Nucleon-Nucleon Scattering in a Three Dimensional Approach

The nucleon-nucleon (NN) t-matrix is calculated directly as function of two vector momenta for different realistic NN potentials. To facilitate this a formalism is developed for solving the two-nucleon Lippmann-Schwinger equation in momentum space without employing a partial wave decomposition. The total spin is treated in a helicity representation. Two different realistic NN interactions, one defined in momentum space and one in coordinate space, are presented in a form suited for this formulation. The angular and momentum dependence of the full amplitude is studied and displayed. A partial wave decomposition of the full amplitude it carried out to compare the presented results with the well known phase shifts provided by those interactions.Comment: 26 pages plus 10 jpg figure

Relativity and the low energy nd Ay 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 interaction that is exactly on-shell equivalent to the high precision CDBonn NN interaction. S-matrix cluster properties dictate how the two-body dynamics is embedded in the three-nucleon mass operator. We find that for neutron laboratory energies above 20 MeV relativistic effects on Ay are negligible. For energies below 20 MeV dynamical effects lower the nucleon analyzing power maximum slightly by 2% and Wigner rotations lower it further up to 10 % increasing thus disagreement between data and theory. This indicates that three-nucleon forces must provide an even larger increase of the Ay maximum than expected up to now.Comment: 29 pages, 2 ps 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

Spin in relativistic quantum theory

We discuss the role of spin in Poincar\'e invariant formulations of quantum mechanics.Comment: 54 page

A study of neutron-deuteron scattering in configuration space

A new computational method for solving the configuration-space Faddeev equations for the breakup scattering problem has been applied to nd scattering both below and above the two-body threshold.Comment: 4 pages, 3 Postscript figures, uses espcrc1.sty Talk at the 18th International IUPAP Conference on Few-Body Problems in Physics, Aug. 21-26, 2006, Santos, Brazi

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.Comment: 49 pages, 18 figure

Angularly localized Skyrmions

Quantized Skyrmions with baryon numbers $B=1,2$ and 4 are considered and angularly localized wavefunctions for them are found. By combining a few low angular momentum states, one can construct a quantum state whose spatial density is close to that of the classical Skyrmion, and has the same symmetries. For the B=1 case we find the best localized wavefunction among linear combinations of $j=1/2$ and $j=3/2$ angular momentum states. For B=2, we find that the $j=1$ ground state has toroidal symmetry and a somewhat reduced localization compared to the classical solution. For B=4, where the classical Skyrmion has cubic symmetry, we construct cubically symmetric quantum states by combining the $j=0$ ground state with the lowest rotationally excited $j=4$ state. We use the rational map approximation to compare the classical and quantum baryon densities in the B=2 and B=4 cases.Comment: 22 page

Quantum Monte Carlo Calculations of A≤6A\leq6 Nuclei

The energies of $^{3}H$, $^{3}He$, and $^{4}He$ ground states, the ${\frac{3}{2}}^{-}$ and ${\frac{1}{2}}^{-}$ scattering states of $^{5}He$, the ground states of $^{6}He$, $^{6}Li$, and $^{6}Be$ and the $3^{+}$ and $0^{+}$ excited states of $^{6}Li$ have been accurately calculated with the Green's function Monte Carlo method using realistic models of two- and three-nucleon interactions. The splitting of the $A=3$ isospin $T=\frac{1}{2}$ and $A=6$ isospin $T=1$, $J^{\pi} = 0^{+}$ multiplets is also studied. The observed energies and radii are generally well reproduced, however, some definite differences between theory and experiment can be identified.Comment: 12 pages, 1 figur

Quantum Monte Carlo Studies of Relativistic Effects in Light Nuclei

Relativistic Hamiltonians are defined as the sum of relativistic one-body kinetic energy, two- and three-body potentials and their boost corrections. In this work we use the variational Monte Carlo method to study two kinds of relativistic effects in the binding energy of 3H and 4He. The first is due to the nonlocalities in the relativistic kinetic energy and relativistic one-pion exchange potential (OPEP), and the second is from boost interaction. The OPEP contribution is reduced by about 15% by the relativistic nonlocality, which may also have significant effects on pion exchange currents. However, almost all of this reduction is canceled by changes in the kinetic energy and other interaction terms, and the total effect of the nonlocalities on the binding energy is very small. The boost interactions, on the other hand, give repulsive contributions of 0.4 (1.9) MeV in 3H (4He) and account for 37% of the phenomenological part of the three-nucleon interaction needed in the nonrelativistic Hamiltonians.Comment: 33 pages, RevTeX, 11 PostScript figures, submitted to Physical Review

Inclusive K+K^+ and exclusive K+YK^+Y photoproduction on the deuteron: Λ\Lambda- and Σ\Sigma-threshold phenomena

Inclusive $K^+$ and exclusive $K^+Y$ photoproduction on the deuteron are investigated theoretically. Modern hyperon-nucleon forces and a recently updated kaon photoproduction operator for the $\gamma +N\to K^++Y$ process are used. Sizable effects of the hyperon-nucleon final state interaction are found near the $K^+\Lambda N$ and $K^+\Sigma N$ thresholds in the inclusive reaction. Angular distributions for the exclusive process show clear $YN$ final state interaction effects in certain kinematic regions. Precise data especially for the inclusive process around the $K^+\Sigma N$ threshold would help to clarify the strength and property of the $\Lambda N-\Sigma N$ interaction.Comment: 14 pages, 10 figure