  New measurements and reaction model calculations are reported for single
neutron pickup reactions onto a fast \nuc{22}{Mg} secondary beam at 84 MeV per
nucleon. Measurements were made on both carbon and beryllium targets, having
very different structures, allowing a first investigation of the likely nature
of the pickup reaction mechanism. The measurements involve thick reaction
targets and $\gamma$-ray spectroscopy of the projectile-like reaction residue
for final-state resolution, that permit experiments with low incident beam
rates compared to traditional low-energy transfer reactions. From measured
longitudinal momentum distributions we show that the $\nuc{12}{C}
(\nuc{22}{Mg},\nuc{23}{Mg}+\gamma)X$ reaction largely proceeds as a direct
two-body reaction, the neutron transfer producing bound \nuc{11}{C} target
residues. The corresponding reaction on the \nuc{9}{Be} target seems to largely
leave the \nuc{8}{Be} residual nucleus unbound at excitation energies high in
the continuum. We discuss the possible use of such fast-beam one-neutron pickup
reactions to track single-particle strength in exotic nuclei, and also their
expected sensitivity to neutron high-$\ell$ (intruder) states which are often
direct indicators of shell evolution and the disappearance of magic numbers in
the exotic regime.
