We describe electromagnetic and $\alpha$-decay transitions to low-lying excited states in even-even nuclei within the coherent state model (CSM). We reproduced the energies and $B\left(E2\right)$ values for ground state bands in 40 daughter nuclei with known $\alpha$-branching ratios to $2^{+}$ states. To this purpose we used two parameters, namely the deformation parameter and the strength of the harmonic CSM Hamiltonian. The Hamiltonian describing the $\alpha$-emission process is given by two terms. The first term describes the dynamics of the daughter nucleus. The second $\alpha$-daughter component contains the monopole potential, estimated within the double folding procedure with M3Y interaction plus a repulsive core simulating Pauli principle and a quadrupole-quadrupole (QQ) interaction. The decaying states are identified with the lowest narrow outgoing resonances in this potential. The $\alpha$-branching ratios to $2^{+}$ states were reproduced by using the QQ strength depending linearly on the deformation parameter, as predicted by CSM. The theoretical intensities to $4^{+}$ and $6^{+}$ states are in a reasonable agreement with available experimental data. We found out that the QQ coupling strength is by one order of magnitude larger in the region above ${}^{208}$Pb, where the $\alpha$ clustering is known to be stronger, in comparison to other nuclei. This formalism is able to simultaneously describe electromagnetic and $\alpha$ decays to excited states in spherical, transitional, and well deformed nuclei.

• Received 14 February 2013

DOI:https://doi.org/10.1103/PhysRevC.87.044314