The application of spectral distribution theory for binding energy, spectra and occupancies using universal-sd interaction in (sd) shell and for Gamow-Teller and M1 strength sums in both (fp) and (sd)-shell is described.

We examine the possible role of electron-capture on the thermally populated first 2⁺ excited state of ⁴⁴Ti in hot astrophysical environments pertaining to post explosive nucleosynthesis supernova debris. We find in a simple schematic model that the astrophysical weak interaction rate for electron-capture decay of ⁴⁴Ti can depend considerably on temperature and hence on time. We propose a time varying decay rate for the evolving supernova debris and demonstrate its consequence for the ⁴⁴Ti mass yield of the supernova Cas A, observed through the measured 1.157 MeV γ-ray flux from the electron-capture decay of ⁴⁴Ti.

The one- plus two-body isospin non-conserving nuclear interactions, namely the isovector and isotensor ones, are included in the prediction of the energies of the ground state and the low-lying states of the $fp$ shell nuclei using spectral distribution theory. This in turn is used to calculate the linear term in the isobaric mass-multiplet equation and the predictions are then compared with experimental values after the addition of the Coulomb contribution. The agreement is found to be good as observed for $sd$ shell nuclei earlier. One also sees that in this method the contribution to the linear term comes almost completely from the one-body isovector Hamiltonian, resulting in a huge simplification of the problem.