Four-body distorted wave theory appropriate for nucleon-nucleus reacti
ons leading to three-body continuum excitations of two-neutron Borrome
an halo nuclei is developed. The peculiarities of the halo bound state
and three-body continuum are fully taken into account by using the me
thod of hyperspherical harmonics. The procedure is applied for A=6 tes
t-bench nuclei; thus we report detailed studies of inclusive cross sec
tions for inelastic He-6(p,p')He-6 and charge-exchange Li-6(n,p)He-6*
reactions at nucleon energy 50 MeV. The theoretical low-energy spectr
a exhibit two resonancelike structures. The first (narrow) is the exci
tation of the well-known 2(+) three-body resonance. The second (broad)
bump is a composition of overlapping soft modes of multipolarities 1(
-),2(+),1(+),0(+) whose relative weights depend on transferred momentu
m and reaction type. Inelastic scattering is the most selective tool f
or studying the soft dipole excitation mode.