  Goal of this work is the consistent description of elastic Compton scattering
from the single nucleon and the deuteron. The theoretical framework chosen is
Chiral Perturbation Theory, which is the low-energy formulation of Quantum
Chromodynamics, where we extend the spectrum of active degrees of freedom from
only pions and nucleons to also the Delta(1232) resonance. In the deuteron
sector, we treat the nucleon-nucleon interaction non-perturbatively. Besides
the Compton cross sections, our main concern is with the nucleon
polarizabilities, which are a useful tool to describe the reaction of the
internal nucleonic degrees of freeedom to the external electromagnetic field.
Experimentally, only a few nucleon polarizabilities are known. Especially our
present knowledge of the neutron polarizabilities is not satisfying. The reason
why it is so difficult to determine these quantities experimentally is the
finite lifetime of the free neutron. Therefore, we want to contribute to the
ongoing discussion of the neutron polarizabilities by fitting the average over
proton and neutron polarizabilities to the elastic deuteron Compton-scattering
data. Similarly, we determine the proton polarizabilities from fits to the
single-proton Compton data. We finally combine both results in order to
identify the neutron polarizabilities.
