Transition charge densities (TCD) for 0⁺ → 2₁⁺ excitation have been calculated for^70,72,74,76Ge nuclei within microscopic variational framework employing 2p_3/2, 1f_5/2, 2p_1/2 and 1g_9/2 valence space. The calculated TCDs for different monopole variants of Kuo interaction are compared with available experimental results. Other systematics like reduced transition probabilitiesB(E2) and static quadrupole momentsQ(2) are also presented. It is observed that the transition density study acts as a sensitive probe for discriminating the response of different parts of effective interactions.

The two-neutrino double beta decay of⁹⁶Zr isotope for 0⁺ → 2⁺ transition has been studied in the PHFB model. In our earlier work, the reliability of the intrinsic wave functions of⁹⁶Zr and⁹⁶Mo isotopes has been established by obtaining an overall agreement between a number of theoretically calculated spectroscopic properties as well as half-lives of 2vββ decay for 0⁺ → 0⁺ transition and the available experimental data. In the present work, the half-life of 2vββ decay for 0⁺ ar 2⁺ transition T₁^2/2v(0⁺ →²⁺) has been calculated using the same set of intrinsic wave functions.

The structure of nuclear transition matrix elements (NTMEs) required for the study of neutrinoless double-$\beta$ decay within light Majorana neutrino mass mechanism is disassembled in the PHFB model. The NTMEs are calculated using a set of HFB intrinsic wave functions, the reliability of which has been previously established by obtaining an overall agreement between the theoretically calculated spectroscopic properties and the available experimental data. Presently, we study the role of short-range correlations, radial evolution of NTMEs and deformation effects due to quadrupolar correlations. In addition, limits on effective light neutrino mass $\langle m_{\nu} \rangle$ are extracted from the observed limits on half-lives $T_{1/2}^{0\nu}$ of neutrinoless double-$\beta$ decay.

With an aim to understand the effects of breakup and transfer channels on elastic scattering and fusion cross-sections in the $^{7}{\text{Li}} + ^{27}{\text{Al}}$ reaction, simultaneous measurement of elastic scattering angular distributions and fusion cross-sections have been carried out at various energies ($E_{\text{lab}} = 8.0–16.0$ MeV) around the Coulomb barrier. Optical model (OM) analysis of the elastic scattering data does not show any threshold anomaly or breakup threshold anomaly behaviour in the energy dependence of the real and imaginary parts of the OM potential. Fusion cross-section at each bombarding energy is extracted from the measured $\alpha$-particle evaporation energy spectra at backward angles by comparing with the statistical model prediction. Results on fusion cross-sections from the present measurements along with data from the literature have been compared with the coupled-channels predictions. Detailed coupled-channels calculations have been carried out to study the effect of coupling of breakup, inelastic and transfer, channels on elastic scattering and fusion. The effect of $1n$-stripping transfer coupling was found to be significant compared to that of the projectile breakup couplings in the present system.