The dissociation reaction ${}^{6}\mathrm{He}\ensuremath{\rightarrow}\ensuremath{\alpha}+2n$ was studied with ${}^{6}\mathrm{He}$ projectiles at 23.9 MeV/nucleon in targets of C, Al, Cu, Sn, Pb, and U. Relative to Al, the $2n$ removal cross section ${\ensuremath{\sigma}}_{\ensuremath{-}2n}$ with each of the other targets was determined. With U, the Coulomb part accounts for 2/3 of ${\ensuremath{\sigma}}_{\ensuremath{-}2n}.$ The widths of the $\ensuremath{\alpha}$ particle and neutron parallel momentum distributions increase with target Z. For the $\ensuremath{\alpha}$ particle, ${}^{6}\mathrm{He}$ dissociation on C gave width $\ensuremath{\sigma}=40.2\ifmmode\pm\else\textpm\fi{}2.3 \mathrm{MeV}/c,$ corresponding to an rms radius of the halo neutrons of (2.95\ifmmode\pm\else\textpm\fi{}0.17) fm, which is (0.35\ifmmode\pm\else\textpm\fi{}0.17) fm larger than the rms radius of all four neutrons. The relation between the widths of the $\ensuremath{\alpha}$ particle and neutron distributions indicates only a small correlation between the two neutrons. This conclusion is supported by the distribution function for the angle between the two neutrons, which was obtained in kinematically complete measurements. The latter measurements with the U target also yielded an $E1$ strength function, and it agreed with one determined in an experiment at ten times our beam energy.