# Nuclear reaction

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Lithium-6 - Deuterium reaction

In nuclear physics, a nuclear reaction is a process in which two nuclei or nuclear particles collide, to produce products different to the initial products. In principle a reaction can involve more than two particles colliding, but such an event is exceptionally rare. If the particles collide and separate without changing (except possibly in energy levels), the process is called a collision rather than a reaction.

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## Representation

A nuclear reaction can be represented by an equation similar to a chemical equation, and balanced in an analogous manner. Nuclear decays, although not reactions strictly speaking, can be represented in the same way.

Each particle taking part in the reaction is written with its chemical symbol, then atomic number subscripted, and atomic mass superscripted. The neutron and electron, not being chemical elements, are given the symbols n and e respectively. The proton may be denoted by "H" (as a hydrogen nucleus) or as "p".

To balance the equation, we must ensure that the sum of the atomic numbers on each side of the equations are equal (required by the conservation law of electric charge), and that the sum of the atomic masses on each side are also equal (required by the law of conservation of baryon number). For example:

63Li + 21H → 42He + ?

Balancing:

• Atomic masses on the left are 6 and 2, giving 8 total. Therefore another 4 is required on the right side.
• Atomic numbers on the left are 3 and 1, giving 4 total. Therefore another 2 is required on the right side.
• Thus the missing particle has mass 4 and number 2, which means it is also a helium nucleus.

The complete reaction is thus:

63Li + 21H → 42He + 42He

which could also be written:

63Li + 21H → 2 42He

### Simplified representation

Many particles appear in reactions so often that they are usually abbreviated. Thus, a helium nucleus (also known as an alpha particle) is written with the Greek letter "α". Deuterons (heavy hydrogen, 21H) are written simply as "d". Also, because the atomic numbers are implied by the chemical symbols, they are redundant after balancing, and often omitted. Finally, many common reactions take the form of a relatively heavy nucleus being struck by one of a small group of common, reactive particles, and emitting another common particle, to produce another nucleus. For these reactions, the notation can be greatly condensed into the form:

<target nucleus> ( incoming particle, outgoing particle(s) ) <product nucleus>

So we could rewrite the preceding example by first abbreviating symbols:

63Li + d → α + α

then dropping atomic numbers:

6Li + d → α + α

and finally using the condensed form:

6Li(d,α)α

## Energy

Energy is usually released during the course of a reaction. This can be calculated by reference to a table of very accurate particle masses, as follows. According to the reference tables, the 63Li nucleus as an atomic weight of 6.015 atomic mass units, the deuteron is 2.014 a.m.u. and the helium nucleus is 4.0026 a.m.u. Thus:

• Total mass on left side = 6.015 + 2.014 = 8.029
• Total mass on right side = 2 × 4.0026 = 8.0052
• Missing mass = 8.029 - 8.0052 = 0.0238 atomic mass units.

This "missing" mass comes from energy released from the reaction; its source is the nuclear binding energy. Using Einstein's famous "E=mc2" formula, we can work out how much energy has been released. In fact, one atomic mass unit is equivalent to 931 MeV, so the energy released is 0.0238 × 931 MeV = 22.4 MeV.

Expressed differently: the mass is reduced by 0.3 %, corresponding to 0.3 % of 90 PJ/kg is 300 TJ/kg.

This is a large amount of energy for a nuclear reaction; the amount is so high because the binding energy per nucleon of the helium nucleus is unusually high, because the helium nucleus is doubly magic. Consequently, alpha particles appear frequently on the right hand side of nuclear reactions.

The energy released in a nuclear reaction can appear mainly in one of three ways:

When the product nucleus is metastable, this is indicated by placing an asterisk ("*") next to its atomic number. This energy is eventually released through nuclear decay.

A small amount of energy may also emerge in the form of X-rays. Generally, the product nucleus has a different atomic number, and thus the configuration of its electron shells is wrong. As the electrons rearrange themselves and drop to lower energy levels, internal transition X-rays (X-rays with precisely defined emission lines) may be emitted.

## Reaction rates

The rate at which reactions occur depends on the particle flux and the reaction cross section. See those articles for more information.

## Neutrons versus ions

In the initial collision which begins the reaction, the particles must approach closely enough so that the short range strong force can affect them. As most common nuclear particles are positively charged, this means they must overcome considerable electrostatic repulsion before the reaction can begin. Even if the target nucleus is part of a neutral atom, the other particle must penetrate well beyond the electron cloud and closely approach the nucleus, which is positively charged. Thus, such particles must be first accelerated to high energy, for example by:

• particle accelerators
• nuclear decay (alpha particles are the main type of interest here, since beta and gamma rays are rarely involved in nuclear reactions)
• very high temperatures, on the order of millions of degrees, producing thermonuclear reactions
• cosmic rays

Also, since the force of repulsion is proportional to the product of the two charges, reactions between heavy nuclei are rarer, and require higher initiating energy, than those between a heavy and light nucleus; while reactions between two light nuclei are commoner still.

Neutrons, on the other hand, have no electric charge to cause repulsion, and are able to effect a nuclear reaction at very low energies. In fact at extremely low particle energies (corresponding, say, to thermal equilibrium at room temperature), the neutron's de Broglie wavelength is greatly increased, possibly greatly increasing its capture cross section. Thus low energy neutrons may be even more reactive than high energy neutrons.

## Notable types

While the number of possible nuclear reactions is immense, there are several types which are more common, or otherwise notable. Some examples include:

• Fusion reactions - two light nuclei join to form a heavier one, with additional particles (usually protons or neutrons) thrown off to conserve momentum.
• Fission reactions - a very heavy nucleus absorbs additional light particles (usually neutrons) and splits into two roughly equal-sized pieces.
• Spallation - a nucleus is hit by a very high energy particle, and is smashed into many fragments.
• (d,n) and (d,p) reactions. A deuteron beam impinges on a target; the target nuclei absorb either the neutron or proton from the deuteron.
• (α,n) and (α,p) reactions. Some of the earliest nuclear reactions studied involved an alpha particle produced by alpha decay, knocking a nucleon from a target nucleus.

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