Direct Nuclear Reaction

a nuclear process in which energy introduced into the atomic nucleus is imparted preferentially to one nucleon or to a small group of nucleons. A number of types exist. Direct nuclear reactions can be caused by all possible incident particles, from gamma quanta to multiply charged ions, over a wide range of energies (from a few million to several billion electron volts). They are characterized by marked angular anisotropy and a comparatively weak dependence of the probability of the process—that is, the effective cross section for the process—on the particle’s energy. The nucleus formed as a result of a direct nuclear reaction is generally in either a weakly excited state or the ground state.

Direct nuclear reactions were discovered in the early 1950’s. The first to be detected were deuteron stripping (d, p) and pickup (p, d) reactions involving light nuclei. The protons and deuterons emitted in these reactions emerge primarily in the direction of the beam of incident particles. Direct nuclear reactions are known wherein a nucleon or group of nucleons crosses over from one of the colliding nuclei to another. A direct nuclear reaction of the type (x, xy) is called quasi-elastic scattering. In these reactions, the relation between the momenta and energies of the incident particle (x) and of the outgoing particles (x, y) is almost the same as in the elastic scattering of the particle x by the free particle y. The quasi-elastic scattering reactions produced by alpha particles, protons, and π-mesons in light nuclei are the best studied. Other reactions that have been observed include the knocking out of weakly bound particles—deuterons—from the nucleus, that is, reactions such as (p, pd).

The characteristics of direct nuclear reactions can be explained by assuming that the particles emitted from the nucleus acquire energy and momentum in the process of direct interaction with the incident particle, while the remainder of the target nucleus is involved in the reaction only as an “onlooker” or “spectator.” In this respect, direct nuclear reactions are quite the opposite of nuclear reactions that pass through a stage of formation of a compound nucleus, where the energy introduced into the nucleus is statistically distributed among all the nucleons because of multiple collisions of the nucleons with each other.

It is assumed in the theory of direct nuclear reactions that such reactions occur at the periphery of the nucleus, where the nucleon density is low. Consequently, a nucleon that has acquired sufficient energy through interaction with an external agent has a considerable probability of leaving the nucleus without any collisions. The peripheral layer of the nucleus has an extent of ~ 1 fermi, and the radius of medium-size and heavy nuclei can reach 10 fermis. Thus, the relative probability of a direct nuclear reaction should be ~ 10 percent (somewhat higher for light nuclei). These estimates have been confirmed experimentally.

The first quantitative theory of direct nuclear reactions was proposed by S. Butler of Australia in the 1950’s and applied to stripping reactions. The theory was based on the quantum mechanical (Schrödinger) description of the nucleus and on the use of the concepts of the potential interaction of the incident particle with the nucleons. The development of this theory led to the formulation of the Born approximation with distorted waves, which, in addition to the interaction event causing the reaction, takes into account the diffraction of the incident particles by the target nucleus and of the outgoing particles by the residual nucleus.

A different approach to the theory of direct nuclear reactions, based on the use of the methods of quantum field theory (Feynman diagrams), was formulated in the 1960’s. This approach, sometimes called the dispersion theory of direct nuclear reactions, was adopted because of the inapplicability of the potential approximation to reactions involving relativistic particles and because of the increase in the variety of direct nuclear reactions. Of particular importance in this regard was the detection of the knocking out of dense particles that do not exist stably in the nucleus and therefore cannot be described by wave functions. Dispersion theory permits the probability of a direct nuclear reaction to be expressed in terms of constants characterizing the nucleus—for example, the effective number of particles of a given kind at the periphery of the nucleus—and in terms of the probability amplitude of an elementary event-that is, of the process of interaction of incident and intranuclear particles. Dispersion theory also permits determination of the range of applicability of the concepts of direct interaction for specific reactions and indicates the experiments that are necessary to establish the mechanism of the process.

Direct nuclear reactions are used to study the spectrum of nuclear levels and the structure of the nuclear periphery, especially peripheral correlated groups of nucleons (clusters). They are also used to obtain data on the interaction of unstable elementary particles with neutrons and nucleonic isobars; such data are important in studies of direct nuclear reactions at high energies.