  In this paper we show that the theory of transfer reactions from bound to
continuum states is well suited to extract structure information from data
obtained by performing "spectroscopy in the continuum". The low energy unbound
states of nuclei such as $^{10}$Li and $^{5}$He can be analyzed and the
neutron-core interaction, necessary to describe the corresponding borromean
nuclei $^{11}$Li and $^{6}$He can be determined in a semi-phenomenological way.
An application to the study of $^{10}$Li is then discussed and it is shown that
the scattering length for s-states at threshold can be obtained from the ratio
of experimental and theoretical cross sections. The scattering single particle
states of the system n+$^{9}$Li are obtained in a potential model. The
corresponding S-matrix is used to calculate the transfer cross section as a
function of the neutron continuum energy with respect to $^{9}$Li. Three
different reactions are calculated $^{9}Li(d,p)^{10}Li$,
$^{9}Li(^{9}Be,^{8}Be)^{10}Li$, $^{9}Li(^{13}C,^{12}C)^{10}Li$, to check the
sensitivity of the results to the target used and in particular to the transfer
matching conditions. Thus the sensitivity of the structure information
extracted from experimental data on the reaction mechanism is assessed.
