  Within the complex-energy configuration interaction framework, we study
correlations of valence neutrons to explain the behavior of charge radii in the
neutron halo nuclei $^{6,8}$He. We find that the experimentally observed
decrease of the charge radius between $^6$He and $^8$He is caused by a subtle
interplay between three effects: dineutron correlations, a spin-orbit
contribution to the charge radius, and a core swelling effect. We demonstrate
that two-neutron angular correlations in the $2^+_1$ resonance of $^6$He differ
markedly from the ground-state correlations in $^{6,8}$He.
