Executive Summary : | The shape of a nuclear state is determined by the microscopic wave function and depends on the number of valence nucleons outside the core. Nuclei with few valence nucleons exhibit a single-particle character, while those with more nucleons lose their single-particle behavior and accumulate collectivity, creating a permanent structural deformation at the mid-shell region. shape coexistence is a phenomenon that has been observed in low-lying states with similar energies, but its experimental establishment is challenging and requires refined techniques. The study of shape coexistence is particularly abundant for even-even nuclei in the mass region of A = 180. For instance, triple shape coexistence has been observed in ¹⁸⁶Pb due to the energy gap between closed shell and multiparticle-multihole configuration. In ¹⁷⁸Hg shape, coexistence has been well established, and multiple shape coexistence has been observed in ¹¹⁰,¹¹²Cd. In the transitional arena of A ~ 70-80 mass region, protons and neutrons occupy g9/2 intruder orbitals, exhibiting shape driving effects near the Fermi surface. The level structure of excited nuclei in these regions provides information on coexisting collective and single-particle levels and rotational bands. The proposal aims to gain clarity and provide better insight into the structure of different nuclei such as ⁷⁵se, ⁷⁵As, and ⁸²sr,⁸⁴sr isotopes using a state-of-the-art detection system comprising LaBr₃(Ce) and clover detectors. |