▪ Abstract  The identification of direct-reaction processes and their subsequent exploitation for the spectroscopy of weak radioactive beams of exotic nuclei are important problems in modern nuclear physics. One- and two-nucleon knockout reactions, studied using intermediate-energy radioactive beams, have been shown to be powerful tools for this purpose. This article discusses the current status of such investigations and reviews what has been learned to date from the experiments and analyses of the past five years. The techniques are still in their formative stages, and the open questions and challenges are outlined.

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There is now a large and increasing body of experimental data and theoretical analyses for reactions that remove a single nucleon from an intermediate-energy beam of neutron-or proton-rich nuclei. In each such measurement, one obtains the inclusive cross section for the population of all bound final states of the mass A − 1 reaction residue. These data, from different regions of the nuclear chart, and that involve weakly and strongly bound nucleons, are compared with theoretical expectations. These calculations include an approximate treatment of the reaction dynamics and shell-model descriptions of the projectile initial state, the bound final states of the residues, and the single-particle strengths computed from their overlap functions. The results are discussed in the light of recent data, more exclusive tests of the eikonal dynamical description, and calculations that take input from more microscopic nuclear structure models. Fast nucleon removal reactions have been developed as an effective direct reaction, producing highly neutron-proton asymmetric nuclei with relatively high cross sections. The combination of intermediate-energy secondary beams and thick reaction targets has led to precise measurements for a large number of the most exotic nuclei. The yields are usefully large because (a) essentially all bound reaction residues are detected, with ≈100% efficiency, and (b) the measured cross sections are highly inclusive, with respect to the target final states. We concentrate here on the systematics of such reactions on light target nuclei, either 9 Be or 12 C, for which nucleon removal associated with the Coulomb interaction (i.e., elastic Coulomb dissociation) is negligible. Here, the two strong-interaction-driven nucleon-removal mechanisms are elastic and inelastic breakup of the projectile in which the target nucleus remains in or is excited from its ground state, respectively [1].In this work we discuss, in the main, the sum of these two contributions. In measurements that determine only the number of bound residual nuclei, the cross sections are, of course, also inclusive with respect to all bound states of the reaction residue. In such proton-neutron asymmetric systems, these final-state spectra are very often unknown or only partially known. In the following analyses these final-state spins, parities, and excitation energies are therefore normally taken from shell-model calculations and the theoretical inclusive cross sections are taken to be the sum of the calculated cross sections to all of the predicted shell-model states of the residue with excitation energies below the empirical, if known, or the evaluated [2] lowest of the particle emission thresholds of the reaction residue; that is S n for neutron-rich and S p for neutron-deficient residues.The eikonal model theoretical description of the nucleonremoval reaction dynamics, that uses the sudden (fast collision) and eikonal (forward scattering) approximations, is presented and discussed in detail elsewhere, e.g., Refs. [1,3] and references t...