Transfer reactions and knockout reactions

Nucleon transfer reactions have a long and venerable history in nuclear reaction studies [1,2]. They have well-defined two-body initial and final states, and the interaction involves the transfer of a nucleon between the target and projectile nuclei. The probability for this process involves kinematic matching conditions as well as structural overlap contributions. The transfer probability falls with increasing beam velocity, and an energy regime of 10 - 20 MeV/u has proven most useful for the study of transfer, free of compound nuclear effects. Differential cross sections are typically of order 10 mb sr^-1. In the most commonly applied theories (e.g. DWBA), the transferred nucleon is represented as being in a single particle orbital before and after the transfer, or at least in a state that can be represented as a linear combination of such wavefunctions. This is a reasonable approximation, so long as the various configurations involved are not strongly coupled together, as they could be for example by a strong collective rotational or vibrational excitation. Experimental measurements give the angular momentum transferred by the nucleon and measure the overlap of the actual nuclear states with specified single-particle states, characterised by a spectroscopic factor. Knockout reactions measure the probability of nucleon removal from the projectile by observing the surviving nuclei [3,4]. These reactions are studied in an energy regime where the interaction with the target can be taken to be extremely peripheral, namely 100 - 200 MeV/u. The nucleon is removed by the interaction between the tail of its wave function, where it extends beyond the core of the projectile nucleus, and the target nucleus. It is then obvious that this mechanism is an excellent probe of halo nuclei and other weakly bound nuclei, such as those found near the neutron drip line. The cross sections in these cases are of order 100 mb sr^-1. Most likely, the applicability of knockout reactions will eventually be demonstrated over a wide range of masses and binding energies, though for more bound nuclei the cross sections will be much closer to those for transfer. In knockout studies, the ground state of the projectile can again be characterised in terms of single particle structure using a spectroscopic factor. The angular momentum of the removed nucleon can be determined directly from the width of the longitudinal momentum distribution of the surviving core, which carries the imprint of the sudden removal. It is clear that transfer reactions can be used to identify single particle levels, and the fragmentation of single particle strength, near closed shells such as ¹³²Sn for example. Another application that is less widely appreciated is to the study of deformed nuclei. Single nucleon transfer on an even-even deformed target can populate states in a rotational band built on a particular Nilsson orbital. The wave function of the orbital can be written as an expansion in terms of the spherical orbitals in the same major shell, which have a well defined angular momentum. When the transferred nucleon populates a state in the rotational band, it carries in a spin j which must match the spin of the state, and it selects just the component of the expansion that has spin j. For each state in the band, this corresponds to a different component in the expansion, and the result is a `fingerprint' pattern across the states in the band, which is characteristic of the Nilsson orbital [5,6]. The ability to identify the Nilsson orbitals helps to determine the deformation. In principle the knockout studies can also be adapted to study `fingerprint' patterns from deformed nuclei.