+ core structure described with an additional interaction in the nuclear matter saturation region

In a phenomenological approach, the $$\alpha $$ + core structure is investigated in the $$^{20}$$Ne, $$^{44}$$Ti, $$^{94}$$Mo, $$^{104}$$Te, and $$^{212}$$Po nuclei through the local potential model using a double-folding nuclear potential with effective nucleon-nucleon interaction of M3Y + $$c_{\textrm{sat}}\delta (s)$$ type, where the term $$c_{\textrm{sat}}\delta (s)$$ acts only between the saturation regions of $$\alpha $$-cluster and core. Properties such as energy levels, $$\alpha $$-widths, B(E2) transition rates, and half-lives are calculated, and good level of agreement with experimental data is obtained in general. It is shown the inclusion of the term $$c_{\textrm{sat}}\delta (s)$$ is determinant for a better description of the experimental energy levels compared to the ground state bands produced with the simple M3Y interaction. The properties calculated for $$^{104}$$Te reinforce the superallowed $$\alpha $$-decay feature for this nucleus, as indicated in previous studies