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Chapter 3
Relativistic Bound State Wave
Functions
For many years, nuclear structure and the nucleon-nucleon interaction have been
studied thoroughly within the context of the nonrelativistic Schrödinger framework.
In this non-relativistic many-body theory, nuclei are regarded as bound states of nucleons
interacting via two- and three-body potentials. The modern nucleon-nucleon
potentials accomodate the exchange of mesons, as well as relativistic effects. Over
the years, complex models for the structure of nuclei have been developed. Some of
these models provide an accurate description of the ground-state properties of nuclei
throughout the mass table.
There are a number of good arguments to prefer a relativistic description of nuclei
above a nonrelativistic one. Firstly, in a field-theoretic approach the mesonic degrees
of freedom can be implemented right at the start of the development of the model.
Furthermore, causality, retardation, and relativistic kinematics can be incorporated
in the most natural fashion. Note that the mean velocity of nucleons in a nucleus
is approximately 25% of the velocity of light. The spin-orbit interaction, which
is inserted by hand in non-relativistic approaches, emerges naturally in relativistic
theories.
There are also less obvious benefits to be gained from a relativistic model. In
Ref. [28] it is demonstrated that the one-pion contribution to the two-body potentials
in the nonrelativistic approach is reduced severely by the nonlocalities, inherent to a
relativistic description, which in turn has its effects on pion exchange currents. Furthermore,
the boost interactions, which are naturally incorporated in a relativistic
description, are proven to be responsible for over one third of the phenomenological
part of the three-nucleon interaction needed in nonrelativistic Hamiltonians. There
are also indications that the small nuclear binding energies arise from a cancellation
between large Lorentz scalar and vector components. Since these potentials are comparable
to the nucleon mass, it becomes essential to adopt a relativistic treatment.
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