Microscopic Calculation of Six-Body Inelastic Reactions with Complete Final State Interaction: Photoabsorption of ${\text{\hspace{0.17em}︀}}^6\mathrm{H}\mathrm{e}$ and ${\text{\hspace{0.17em}︀}}^6\mathrm{L}\mathrm{i}$

Six-body inelastic reactions are calculated microscopically including the full six-nucleon final state interaction. The total cross sections of $\gamma +{\text{\hspace{0.17em}︀}}^6\mathrm{H}\mathrm{e}\left({\text{\hspace{0.17em}︀}}^6\mathrm{L}\mathrm{i}\right)\to X$ are considered as examples. The Lorentz integral transform method and the effective interaction approach for the hyperspherical formalism are employed. While ${\text{\hspace{0.17em}︀}}^6\mathrm{L}\mathrm{i}$ has a single broad giant resonance peak, there are two well separated peaks for ${\text{\hspace{0.17em}︀}}^6\mathrm{H}\mathrm{e}$ corresponding to the breakup of the neutron halo and the $\alpha$ core, respectively. The comparison with the few available experimental data is discussed.