  Fragment separator ACCULINNA-2 has been built in the Flerov Laboratory of
Nuclear reactions (JINR, Dubna). It is timely now to choose meaningful and
challenging objectives for experiments dedicated to the study of light
drip-line nuclei. Considerable interest makes the search for the minor
$2p$-decay branch of the first excited state of $^{17}$Ne. The knowledge on the
$\Gamma_{2p}/\Gamma_{\gamma}$ width ratio for this excited state is of
considerable interest because the reverse process of simultaneous two-proton
radiative capture could be a bypass for the $^{15}$O "waiting point" occurring
in the rp-process of nucleosynthesis. Accumulation of high-statistics data for
the $^{10}$He excitation spectrum populated in the $^2$H($^8$He,$p$)$^9$He and
$^3$H($^8$He,$p$)$^{10}$He reactions, as well as the study of cross-check
reactions made with the $^{11}$Li and $^{14}$Be beams, will make an effective
way to clarify the succession of $^{10}$He excited states. A hot topic beyond
the neutron drip line makes the observation of results capable to elucidate the
low-energy resonance states anticipated for the $4n$ decay of $^{7}$H. The RIB
beams provided by ACCULINNA-2 will allow one to perform experiments where
luminosity coming to a level of more than $2 \times 10^{26}$ cm$^{-2}$ s$^{-1}$
will be achievable in experiments aimed study of the $^2$H($^8$He,$^3$He)$^7$H
and $^2$H($^{11}$Li,$^6$Li)$^7$H reactions.
