Binding of charmonium with two- and three-body nuclei

The energies of the (eta_c d) and (eta_c 3He) bound states are calculated on the basis of exact three- and four-body AGS equations. For the eta_c N interaction a Yukawa-type potential has been adopted. The calculations are done for a certain range of its strength parameter. The results obtained are quite different from calculations based on the folding model.

The Three-Body Problem

The quantum mechanical three-body problem has been studied with increasing interest in the last decade. The main progress was achieved by deriving integral equations which are not only theoretically correct, but also practically applicable. Such equations allow us in particular to investigate, besides three-body bound states, the scattering of an elementary particle from a bound two-particle system.

Collision Theory for Two- and Three-Particle Systems Interacting via Short-Range and Coulomb Forces

In two- and three-particle reactions with light nuclei, a rich body of precise experimental data exists in which both projectile and target and/or the fragments occurring in the final state are charged. In order to make optimal use of these data for extracting physically interesting information about the nuclear interactions, the effects of the Coulomb force must be separated out in a reliable manner. For this purpose the mastering of the intricacies of charged-particle scattering theory is of vital importance.

Scattering amplitudes for two charged fragments

Excited states in the three-body system

Three-body excited states are calculated in a local potential model by means of the quasi-particle method. The improvement over the approach in which the local potential is approximated by a separable one is demonstrated.

SYSTEMATICAL MULTIPARTICLE THEORY AND ITS APPLICATION TO THE FOUR-NUCLEON PROBLEM

Publisher Summary This chapter discusses the systematical multiparticle theory and its application in the four-nucleon problem. The chapter describes the structure of the 2- body and 3-body equations and shows that the generalization to n particles can be accomplished in a natural way. It is a characteristic feature of this approach that the kernel of the occurring integral equations is built up by all subsystem transition operators in an explicit way. One of the important features of the 3-body theory is also achieved in the n-body formalism. This enables the application of the quasiparticle concept in a direct way. The 2-body problem is completely determined by the solution of the Lippman…

Coulomb Corrections in Proton-Deuteron Scattering

We present the first calculations of differential cross sections for elastic proton-deuteron scattering using a three-body formalism which correctly takes into account the Coulomb repulsion between the two protons.

Time dependent approach to the collision of two charged composite particles

QUASIPARTICLE CALCULATIONS FOR THE THREE-NUCLEON SYSTEM

Publisher Summary This chapter discusses the quasiparticle calculations for the three-nucleon system. There are three methods for solving the integral equations for the three-body problem with local two-body potentials; one method consists of the direct solution of the Faddeev equations, and the other two methods make different use of the quasiparticle idea that is based on the splitting of the occurring two-body potentials into a sum of separable terms and a rest potential. The chapter describes the term “form factors” and “coupling strengths.” A similar splitting is obtained for the T-matrices Tγ. With its help, it is possible to transform the Faddeev-type equations for the three-body tra…

Coulomb effects in three-body reactions with two charged particles

We present the details of a novel approach to the treatment of Coulomb effects in atomic and nuclear reactions of the three-body type in which two of the particles are charged. Based on three-body integral equations the formalism allows the practical calculation of elastic, inelastic, rearrangement, and breakup processes with full inclusion of the Coulomb repulsion or attraction in a mathematically correct way. No restrictions need to be made concerning the form of the short-range interactions between the three pairs. A particular virtue of our method lies in the fact that it corroborates, and gives precise meaning to, the intuitively anticipated conception of how to describe such reactions.

Scattering amplitudes and integral equations for the collision of two charged composite particles

Transition operators for the collision of two clusters composed of an arbitrary number of charged and neutral particles are represented as a sum of pure Coulomb and Coulomb-modified short-range operators. Sandwiching this relation between the corresponding channel states, correct two-fragment scattering amplitudes are obtained by adapting the conventional two-body screening and renormalization procedure. Furthermore, integral equations are derived for off-shell extensions of the full screened amplitudes and of the unscreened Coulomb-modified short-range amplitudes. For three particles, the final results coincide with those derived previously in a different approach. The proposed theory is v…