<p> An expression for the semiclassical density of states for a particle in a smooth potential well is obtained from the Kirkwood expansion of the partition function. This expression for the semiclassical density of states is then shown to be essentially equivalent to the expression obtained from the Green's function method of Balian and Bloch.</p> <p> The Strutinsky shell correction to the nuclear binding energy is then analytically shown to be equivalent to the shell correction obtained from a consideration of the semiclassical partition function if certain restrictions on the Strutinsky smoothing parameter can be met.</p> / Thesis / Master of Science (MSc)

Clustering effects are studied experimentally in 24Mg and are searched for in 28Si and 56Ni. The mechanisms of reactions that populate fissioning states are also studied. The angular distribution of the 12C(24Mg,12C12C)12C reaction at 170 MeV has been measured near 180&deg; in the centre of mass frame by reversing the kinematics. Compared to previously measured forward angle data, the backward angle cross section is a factor of 45 lower. This is interpreted as a strong indication that the reaction mechanism is direct. Measurements of the 12C(16O,12C12C)alpha reaction at beam energies between 67 and 77 MeV reveal symmetrically fissioning states in 24Mg with spins of 6-12h and excitation energies of 22-32 MeV. Two states at 23.7 MeV (Jpi=(6,8)+) and 25.1 MeV (Jpi=10+) have not been observed in previous data at 99 and 113 MeV. The observed states show no clear correlation with 12C+12C scattering resonances. The variation of yield with bombarding energy supports previous indications of a compound reaction mechanism. Measurements of the 40Ca+16O reaction at a 40Ca beam energy of 190 MeV, previously proposed as a molecular resonance energy in this channel, show no yield into the sequential breakup channel 16O(40Ca,12C16O)28Si. This is apparently at variance with the predictions of a widely successful model for cluster reactions (the Harvey model). Measurements of other exit channels, in particular the 28Si+28Si, 24Mg+ 32S and 20Ne+36Ar channels, agree with statistical model Hauser-Feshbach calculations. Tests have been performed on the gas cells of the hybrid detectors used in these experiments. Optimum values for the operating parameters are determined. A systematic variation of detector signal with position is observed, which can be corrected in analysis. It is shown that two gridded electrodes of 100 mum wires can be replaced with a single 20 mum grid increasing the two-fold coincidence efficiency from 64% to 96%.