Spectroscopy of Radioactive Beams from Single-Nucleon Knockout Reactions: Application to the $\mathit{sd}$ Shell Nuclei ${}_{}{}^{25}{}_{}{}^{}Al$ and ${}_{}{}^{26,27,28}{}_{}{}^{}P$

Measurements of deexcitation $\gamma$ rays in coincidence with the momentum distribution of the projectile residues produced in reactions of the type ${}^9\mathrm{Be}{(}^{28}\mathrm{P}{,}^{27}\mathrm{Si}+\gamma )X$ at energies around 65 MeV/u are used to study single-nucleon stripping to individual states. The cross sections are compared with calculations based on an eikonal model description of the reaction and the shell model. The measurements indicate that the halo character of the ground state and other detailed spectroscopic information can be derived using knockout reactions in inverse kinematics.