Search for the $\alpha$ + core structure in the ground state bands of $22 \leq Z \leq 42$ even-even nuclei

A systematic analysis of the $\alpha$ + core structure is performed in the ground state bands of even-even nuclei of the $22 \leq Z \leq 42$ region in terms of the Local Potential Model. The $\alpha$ + core interaction is described by the nuclear potential of (1 + Gaussian)$\times$(W.S. + W.S.$^3$) shape with 2 free parameters. Properties such as energy levels, reduced $\alpha$-widths, $B(E2)$ transition rates and rms charge radii are calculated and compared with experimental data. A good agreement with the experimental data is obtained in general, even for the nuclei without the $\alpha$ + {doubly closed shell core} configuration. The analysis of the selected nuclei in the $22 \leq Z \leq 42$ region indicates that $^{44}$Ti and $^{94}$Mo have a greater $\alpha$-clustering degree in comparison with their respective neighboring nuclei of this set. In addition, the model points to the existence of nuclei without the $\alpha$ + {doubly closed shell core} configuration with a significant $\alpha$-clustering degree compared to $^{44}$Ti, $^{60}$Zn, and $^{94}$Mo. The study shows that the $\alpha$ + core approach is satisfactorily applicable to nuclei other than those with $\alpha$-clustering above double-shell closures.