J.A. Tjon

Solution of the Faddeev equations for the triton problem using local two-particle interactions

Abstract A simple method is described to compute exactly the binding energy (B.E.) of the ground state of three nucleons in the framework of the Faddeev equations. The two-body potentials thereby used are of the local central Yukawa type. The effect of including repulsion in the two-body forces is also studied and it is found to be considerable. As a result of this calculation a value of 8.4 MeV is obtained for the B.E. of triton.

A study of break-up processes in neutron-deuteron scattering

Abstract Neutron-deuteron break-up reactions for kinematically complete and incomplete situations are examined for various types of local two-nucleon S-wave potentials and for the separable Yamaguchi potential. In particular, a systematic search has been made in the entire phase space of three free nucleons for large differences between the results of the various interactions. Certain parts outside the final state peaks and the quasifree scattering regions are found which are significantly sensitive to the two-nucleon interactions studied.

BETHE-SALPETER EQUATION FOR J=0 NUCLEON-NUCLEON-SCATTERING WITH ONE-BOSON EXCHANGE

Abstract The Bethe-Salpeter equation is solved numerically for the J = 0 nucleon-nucleon phase shifts by iteration and summation of the perturbation series with Pade approximants. As kernel a superposition of π -, η -, ϵ -, δ , ϱ - and ω -exchange is used, taking completely into account the complications due to the various spin- and positive and negative energy-states. Considerable deviations of our phase shifts from the ones as calculated by means of the Blankenbecler-Sugar equation are found. A reasonable reproduction of the 1 S 0 and 3 P 0 phase shifts in the framework of the Bethe-Salpeter equation is obtained by introducing a large ωNN coupling.

THE THREE AND FOUR NUCLEON SYSTEMS (THEORY)

Abstract Some theoretical studies of the few nucleon systems A = 3,4 are briefly discussed. Bound state calculations indicate that a nonrelativistic description with pairwise nuclear forces does not suffice and additional degrees of freedom are needed. Developments in the actual numerical solutions of Faddeev type equations are such that a detailed comparison can be made with experiment. Employing realistic two-nucleon interactions, the principal features of both elastic and breakup processes in neutron deuteron scattering can be accounted for.

Calculations of elastic n-d scattering for the Reid potential

Abstract A perturbational scheme is used to study neutron-deuteron elastic scattering with the Faddeev equations in momentum space. The pure s-wave parts of the two-nucleon T -matrix are treated in an exact way, while the higher partial-wave components are retained in first order. This is done for the full Reid soft-core potential. The lab energies considered in this study are between 5 and 50 MeV. It is found that the perturbation method can give insight in the sensitivity to details of the potential, and at higher energies can give quantitatively reliable results, for most of the observables.

Three-nucleon calculations without the explicit use of two-body potentials

Abstract Using as two-nucleon interaction input the 3 S 1 - 3 D 1 and 1 S 0 partial waves, the Faddeev equations are solved for the three-nucleon bound state. The 3 S 1 3 D 1 T -matrix is calculated from the Reid potential. Avoiding the usual potential fit, the 1 S 0 T -matrix is directly continued off-shell and is constructed consistent with the 1 S 0 phase shift of elastic two-nucleon scattering. The off-shell part of the 1 S 0 T -matrix is parametrized and with this parametrization the dependence of the three-nucleon bound-state properties is studied. As a result it is found that the binding energy varies only between 6.2 MeV and 6.8 MeV, while the minimum in the charge form factor for electron scattering from 3 He lies between 12.9 fm −2 and 18.7 fm −2 . The larger (smaller) 3 He binding energy is accompanied by a 3 He charge form factor whose minimum is at larger (smaller) momentum transfers.

Bethe-Salpeter Equation for I=1 Nucleon-Nucleon Scattering with One Boson Exchange

We extend our earlier work on the Bethe-Salpeter equation for J = 0 by considering in addition the isospin I = 1 phase shift /sup 3/P/sub 1/, /sup 3/P/sub 2/, /sup 3/F/sub 2/ epsilon/sub 2/, and /sup 1/D/sub 2/. These require the solution of a system of eight (instead of four for J = 0) coupled integral equations which have again been solved by iteration and application of the Pade method. The kernel is the same as before; i.e., the same particles are exchange with the same analytic form of the cutoff. However, in order to find a fair agreement of our phase shifts with the experimental data, it was necessary to lower the cutoff mass. The phase shifts obtained show the general deficiency of dropping too fast at higher energies. In addition, we have studied the operator Pade approach and find that relatively few off-shell states are indeed sufficient to obtain reasonable accuracy for the summation of the Born series in a one-loop approximation.

A relativistic dynamical model of πN scattering

Abstract We present a unitary relativistic quasi-potential model for describing the low-energy πN interaction, based on the equal time Bethe-Salpeter equation. It preserves the covariant structure of a relativistic spin 1 2 particle for the nucleon propagator, to be contrasted to other quasi-potential approximations.

Relativistic and meson exchange current effects in few nucleon systems

Abstract The Bethe-Salpeter approach is discussed for the A=2 and 3 system. Using a relativistic one boson exchange model the elastic em form factors are calculated. Predictions compare well with the experimental data. Within the same dynamical model fully relativistic meson exchange current contributions are determined and the structure functions for unpolarized deuteron disintegration are studied. Boost effects and the relativistic structure of the nucleon em operators are found to be important in certain kinematic regions. Relativistic corrections to the trinucleon binding energy are discussed using separable representations of the Paris and Bonn potentials.

Effects of annihilation on resonances in the N system

The widths and positions of resonances of the N N system for l = 0, 1 are studied in a relativistic potential model, where the absorption is described in terms of an annihilation box diagram. The trajectories of the singularities in the complex E-plane are determined as a function of the coupling strengths. For coupling constants fitted to the experimental cross sections, the widths of the quasi- nuclear states are of the order of 40 MeV. In addition, also resonances occur due to the coupling to the annihilation channels. These coupled channel resonances can have small widths and give in general rise to complicated Argand plots. For their description a simple phenomenological form for the scattering amplitude is used.