Dineutron clusters in $^7$He and $^8$He structure

The hyper-radial barrier strongly hinders formation of more than three clusters. We investigate how well the dominating cluster components in $^7$He and $^8$He, respectively can be described as $\alpha$+$n$+$^2n$ and $\alpha$+$^2n$+$^2n$, where $^2n$ is the dineutron. Effective interactions compatible with $^5$He and $^6$He are used. We vary the lesser known $n$-$^2n$ and $^2n$-$^2n$ interactions, where very small strengths are required. We provide energies, radii, and partial wave decomposition of all computed, predicted or measured, ground and resonance states. We predict substructures within each of the three-body quantum states. We also calculate the neutron-structure sensitive invariant mass spectrum of the four-nucleon system, after fast removal of the $\alpha$-particle from $^8$He. We show that all available experimental information are fairly well reproduced. Very little room is left for variation of the effective interaction parameters. Thus, the dominating features of the subsequently derived reaction and structure properties are well supported.