Model Dependence of the 2H Electric Dipole Moment

Background: Direct measurement of the electric dipole moment (EDM) of the neutron lies in the future; measurement of a nuclear EDM may well come first. The deuteron is one nucleus for which exact model calculations are feasible. Purpose: We explore the model dependence of deuteron EDM calculations. Methods: Using a separable potential formulation of the Hamiltonian, we examine the sensitivity of the deuteron EDM to variation in the nucleon-nucleon interaction. We write the EDM as the sum of two terms, the first depending on the target wave function with plane-wave intermediate states, and the second depending on intermediate multiple scattering in the 3P1 channel, the latter being sensitive to the off-shell behavior of the 3P1 amplitude. Results: We compare the full calculation with the plane-wave approximation result, examine the tensor force contribution to the model results, and explore the effect of short range repulsion found in realistic, contemporary potential models of the deuteron. Conclusions: Because one-pion exchange dominates the EDM calculation, separable potential model calculations will provide an adequate description of the 2H EDM until such time as a better than 10% measurement is obtained.Comment: 21 pages, 2 figures, submitted to Physical Review

Covariant four-dimensional scattering equations for the NN−πNNNN-\pi NN system

We derive a set of coupled four-dimensional integral equations for the $NN-\pi NN$ system using our modified version of the Taylor method of classification-of-diagrams. These equations are covariant, obey two and three-body unitarity and contain subtraction terms which eliminate the double-counting present in some previous four-dimensional $NN-\pi NN$ equations. The equations are then recast into a from convenient for computation by grouping the subtraction terms together and obtaining a set of two-fragment scattering equations for the amplitudes of interest.Comment: Version accepted for publication in ``Annals of Physics''. New section containing two new figures added. 58 pages, 20 figures. Uses RevTeX. For copies of figures email [email protected]

The classification of diagrams in perturbation theory

The derivation of scattering equations connecting the amplitudes obtained from diagrammatic expansions is of interest in many branches of physics. One method for deriving such equations is the classification-of-diagrams technique of Taylor. However, as we shall explain in this paper, there are certain points of Taylor's method which require clarification. Firstly, it is not clear whether Taylor's original method is equivalent to the simpler classification-of-diagrams scheme used by Thomas, Rinat, Afnan and Blankleider (TRAB). Secondly, when the Taylor method is applied to certain problems in a time-dependent perturbation theory it leads to the over-counting of some diagrams. This paper first restates Taylor's method, in the process uncovering reasons why certain diagrams might be double-counted in the Taylor method. It then explores how far Taylor's method is equivalent to the simpler TRAB method. Finally, it examines precisely why the double-counting occurs in Taylor's method, and derives corrections which compensate for this double-counting.Comment: 50 pages, RevTeX. Major changes from original version. Thirty figures available upon request to [email protected]. Accepted for publication in Annals of Physic

The energy dependence of the πN\pi N amplitude and the three-nucleon interaction

By calculating the contribution of the $\pi-\pi$ three-body force to the three-nucleon binding energy in terms of the $\pi N$ amplitude using perturbation theory, we are able to determine the importance of the energy dependence and the contribution of the different partial waves of the $\pi N$ amplitude to the three-nucleon force. A separable representation of the non-pole $\pi N$ amplitude allows us to write the three-nucleon force in terms of the amplitude for $NN\rightarrow NN^*$, propagation of the $NNN^*$ system, and the amplitude for $NN^*\rightarrow NN$, with $N^*$ being the $\pi N$ quasi-particle amplitude in a given state. The division of the $\pi N$ amplitude into a pole and non-pole gives a procedure for the determination of the $\pi NN$ form factor within the model. The total contribution of the three-body force to the binding energy of the triton for the separable approximation to the Paris nucleon-nucleon potential (PEST) is found to be very small mainly as a result of the energy dependence of the $\pi N$ amplitude, the cancellation between the $S$- and $P$-wave $\pi N$ amplitudes, and the soft $\pi NN$ form factor.Comment: RevTex file, 36 pages, 10 figures available from authors: [email protected]

Resonance energy of the barKNN-piYN system

The resonance energies of strange dibaryons are investigated with the use of the \bar{K}NN-\pi Y N coupled-channels Faddeev equation. It is found that the pole positions of the predicted three-body amplitudes are significantly modified when the three-body coupled-channels dynamics is approximated, as is done in the literature, by the effective two-body \bar{K}N interactions.Comment: 14 pages, 5 figure