Abstract
In this thesis, we investigate the processes of charge transfer and
electron-positron pair creation in relativistic collisions of heavy
ions. Peripheral collisions are considered, also referred to as atomic
collisions, in which the atomic nuclei remain intact. In such
collisions the closest approach of the nuclei is large enough
such that the strong interaction between the nuclei is of no
importance. Electromagnetic interactions of the particles prevail.
The theoretical treatment is based on a semiclassical model. The
movement of the atomic nuclei, that are regarded as classical charge
distributions, is described by relativistic classical trajectories,
whereas for electrons a description by quantum theory is required. We
consider collision systems with nuclear charge numbers ranging between
Z=66 and Z=92. Collision energies, given in terms of the total
kinetic energy in a rest frame of either nucleus, are in the
1 GeV/nucleon range. In such collision systems the motion of
electrons and positrons is relativistic and a suitable description of
their dynamics is given by the two-centre Dirac equation. The
experimental investigation of these collision systems became feasible
by the use of heavy-ion accelerators, beginning in the mid 1980's in
Berkeley.
The nonperturbative solution of the time-dependent two-centre Dirac
equation is the principal topic of this work. After introducing this
model of relativistic atomic collisions, we formulate and investigate
analytically a relativistic multi-channel scattering theory in
chapter 3. In particular, asymptotic
convergence and relativistic invariance are shown for a class of
two-centre Dirac equations with screened nuclear charges.
For the numerical solution of the Dirac equation we use the coupled
channel method (see chapter 4). Contrary to
similar calculations reported in the literature, the numerical code
newly written for this work (see chapter A)
allows for the solution of the coupled channel equations in various
different Lorentz frames. Hence, the violation of Lorentz invariance,
owing to the coupled channel approximation, can be investigated
quantitatively for the first time, thereby allowing for the estimation
of the accuracy of relativistic coupled channel calculations (see
chapter 6). Generally, we find that the frame
dependence of the numerical results is less pronounced if so-called
phase-distorted basis functions are used. Another innovation of the
present calculations is the type of coupled channel basis used.
Different approaches of previously reported calculations are combined
to a unified treatment, namely a basis which is symmetric with respect
to the centres and which is capable of describing free particles at
the same time.
We present numerical results for relativistic electron transfer,
beginning with calculations which reproduce previously published
theoretical data. For the first time, the parametric dependencies of
the charge transfer process on the charge numbers of the nuclei and
the collision energy are investigated using a nonperturbative method.
The results are in qualitative agreement with experimental
measurements for heavy collision systems. However, they are distinctly
different from the parametric dependencies obtained by most
perturbative calculations for higher collision energies.
Furthermore, we consider the process of bound-free pair production, in
which a free positron and a bound electron are created. The emphasis
of the theoretical studies is on a qualitative understanding of the
importance of a symmetrical basis of positron states for the
description of this process at intermediate relativistic collision
energies. In the literature only asymmetrical approaches are used,
which are computationally less demanding. Furthermore, we investigate
the Lorentz frame dependence of the numerical calculations for the
pair creation process, which has likewise not been considered before.
Owing to the pronounced frame dependence found, the necessity of a
symmetrical basis for the description of the pair creation process
cannot be assessed unambiguously. However, a symmetrical basis is
important in calculations in the collider frame, which not only
preserve a symmetry of the exact scattering theory, but are closest to
the experimental findings as well. Finally, we confirm the conjecture
that the addition of free-particle states to a coupled channel basis of
bound states reduces the frame dependence of numerical results for the
charge transfer process. |
