Alpha-induced fragmentation of 28Si in a statistical model

Within the context of a statistical model, that incorporates final-state interaction between a pair of fragments, we have calculated the energy spectra associated with the production of different isobaric pairs as a function of their lab kinetic energy and isobaric and elemental distributions of nuclei produced in the ⁴He$ + $²⁸Si reaction at cm incident energies of 102.7, 173.7, 300, 500, and 1000MeV. Double differential cross-section of isobars 16, 20, and 24 as a function of their lab kinetic energies at 30^° and the same for isobar 24 at 10^°, 30^°, 60^°, and 90^° have been calculated at cm incident energies of 102.7 and 173.7MeV and compared with the data of Woo et al. Calculated yields follow the trend of the data at each angle, and calculated angular distributions also reproduce the general trend of the observed ones. A key feature of the model is that it allows for fragments to be emitted in ground states as well as in excited states that are allowed by the conservation of energy. The analysis establishes that the fragments are emitted in excited state. The excitation energies for A = 24 and 16 are deduced from the data. The observed angular distributions for A = 7, 12, 16, 20, 24, and 28 are well accounted for assuming them to be emitted in excited states. The relative production probabilities for different elements and isobars are energy dependent. The yields for unstable elements, ⁵Li, ⁸Be, and ²⁶Al, are found to be significant. The relative fragmentation probabilities of all allowed isotopic pairs have been presented.