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Calculations of inclusive ${\alpha}$ particle production are performed tointerpret reaction experimental data induced by the two-neutron halo $^6$He andthe isotopes $^{6,7}$Li on different target nuclei. We have implemented thezero-range post-form DWBA to compute the elastic and nonelastic breakup crosssections. Integrated cross sections, angular distributions and spectra arepresented. Projectiles are approximated as two-body clusters, namely $^6$He as${\alpha}$+dineutron and $^{6}$Li ($^{7}$Li) interpreted as${\alpha}$+deuteron(triton). The S\~ao Paulo optical potential is employed inthe calculation of the distorted wave functions for the incident channels,while standard phenomenological interactions are used for the fragment-targetinteractions. Calculations for $^6$Li and $^7$Li furnish a good description ofthe data, while the reaction involving $^6$He is found to be a complicatedcase, where data interpretation is still considered a major obstacle. Thepresent analysis identifies an overall large contribution from inclusivebreakup emissions for all the cases studied.

Inclusive Breakup Cross Sections in Reactions Induced by the Nuclides $^6$He and $^{6,7}$Li in the Two-Body Cluster Model