The three-nucleon continuum: achievements, challenges and applications

Charge exchange in energetic ion-atom collisions

A novel method for calculating resonances in three-body Coulombic systems is presented. The Faddeev-Merkuriev integral equations are solved by applying the Coulomb-Sturmian separable expansion method. To show the power of the method we calculate resonances of the three-α and the H − systems.

https://arxiv.org/pdf/physics/0101048.pdf

Resonant-state solution of the Faddeev-Merkuriev integral equations for three-body systems with Coulomb potentials

The statistical mechanics of reacting fluid mixtures is considered using arrangement channel quantum mechanics. In this theory, the many body wave function, ψ, is expressed in terms of arrangement channel components ψα which satisfy coupled time dependent equations. Using the properties of the ψα, we obtain the corresponding generalization of the density matrix ρ denoted ραβ and the quantum ’’Liouville equation’’ which it satisfies. Reduced arrangement channel density matrices are introduced and are found to satisfy a generalization of the BBGKY hierarchy for reactive mixtures. The properties of the hierarchy are explored, and it is shown that the streaming terms in succeeding members of the hierarchy have increasing connectivity appropriate to the number of atoms in the contributing arrangement channels. The resulting hierarchy can serve as the rigorous starting point for developing statistical theories of reactive fluids. For example, it can be used to derive a Boltzmann equation appropriate to reacting gaseous mixtures.

Kinetic theory of reacting fluid mixtures. I. The BBGKY hierarchy in arrangement channel quantum mechanics

We derive several classes of distribution properties for the channel internal and external interactions, as well as for generalized residual interactions, in the framework of theN-body scattering theory An essential feature of our distribution properties is that all coefficients are unity (natural distributions). We give several examples of the great advantages coming from the employment of the natural distributions in practical applications. Several classes of cluster expansions are derived for the channel resolvent operators and the Hepp-Narodetskii-Yakubovskii expansion is proved in a simple algebraic way. We present compact procedures leading to both the Sloan-Bencze-Redish equations and the Faddeev-Yakubovskii equations with artificial indices in the unknowns. We consider also many types of decompositions for the fullN-body scattering wave functions and, finally, we present general operatorial reversion properties for linked-cluster strings of resolvents and interactions.

W. Glöckle

Papers

A new approach to the three-body problem