The aim of this work is to calculate the transfer strengths to the excited $0^{+}$ states in ${}^{130,132,134}\mathrm{Ba}$ which have been identified in ($p,t$) reactions and to investigate their related properties. For this purpose, we have used a model Hamiltonian which includes monopole pairing, quadrupole-quadrupole, and spin-quadrupole interactions. The model Hamiltonian has been diagonalized with the random phase approximation (RPA). To investigate the general trend of the transfer strengths to the excited $0^{+}$ states, two-nucleon transition intensities relative to the transition to the ground state and their cumulative values have been calculated versus energy and compared with the data. The comparisons revealed that fairly good results for the distribution of the energies and the transfer strengths have been obtained. For almost all nuclei, the cumulative values of the transfer strengths were nicely predicted. Moreover, qualitatively, a parallel result that agrees with the data and the prediction of the O(6) limit of the IBM model which is a weak excitation for the first $0^{+}$ state and a strong one for the second $0^{+}$ state has been obtained for ${}^{130}\mathrm{Ba}$ and ${}^{132}\mathrm{Ba}$.

• Received 6 April 2010

DOI:https://doi.org/10.1103/PhysRevC.82.024306