  There exists a class of nuclei that are obtained by adding one nucleon to a
loosely-bound nucleon-core system, for example $^{12}$Be, $^9$C, $^{18}$Ne. For
such nuclei, one-nucleon overlap integrals that represent single-particle
motion can strongly differ from the standard ones due to the correlations
between the two nucleons above the core. The possible non-standard overlap
behaviour should be included in the interpretation of the experimental data
derived from one nucleon removal reactions such as knockout, transfer and
breakup, as well as the predictions of low-energy nucleon capture that leads to
these nuclei. We investigate the non-standard behaviour within a three-body
model and discuss the challenges associated with this problem.
