Background

Though the concept of the nucleus and the subsequent evolution of nuclear physics are credited to Rutherford, the earlier discovery of radioactivity by A. Henri Becquerel, Pierre and Marie Curie (1896–1898) played the most crucial role in these developments. The discovery of radioactivity opened up the way to new techniques of exploring subatomic systems – for example, by bombarding them with fast moving charged particles, a technique which is still in use, and used more vigorously now, even after hundred years.

In 1898, Pierre and Marie Curie succeeded in isolating significant amounts of two new elements from pitchblende, a uranium ore. They named the two elements polonium and radium. These new elements were found to undergo spontaneous self-destruction by emitting mysterious radiations. Passing of the collimated beam of these radiations through electric and magnetic fields revealed that they are made up of three components: negatively charged components, called beta particles; neutral components of electromagnetic waves of very short wavelength or gamma rays and a third component of positively charged particles. The negatively charged beta particles were identified as electrons, while the Curies established that the positively charged particles were doubly-ionized helium atoms, called alpha particles. The average kinetic energies of these alpha particles, beta particles and neutral gamma rays had different values for different radioactive sources. Radium and polonium, the two natural radioactive sources, emit alpha particles of energies in the range of 5 to 7 MeV. Rutherford, in his famous alpha scattering experiments, actually carried out by Geiger and Marsden, bombarded thin metallic foils by a collimated beam of alpha particles obtained from radium. In these experiments, it was observed that, on an average, one to five alpha particles out of about 20,000 particles, get scattered by more than 90°. Rutherford concluded that this is possible only if the target atoms have very small volumes at their centres where total positive charge and almost all mass of the atom are concentrated. Rutherford named this small volume as the nucleus of the atom, a term he borrowed from biological science. The layout of the experimental setup used by Rutherford is shown in Figure 1.1. The alpha particle source (radium) was kept in a lead box with a small hole to get the collimated beam.

Introduction

As has been mentioned in the introductory chapter, the initial interaction between a projectile and the target may result in the formation of an excited composite system from which nucleons or clusters may be emitted before a completely fused compound nucleus is formed. Such a process is generally referred to as the pre-compound emission (in case of nucleonic emissions) or incomplete fusion (when cluster emission takes place). Incomplete fusion/PE-emissions become more important as the incident beam energy increases; in fact, they become dominant at energies above 15 MeV/n. The measurement and analysis of excitation functions for the population of reaction residues may provide valuable information regarding the dynamics of incomplete fusion reactions. The resulting product nucleus of incomplete fusion has a momentum that is severely reduced as compared to the residues of complete fusion events. The measurement and analysis of momentum transfer via recoil range distribution is one of the most direct and irrefutable method of identifying incomplete fusion events. Details of the measurement of linear recoil range distributions (RRD) will be discussed later in the chapter. In incomplete fusion (ICF), residues recoil before the establishment of a thermodynamic equilibrium, and therefore, carry information about the initial system parameters that is reflected in the angular distribution of residues. Details of the measurement and analysis of residue angular distributions will also be presented in this chapter. In a typical experiment, residues are formed via complete fusion as well as via incomplete fusion processes. The product residues of complete fusion carry larger excitation energy and higher spin angular momentum when compared to the residues populated via incomplete fusion. This difference in their properties affects the spin distributions of their excited levels. In order to further investigate such systems and study the role of input angular momenta in ICF reactions, in-beam experiments involving particle–gamma coincidence method have been performed. Details of these experiments will be presented in the following sections. In recent years, incomplete fusion reactions have been observed even at energies as low as 3 – 7 MeV/n, where only complete fusion is likely to dominate. The present monograph deals with the description of such reactions in the low energy regime.

Complete Fusion of Heavy Ions

Complete fusion of heavy ions is theoretically treated in the framework of a statistical compound reaction mechanism. In heavy ion collisions, a large number of resonances is excited in the compound system, involving many degrees of freedom. A complete description of such a complex collision process is almost impossible to obtain. However, the mean value of crosssection averaged over several resonances is generally of interest, and can be estimated using the statistical approach. The statistical compound reaction model is founded on the works of Bohr, Bethe, and Weisskopf. Wolfenstein and Hauser and Feshbach extended the model to include the conservation of total angular momentum. The statistical compound model was further refined by Moldauer and Lane and Lynn.

Nuclear reactions may be classified in terms of different parameters, including the reaction time. Fast reactions involving reaction times of the order of the time taken by a nucleon to pass through the nucleus (≈10–21 s) corresponds to direct reactions. Slower processes of reaction times of the order of 10–16 s or so come in the category of compound and pre-compound (or pre-equilibrium, or multistep compound and multistep direct) reactions. The compound reaction mechanism, being the slowest, assumes that the excited compound nucleus formed by the fusion of the target and the projectile lives long enough, without decay, for thorough mixing of the target and projectile nucleons to take place and a thermodynamic equilibrium be established in the compound system. Sometimes, it is convenient to call the fused system formed by the amalgamation of the projectile with the target, before the establishment of thermal equilibrium, as an excited composite system that becomes the compound nucleus (CN) when thermal equilibrium is established. Pre-compound reactions occur during the time taken by the excited composite system to transit to the compound nucleus. In this section, we consider the pure compound reaction mechanism and assume that the composite system becomes a compound nucleus without losing any nucleons or clusters. Almost all nuclear models that aim to determine reaction cross-sections make use of the optical model which enables the separation of the total cross-section into different components and provides transmission coefficients that are used in the compound nucleus model.

This book addresses the single particle dynamics heart of the question; ‘How does an accelerator work?’, for readers who are accelerator users and operators, who are accelerator physicists or who are interested in real-world linear and nonlinear difference systems. The reader might be a synchrotron light source user, a collider experimentalist, a medical accelerator operator, an engineer in a beam instrumentation group or a controls professional in industry.

The level of the discussion is appropriate for graduate students, final-year undergraduates and practicing accelerator professionals. This is not an exhaustively complete reference handbook, at a high technical level. Rather, it is a pedagogical introduction to the subject, telling a self-contained and accurate story about a field of physics that was born and grew rapidly in the second half of the twentieth century, and which continues to mature by leaps and bounds in the twenty first. The treatment is rigorous enough to be accurate and useful, without letting unnecessary detail obscure the central theme. Deeper investigations of the ‘back-stories’ are left to other sources.

The central theme is that repetitive motion through an accelerator is a natural, convenient and well-motivated introduction to the generic linear and nonlinear behaviour of highly iterated difference systems. A circular accelerator – or even a linear accelerator – is one answer to another question: ‘How do difference systems manifest themselves in the real world?’