Four-body distorted wave theory appropriate for nucleon-nucleus reactions leading to three-body continuum excitations of two-neutron Borromean halo nuclei is developed. The peculiarities of the halo bound state and three-body continuum are fully taken into account by using the method of hyperspherical harmonics. The procedure is applied for $A=6\mathrm{}$ test-bench nuclei; thus we report detailed studies of inclusive cross sections for inelastic ${}^6$He${(p,p}^{\prime }{)}^6$He${}^{*}$ and charge-exchange ${}^6$Li${\mathrm{}(n,p)\mathrm{}}^6$He${}^{*}$ reactions at nucleon energy 50 MeV. The theoretical low-energy spectra exhibit two resonancelike structures. The first (narrow) is the excitation of the well-known $2^{+}$ three-body resonance. The second (broad) bump is a composition of overlapping soft modes of multipolarities $1^{-}{,2\mathrm{}}^{+}{,1\mathrm{}}^{+}{,0\mathrm{}}^{+}$ whose relative weights depend on transferred momentum and reaction type. Inelastic scattering is the most selective tool for studying the soft dipole excitation mode.

• Received 1 May 1997

DOI:https://doi.org/10.1103/PhysRevC.56.1483