47. Which nuclei undergo fission?

Generally, all actinides (heavy nuclei starting from Th-232) can undergo fission induced by neutron. Of these, nuclei beyond uranium are unavailable in nature, but may be produced (artificially) in nuclear transmutations. U-233, U-235, Pu-239, and Pu-241 are called fissile nuclides, and can be fissioned with neutrons of any energy. Nuclides like Th-232, U-238,  etc., can undergo fission with neutron of certain minimum kinetic energy, called threshold energy, below which the probability of fission is too small to be significant. Other actinides undergo fission with varied probabilities. Many of the actinides exhibit spontaneous fission. The spontaneous fission probability of Cf-254 is significant.

48. What is spontaneous fission?

In the case of spontaneous fission, which is not caused by neutron, the original actinide of mass A itself fissions. Such a fission event must be understood as a mode of radioactive decay, like a decay. In other words, in a radioactive decay, just energy in the form of g rays, electrons (b particles), helium (a partilcles), etc., or, heavy nuclides like Xenon, Krypton, Barium, etc. could be emitted. U-238 mostly decays through a emission, while Cf-254 decays mostly through fission.

49. Which reactions are likely when a neutron hits a nucleus?

Many types of reactions are possible when a neutron hits a nucleus. The probability of each type of reaction happening depends on the nucleus and is very sensitive to the energy of the neutron. In this regard, two neighbouring nuclides (say, of masses A and A+1) may differ drastically. Some of the reactions are explained below:

Elastic scattering: The neutron and the nuclide collide and share a part of their kinetic energies. They rebound with speeds different from the original speeds, such that the ‘total kinetic energy’ before and after the collision remains the same. If the nucleus is stationary before collision, it will gain energy from the neutron and start moving, and the neutron gets slowed down due to loss of kinetic energy. This is the type of reaction that mostly helps fast neutrons to be slowed down to low energies in a reactor. Can the neutron gain energy? Yes. However, this is obviously possible when the nucleus has higher kinetic energy than the neutron. In a reactor, the average energy of a neutron produced in fission is about 2 MeV, whereas the average energy of the nuclei of the reactor materials is much below 1 eV. Therefore, the neutrons mostly undergo slowing down rather than gain energy. When the neutron is slowed to energies below the energies of the materials, the neutrons experience gaining energy as well. This would mostly happen below 1 eV, in a thermal reactor. In this range of energies, the neutrons and the nuclei would establish a thermal equilibrium.

Inelastic scattering: The neutron and the nuclide collide and rebound with speeds different from the original speeds, but the rebounding nuclide is left in an excited energy state. Hence the ‘total kinetic energy’ after the collision is less than that before the collision, and this difference accounts for the energy of excitation. If the nucleus is stationary before collision, the neutron must have kinetic energy exceeding the excitation energy, so that such a reaction is possible. Hence inelastic scattering is said to be a ‘threshold reaction’, the threshold being the minimum kinetic energy of the neutron required for the reaction to be possible. The excited nucleus subsequently de-excites by emitting g radiation. Heavy nuclides have lower thresholds than light nuclides. Though the probability of inelastic scattering is generally lower than elastic, the energy loss to the neutron is higher in an inelastic collision. Inelastic scattering in heavy nuclides degrades fission neutron energies heavily.

Capture: The neutron is absorbed by the target nucleus to form the next higher isotope (of mass A+1), in an excited state of energy. The new isotope de-excites by emitting g rays. The neutron is thus lost in this reaction. This is often known as ‘radiative capture’.

Fission: As explained earlier.

(n,x) reaction: In this reaction, ‘n’ represents neutron, and ‘x’ represents any particle like neutron, proton, deutron, a particle, etc. or a combination of such particles. It means that a neutron interaction with a nuclide results in emission of the particle(s) represented by ‘x’. (e.g.) if the emitted particle is a, it is called (n,a) reaction. If a neutron and a proton are emitted, then it is called (n,np) reaction. If 2 neutrons are emitted, it is then (n,2n) reaction. Such reactions are generally threshold reactions.

50. The term ‘cross-section’ is used in an unusual sense in the nuclear jargon. What does it really mean?

The term ‘cross-section’ generally refers to a plane surface or area of a cut-out section. The basic meaning of cross-section remains the same in the nuclear jargons as well. However, it is used to represent the probability of interaction between a projectile (a particle, say neutron that impinges on a target) and a target (say, an atom, that is hit by the projectile). Imagine a projectile approaching a target as in the figure below. Obviously the chance (probability) of a collision depends on the surface area projected by the target. i.e. The probability of collision is larger if the area is larger. If there are a large number of projectiles, the number of projectiles that could hit the surface is larger if the surface area is larger. Arguing in this manner, it is easy to visualize that the probability of collision (i.e. interaction) between the target and the projectile could be expressed by the effective surface area available for the collision.

The idea is extended to represent probabilities of nuclear interactions, but a precise definition consistent with physics is employed. As the boundaries of sub-atomic systems are not sharp, the surface area supposed to be presented by a target can be larger than its geometric surface area. Thus it is now clear, in the nuclear jargons, that the term cross-section represents a measure of the ‘probability of interaction between a projectile and a target’. This quantity is usually called ‘microscopic cross-section’, represented by the symbol ‘s’, and is expressed in area units. The practical unit of microscopic cross-section is a ‘barn’, where 1 barn = 10^-24 cm² (i.e 10^-28 m²).

A nuclear collision may result in a variety of reactions. As explained earlier, a neutron-nuclear collision could give rise to elastic or inelastic scattering, fission, or capture. The microscopic cross-section is accordingly defined to represent the measure of the probabilities of each such reaction. The reaction is indicated by a subscript in the symbol. Thus s_el refers to elastic scattering, s_in to inelastic scattering, s_f to fission, s_g  (or s_(n,g)) to radiative capture probabilities and so on. The symbol s_t called the ‘total cross-section’ is the sum of all the partial cross-sections.

The neutron-nuclear microscopic cross-sections vary significantly from nuclide to nuclide and drastically with respect to neutron energy. Knowledge of cross-sections is essential to understand the physics behind the design of a nuclear reactor and also to select the composition for reactor materials. Properly averaged cross-sections are usually used. The table below gives representative values of microscopic cross-sections for various materials of importance to thermal and fast reactors.

Table: Cross-sections of some important reactor materials