One of the recent discoveres in nuclear Physics is the existance of Halo nuclei .Therefore, halo nuclei are very weakly-bound exotic states of nuclear matter in which the outer one or two valence nucleons (usually neutrons), and a nuclear core with normal nuclear density is surrounded by a region of dulite nuclear matter, referred to as the neutron halo. Such nuclei occur from light to heavy masses and have been the subject of a alarge 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 examind through a fully microscopic variational model, where the Pauli exclusion princple explicity satisfied and semi-realistic nucleon-nucleon interactions are used. The model is an extension of previous work of closed shell nuclei. The wavefunction is obtained from a starting or reference state, which includes the required symmetries nd provides a translationally invariant description of the system in terms off several uncorrelated clusters. Medium to long-rang linear and short-range non-linear corrlation operators are then applied to obtained a good wavefunction, these models are important to solve the Shrodenger equation.The model developed is then used to examine the nuclei , , and . By making use of one-and two-body density distributions a qualitative picure of the matter distribution in the nucleus is obtained. The analysis provided indicates for a bound state one requires spin-orbit force, something that we don’t include. Nevertheless working in the L-S coupling scheme have shown that our model is capable of producing bound states for open-shell sysytems by artificially altering the central term of the semi-realistic interactions in use. And to find the relashonshipe between the energy and the width of shell, and find the behavioer of nuclei from throught the relation between energy and distance to the center of mass of alpha partical, 5He and 8Be are known halo nuclei. The general behaviour obtained was that the energy approached a minimum, as the separation between the several constituents increased. This could be monitored by observing the spherically averaged one–and two–body density distributions. We could clearly see that the energy was minimized as the one–body distribution broadened with the center shifting a way from the origin. The two–body density distribution separated into two parts: a main body similar to the alpha–particle and a small tale effect. We used algorithmic scaling in order to distinguish the two parts.Despite the fact our interaction is not adequate for the light halo nuclei of 6He and 9Be we demonstrated that our model can produce bound state for such open–shell systems by modifying the inter–nucleon force.in this thesis used programes in Fortran (77).
