**
Translationally Invariant Treatment**

**
of Light Nuclei**

** **

**Theodoros Leontiou**

** **

Department of Physics, UMIST, Manchester, UK

A thesis submitted to the University of Manchester Institute of Science and Technology for the degree of Doctor of Philosophy

**June 2004**

Abstract

One of the recent discoveries in nuclear physics is the existence of halo nuclei. These can be thought of as loosely bound systems where a nuclear core with normal nuclear density is surrounded by a region of dilute nuclear matter, referred to as the neutron halo. Such nuclei occur from light to heavy masses and have been the subject of a large number of theoretical studies to try and understand them. A number of theoretical models have been proposed over the years.

In this thesis the structure of light halo nuclei is examined through a fully microscopic variational model, where the Pauli exclusion principle is explicitly satisfied and semirealistic nucleon-nucleon interactions are used. The model is an extension of previous work for closed shell nuclei. The wavefunction is obtained from a starting or ‘reference’ state, which includes the required symmetries and provides a translationally invariant description of the system in terms of several uncorrelated clusters. Medium- to long-range linear and short-range non-linear correlation operators are then applied to obtain a good wavefunction.

In order to evaluate the many-body matrix elements that occur in the linear eigenvalue problem associated with the variational approach, we make use of the variational Monte Carlo method. The numerical accuracy of the Monte Carlo method is thoroughly examined, paying particular attention to the specific requirements of the model. It is shown that the presence of correlations in the random walk must be taken into account for a reliable error estimate.

The model
developed is then used to examine the nuclei ^{5}He, ^{6}He, ^{8}Be and ^{9}Be. By
making use of one- and two-body density distributions a qualitative picture of
the matter distribution in the nucleus is obtained. The analysis provided
indicates that for a bound state one requires spin-orbit force, something that
we do not include. Nevertheless,
working in the *L* – *S* coupling scheme we have shown that
our model is capable of producing bound states for open-shell systems by
artificially altering the central term of the
semirealistic interactions in use. In general this model is a successful
first step in extending past developments for closed-shell systems into the
area of halo nuclei.