Resonance Effects in Nuclear Processes

Abstract

A general formula is developed for the probability of nuclear processes with particular consideration of resonance (\textsection{}2). The dependence of the cross section on the energy of the incident particle can be divided into two parts: Firstly, the dependence over energy regions small compared to nuclear energies, and secondly that over large energy regions, of the order of a million volts or more. The first dependence is completely given by the resonance formula; it shows resonance maxima and besides a simple general trend with the particle energy such as the $\frac{1}{v}$ law. The dependence over large energy regions cannot be found without referring to a special nuclear model. (If the problem of nuclei were a one-body rather than a many-body problem, there would be only the dependence over large energy regions. Thus much more theoretical information of a general nature can be obtained for the many-body than for the one-body problem.) The nuclear processes may be divided into several classes according to whether light quanta or material particles are concerned. The selection rules for the various kinds of processes are given (\textsection{}3). Another useful classification is according to the speed of the particles involved: Slow particles are such whose wave-length is long compared to nuclear dimensions. This means energies below about 300,000 volts for heavy, 1 MV for light nuclei. $\ensuremath{\gamma}$-rays are to be classed as fast particles. When a slow particle produces a nuclear reaction, the cross section contains a factor $\frac{1}{v}$ ($v=\mathrm{velocity}$ of the incident particle) besides the resonance factor; when a slow particle is produced, a factor ${v}^{\ensuremath{'}}$ ${v}^{\ensuremath{'}}=\mathrm{velocity}$ of the outgoing particle) appears in the cross section. If the reaction involves only fast particles, the resonance factor is the only significant one; the same is true for the of slow particles. Explicit formulae for the various cases are given. The problem of the wave functions to be chosen for the incident particle is discussed in \textsection{}4. Arguments are given for using wave functions in a repulsive potential, corresponding to the assumption that the particle as a free particle cannot exist inside the nucleus. The scattering arising as a consequence of this assumption, is discussed and compared to the resonance scattering. In \textsection{}\textsection{}5 to 7 the capture of slow neutrons is discussed. The influence of the Doppler effect on the capture cross section is taken into account. Expressions are derived for the activation and for the absorption coefficient with self-indication, both for resonance and for thermal neutrons. These expressions allow for the influence of the line shape in the former case and for the $\frac{1}{v}$ law in the latter. Methods for the determination of the energy, radiation width and neutron width of the compound levels are discussed (\textsection{}6) and applied (\textsection{}7) to Ag, Rh, I and Cd. The importance of the interference of several resonance levels is emphasized, particularly for the capture of thermal neutrons. The properties of fast neutrons are briefly discussed (\textsection{}8). In the case of charged particles (\textsection{}10), the width of the resonance levels is reduced by the potential barrier. The width of resonance levels observed in the simple capture of protons is found in agreement with reasonable expectations. The widths of the levels in reactions produced by $\ensuremath{\alpha}$-particles are probably smaller than has been observed. In the reaction of charged particles with heavy nuclei, no resonance effects can be observed because the energy of the incident particles cannot be defined accurately enough. The photodissociation of nuclei by $\ensuremath{\gamma}$-rays (\textsection{}11) is not the inverse process of the radiative capture of particles. The cross section for the photodissociation of a heavy nucleus is about ${10}^{\ensuremath{-}28}$ ${\mathrm{cm}}^{2}$ if the energy of the particle produced (neutron) is larger than about 1 MV. This should make the process just observable. The of $\ensuremath{\gamma}$-rays by heavy nuclei has a cross section of the same order which makes it unobservably small compared to the Klein-Nishina scattering.