scattering theory

A unified treatment of different reaction mechanisms in nonrelativistic N-body scattering is presented. The theory is based on connected kernel integral equations that are expected to become compact for reasonable constraints on the potentials. The operators T/sub +-//sup ab/(A) are approximate transition operators that describe the scattering proceeding through an arbitrary reaction mechanism A. These operators are uniquely determined by a connected kernel equation and satisfy an optical theorem consistent with the choice of reaction mechanism. Connected kernel equations relating T/sub +-//sup ab/(A) to the full T/sub +-//sup ab/ allow correction of the approximate solutions for any ignored process to any order. This theory gives a unified treatment of all few-body reaction mechanisms with the same dynamic simplicity of a model calculation, but can include complicated reaction mechanisms involving overlapping configurations where it is difficult to formulate models.

Relativity and the low energy nd A(y) puzzle

We solve the Faddeev equation in an exactly Poincare invariant formulation of the three-nucleon problem. The dynamical input is a relativistic nucleon-nucleon (NN) interaction that is exactly on-shell equivalent to the high-precision CD Bonn NN interaction. S-matrix cluster properties dictate how the two-body dynamics is embedded in the three-nucleon mass operator (rest Hamiltonian). We find that for neutron laboratory energies above {approx_equal}20 MeV relativistic effects on A{sub y} are negligible. For energies below {approx_equal}20 MeV dynamical effects lower the nucleon analyzing power maximum slightly by {approx_equal}2% and Wigner rotations lower it further up to {approx_equal}10%, thereby increasing disagreement between data and theory. This indicates that three-nucleon forces (3NF) must provide an even larger increase of the A{sub y} maximum than expected up to now.

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 decom- position. Relativistic invariance is achieved by constructing a dynamical unitary representation of the Poincare 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 sec- tions 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.

Combinatorics, Partitions, and Many Body Physics

Some combinatorial techniques are presented which streamline the graphical analysis used in N‐body scattering theory. The basic results are derived using properties of the lattice of partitions of N particles, which naturally arises on classifying translational symmetry properties of N‐body operators. Classical cumulant expansions are recovered, previously obtained results are presented from a unified point of view, and some new theorems concerning connectivity of N‐body equations are presented.

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 Poincare 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 into a nonrelativistic momentum-space three-body code.

Mini Review of Poincaré Invariant Quantum Theory

We review the construction and applications of exactly Poincaré invariant quantum mechanical models of few-degree of freedom systems. We discuss the construction of dynamical representations of the Poincaré group on few-particle Hilbert spaces, the relation to quantum field theory, the formulation of cluster properties, and practical considerations related to the construction of realistic interactions and the solution of the dynamical equations. Selected applications illustrate the utility of this approach.