We study the effects of the isospin-symmetry breaking on the superallowed Fermi $\beta$ decay of the ground state of $^{82}$Nb to $^{82}$Zr. Results on the analog as well as non-analog $\beta$ decay branches are self-consistently obtained within the $complex$ Excited Vampir approach. The $^{82}$Nb$\to ^{82}$Zr $\beta$ decay to the first two excited 0$^+$ states with significant strength is predicted to coexist with the superallowed decay. The structure and electromagnetic properties of the analog and non-analog low- and high-spin states in $^{82}$Nb and $^{82}$Zr are compared with the available experimental data.
2.The Gamow-Teller strength distributions for the beta decay of the ground state and the lowest-excited states in the nucleus $^{72}$Kr to the nucleus $^{72}$Br are investigated within the {\it complex} Excited Vampir variational approach using a rather large model space. The shape mixing is consistently described for both the 0$^+$ and 2$^+$ states in the even-even $^{72}$Kr, and the 1$^+$, 2$^+$ and 3$^+$ states in the odd-odd $^{72}$Br. The influence of shape mixing, comparison with the available data and predictions concerning the half-life of the first excited 0$^+$ and yrast 2$^+$ states of $^{72}$Kr are presented.
The work is done in collaboration with Institute fuer Theoretische Physik,
Universitaet Tuebingen, Germany.