  Five $\Xi^- p\to \Lambda\Lambda$ two-body capture events in $^{12}$C and
$^{14}$N emulsion nuclei, in which a pair of single-$\Lambda$ hypernuclei is
formed and identified by their weak decay, have been observed in $(K^-,K^+)$
emulsion exposures at KEK and J-PARC. Applying a $\Xi^-$-nucleus optical
potential methodology to study atomic and nuclear transitions, we confirm that
these capture events occur from Coulomb assisted $1p_{\Xi^-}$ nuclear states.
Long-range $\Xi N$ shell-model correlations are found essential to achieve
consistency between the $^{12}$C and $^{14}$N events. The resulting
$\Xi$-nuclear interaction is strongly attractive, with $\Xi$ potential depth in
nuclear matter $V_{\Xi}\gtrsim 20$ MeV. Implications to multi-strangeness
features of dense matter are outlined.
