The Hartree-Fock (HF) minima for the nucleus²⁸Si were obtained for the prolate, oblate and spherical shapes using the interaction obtained by Preedom and Wildenthal. The interaction gives rise to large energy separation between the prolate and the oblate shapes. The spherical solution is just 2 MeV above the lowest HF (oblate) minimum. The spectrum projected from the oblate HF state is in good agreement with the experimental spectrum. The transition probabilities for the different energy levels also agree reasonably well. The configuration mixing calculations performed on the basis of states projected from the three shapes indicate that there is no significant mixing of different projected states. The second 0₂⁺ state, thus obtained, corresponds to the third 0₃⁺ state in the experimental spectrum and stems dominantly from the spherical HF state. It is seen that the structure of the energy levels of²⁸Si, especially the second 0₂⁺ level is very sensitive to the two body interaction. The results are compared with those obtained using the renormalised interaction of Kuo.

Band mixing calculations have been done for²⁴Ne including the two degenerate prolate and oblate Hartree-Fock states and also some particle-hole excited states in the projection formalism using an interaction obtained by Preedom and Wildenthal. The energy spectrum agrees very well with the experimental results as well as the exact shell model calculations. Thus the band mixing calculations provide a good approximation to the lengthy exact shell-model calcuations. In addition they offer a physical insight into the collective nature of the nucleus as nuclear states are described in terms of only a few ‘intrinsic’ states.

The structure of the low-lying states of⁵⁸Ni has been calculated in shell model by assuming an inert⁵⁶Ni core plus two valence nucleons in the p_3/2, f_5/2 and p_1/2 orbitals. The two-body matrix elements are first expressed in terms of seven radial matrix elements and these are then parametrized to give best fit between the computed and the observed energies of the levels below 4 MeV. The wave-functions obtained using these two-body matrix elements are used to study the concept of effective charges. It is found that a single effective charge is not sufficient to predict theB(E2) rates equally well for the thirteen known transitions for which experimental values are available. Assumption of state-dependent effective charges gives a far better agreement. An analysis using wavefunctions obtained with Kuo’s two-body matrix elements also gives a similar result.

Energy levels and electromagnetic transitions in⁶²Zn have been calculated using band-mixing formalism in the framework of deformed Hartree-Fock theory. Matrix elements of Adjusted-Surface Delta Interaction (ASDI) and of Tabakin interaction have been used. Detailed structure of various nuclear states in terms of bands has been discussed. Although the calculated spectra for both the interactions are somewhat compressed as compared to the observed spectra, the ASDI results are in substantially better agreement with experiments. Several additional states of high spin (J>4) have been predicted.B(E2) transitions between inter-band as well as some of the intraband states are calculated to stimulate further experiments.

The structure of the selenium nuclei in the regionA = 70 is studied using our deformed configuration mixing (DCM) shell model based on Hartree-Fock states. An effective interaction given by Kuo and modified by Bhatt is used. An attempt is made to understand the coexistence of shapes in selenium nuclei.