Abstract
This study investigates the structures of multiparticle systems with a specic focus
on the concept of shells. Shells have signicant importance in understanding the
behaviour of matter in the universe, as both atoms and nuclei may be described in
terms of shells of either electrons (atoms) or nucleons (nuclei). The historical background
of shells and their role in atomic and nuclear structure is explored. While
the nuclear shell model has been successful in describing structural properties of
nuclei, this study considers alternative explanations for the existence of shells.
Taking the strong potential limit of the Hamiltonian, with the kinetic energy as
a perturbation, one can reduce the problem to that of sums over the fundamental
two-body interactions governing the dynamics of the many-body system. In that
limit also, one can treat the system classically, as the spectrum of the potential is
continuous, with a correspondence between the classical and quantum mechanical
solutions.
The spatial distribution of particles displaying the emergence of shell structures
is obtained. This is demonstrated as a consequence of applying a nite, short-range
force with a hard core to a many-particle system, as well as the consequence of
steric blocking. The signicance of rotational symmetries is discussed in relation to
the emergent shell structures. As a result of the structures, angular momentum as
a symmetry emerges as a natural symmetry
Furthermore, the study explores the geometric congurations of a particles in a
cluster models of nuclei. Correspondence between optimal congurations in the toy
model and the a congurations in a cluster models is found. Chapter 8 uncovers
the natural explanation to the assumed a cluster congurations in a cluster models.
In Chapter 2, the fundamental principles of group theory and their connection
to conservation laws are discussed. Chapter 3 brie y presents atomic and nuclear
shell models. The model developed for this study employs strong potential approximations,
which are presented in Chapter 4, along with the results of the toy model
for small number particle systems. Chapter 5 presents and discusses the results of
the toy model for large number particle systems. The results of the toy model using
strong hard core potentials are presented in Chapter 6. In Chapter 7, the toy model
results in 3 dimension are presented and discussed.