Nuclear Engineering

Reaction Cross section and Examples of various Nuclear Reactions

As nuclear reaction is a statistical phenomenon, it is required to define some physical quantity to determine the probability of a nuclear reaction. The quantity which gives the idea of the probability of any physical process (e.g. nuclear reaction) to occur is known as cross-section. Nuclear reaction cross section can be defined in the following manner:

σ = Number of given types of events per unit time per nucleus/number of projectile particles per unit area, unit time.

Considering two broad physical process i.e. scattering and absorption, the total cross section σ_tot is written as:

σ_tot = σ_sc + σ_a ————- (m3.12)

where σ_sc = scattering cross-section

and σ_a = absorption cross-section

The unit of cross-section is ‘barn’ having the dimension of area (1 barn = 10^-24 cm² = 10^-28m²).

Now we will see examples of various nuclear reactions:

A nuclear reaction is symbolized by a parenthesis containing the projectile and product particle symbolically. At the beginning of the parenthesis, the symbol of target nucleus, and after the parenthesis, the symbol of the product nucleus is written. To represent a particular reaction, say, a deuteron irradiating to produce and a proton, the symbol is . Depending on the projectile and the product particle, a large number of nuclear reactions are possible.

(d, α) Reactions

These reactions yield α particles, while projectile is deuteron. For example,

The Q values of these reactions are positive and the reactions are exoergic.

(d, p) Reactions

These reactions yield protons. For example,

The Q-values are usually positive and the reactions are exoergic.

(d,n) Reactions

These reactions yield neutrons. For example,

The reaction (4.21) has the importance, as it serves as sources of neutrons.

(α, p) Reactions

These reactions yield protons while projectile is α particle. For example

(α, n) Reactions

These reactions yield neutrons and also utilized as convenient source for neutrons. For example,

For reaction (4.25), the α-particles is supplied by radium and its products and beryllium provide an inexpensive source for neutrons.

(α, γ) Reactions

If a light element such as Li is bombarded with α particles of variable energy, it is observed that at certain values of energy, the compound nucleus de-excites by γ-emission. The process is called radiative capture of α-particles. For example,

(p, α) Reactions

These reactions yield α-particles with protons as projectile. For example,

which is an exoergic reaction. Another example of this reaction is

γ – Induced Transmutationss

Target nucleus bombarded with γ-radiation usually results in a compound nucleus in an excited state. The excess excitation energy is released by the nuclei through neutron emission of different particles. Some typical examples are

Neutron Induced Transmutations

Depending on the energy, neutrons are classified as fast and slow (discussed in chapter 2). Slow neutrons with thermal equilibrium with the medium through which they pass are termed as thermal neutrons. When neutrons strike a target, they may either be scattered or captured by the target nuclei to form compound nuclei, which eventually emit γ-photons, α-particles, deuterons etc. Some typical examples of neutron induced transmutations are:

This reaction is useful to produce tritium, which is useful in nuclear fusion.

which is an example of (n,p) reaction. These reactions finally produce the same target nucleus. Almost all elements exhibit radiative capture of low energy neutrons. This capture raises the target nucleus to an excited isomeric state. This excitation energy is subsequently released in the form of γ-photons and the product nucleus becomes an istope of the original nucleus. For example,

Now we will see two most important nuclear reactions as far as energy production is concerned known as nuclear fission and fusion reaction.

Nuclear Fission Reaction

In 1939, Otto Hahn and Strassmann discovered a very important nuclear reaction where

was bombarded with slow neutrons forming a compound nucleus, which eventually got fragmented into two nuclei and further neutrons were produced. This is known as fission reaction and is represented by:

where is a highly unstable isotope and X ,Y are the fission fragments. There could be various combinations of the fission fragments and that a number of neutrons are also given off. Typical fission reactions are

where, Q is the energy released in the reaction. The detail of energy release in nuclear fission reaction and its importance in electrical power generation will be discussed in the next chapter.

Nuclear Fusion Reaction

Another important nuclear reaction is the nuclear fusion reaction. In this reaction, light nuclei combine or fuse together to produce a relatively heavy nucleus, there would be a greater binding energy and consequent decrease in nuclear mass resulting in a positive Q-value of the reaction. Example of a typical fusion reaction is

The importance of the fusion reaction in the stellar energy production was first suggested by Hans Bethe in 1938. In the next chapter, we will discuss the energy release of this equation and its importance in future power generation process.

Nuclear Engineering

Nuclear Engineering

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Reaction Cross section and Examples of various Nuclear Reactions

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