Continuum excitations in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow/><mml:mrow><mml:mn>6</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mi mathvariant="normal">He</mml:mi></mml:math>

The three-body breakup ${}^{6}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{He}}}^{4}\mathrm{He}+n+n$ is studied experimentally, using a secondary ${}^{6}\mathrm{He}$ ion beam of 240 MeV/nucleon incident on carbon and lead targets. Integrated cross sections for one- and two-neutron knockout and differential cross sections $d\ensuremath{\sigma}{/dE}^{*}$ and $d\ensuremath{\sigma}/d\ensuremath{\vartheta}$ for inelastic nuclear or electromagnetic excitations into the ${}^{6}\mathrm{He}$ continuum are presented. The $E$1-strength distribution is deduced from electromagnetic cross sections and is found to exhaust $(10\ifmmode\pm\else\textpm\fi{}2)%$ of the energy-weighted Thomas-Reiche-Kuhn sum rule or $(40\ifmmode\pm\else\textpm\fi{}8)%$ of the cluster sum rule for excitation energies below 5 MeV. Both the energy-weighted and non-energy-weighted dipole cluster sum rules are almost exhausted integrating the strength up to 10 MeV, a fact from which the root-mean-square distance between the $\ensuremath{\alpha}$ core and the two valence neutrons of ${r}_{\ensuremath{\alpha}\ensuremath{-}2n}=(3.36\ifmmode\pm\else\textpm\fi{}0.39)$ fm is derived. The known ${I}^{\ensuremath{\pi}}{=2}^{+}$ (1.80 MeV) resonance in ${}^{6}\mathrm{He}$ is observed in nuclear inelastic scattering; model-dependent values of the quadrupole deformation parameter ${\ensuremath{\delta}}_{2}=(1.7\ifmmode\pm\else\textpm\fi{}0.3)$ fm or ${B(E2,0}^{+}\ensuremath{\rightarrow}{2}^{+})=(3.2\ifmmode\pm\else\textpm\fi{}{0.6)e}^{2} {\mathrm{fm}}^{4}$ are derived. No clear signature could be obtained for predicted higher-lying ${2}^{+}$ resonances, but low-lying continuum strength of multipolarity other than dipole, likely of monopole and quadrupole multipolarity, is indicated by the data. Two-body correlations in the decaying ${}^{4}\mathrm{He}+n+n$ system are investigated. The astrophysical relevance of the data with regard to the two-neutron capture process ${}^{4}\mathrm{He}(2n,\ensuremath{\gamma}{)}^{6}\mathrm{He}$ is briefly discussed.