Thesis (MSc)--University of Stellenbosch, 2011. / ENGLISH ABSTRACT: We investigate the nuclei 20Ne, 44Ti, 94Mo, 136Te and 212Po using a model of an α-cluster orbiting a closed shell core. A purely phenomenological cluster-core potential is found to provide a successful description of the spectra, B(E2↓) transition strengths, and α-decay rates of the low-lying positive parity states of these nuclei. We then use the same potential as the real part of an optical model potential to describe the α elastic scattering by 16O, 40Ca, 90Zr and 208Pb. The experimental differential cross-section data are reasonably well reproduced with the imaginary potential depth as the only free parameter. The special case of the 8Be system is also analysed. / AFRIKAANSE OPSOMMING: Ons ondersoek die kerne 20Ne, 44Ti, 94Mo, 136Te en 212Po deur gebruik te maak van ’n model waar ’n α-bondel om ’n kern met ’n geslote skil wentel. ’n Suiwer fenomenologiese bondelkern potentiaal is gevind wat die energie spektra, B(E2 ↓) oorgangs sterktes, en α-verval tempo vir laagliggende positiewe pariteitstoestande vir hierdie kerne beskryf. Ons gebruik dieselfde potentiaal as die reele deel van die optiese potentiaal om die alpha elastiese verstrooiing deur die kerne 16O, 40Ca, 90Zr en 208Pb te beskryf. Die eksperimentele differensiele kansvlak data word redelik goed gereprodukseer met slegs die imaginere potensiaal diepte as die enigste vrye parameter. Die spesiale geval van 8Be is ook ondersoek.