The Coulomb barrier, named after

Coulomb's law Coulomb's inverse-square law, or simply Coulomb's law, is an experimental law of physics that quantifies the amount of force between two stationary, electrically charged particles. The electric force between charged bodies at rest is convention ...

, which is in turn named after physicist

Charles-Augustin de Coulomb Charles-Augustin de Coulomb (; ; 14 June 1736 – 23 August 1806) was a French officer, engineer, and physicist. He is best known as the eponymous discoverer of what is now called Coulomb's law, the description of the electrostatic force of attra ...

, is the energy barrier due to

electrostatic Electrostatics is a branch of physics that studies electric charges at rest ( static electricity). Since classical times, it has been known that some materials, such as amber, attract lightweight particles after rubbing. The Greek word for ...

interaction that two nuclei need to overcome so they can get close enough to undergo a

nuclear reaction In nuclear physics and nuclear chemistry, a nuclear reaction is a process in which two nuclei, or a nucleus and an external subatomic particle, collide to produce one or more new nuclides. Thus, a nuclear reaction must cause a transformatio ...

Potential energy barrier

This energy barrier is given by the electric potential energy: :

U_\text = k  =

where :''k'' is the

Coulomb constant The Coulomb constant, the electric force constant, or the electrostatic constant (denoted , or ) is a proportionality constant in electrostatics equations. In SI base units it is equal to .Derived from ''k''e = 1/(4''πε''0) – It was named ...

= ; :''ε''₀ is the

permittivity of free space Vacuum permittivity, commonly denoted (pronounced "epsilon nought" or "epsilon zero"), is the value of the absolute dielectric permittivity of classical vacuum. It may also be referred to as the permittivity of free space, the electric const ...

; :''q''₁, ''q''₂ are the charges of the interacting particles; :''r'' is the interaction radius. A positive value of U is due to a repulsive force, so interacting particles are at higher energy levels as they get closer. A negative potential energy indicates a bound state (due to an attractive force). The Coulomb barrier increases with the

atomic number The atomic number or nuclear charge number (symbol ''Z'') of a chemical element is the charge number of an atomic nucleus. For ordinary nuclei, this is equal to the proton number (''n''p) or the number of protons found in the nucleus of ever ...

s (i.e. the number of protons) of the colliding nuclei: :

U_\text =

where ''e'' is the

elementary charge The elementary charge, usually denoted by is the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 . This elementary charge is a fundam ...

, , and ''Z_i'' the corresponding atomic numbers. To overcome this barrier, nuclei have to collide at high velocities, so their kinetic energies drive them close enough for the

strong interaction The strong interaction or strong force is a fundamental interaction that confines quarks into proton, neutron, and other hadron particles. The strong interaction also binds neutrons and protons to create atomic nuclei, where it is called th ...

to take place and bind them together. According to the

kinetic theory of gases Kinetic (Ancient Greek: κίνησις “kinesis”, movement or to move) may refer to: * Kinetic theory, describing a gas as particles in random motion * Kinetic energy, the energy of an object that it possesses due to its motion Art and ent ...

, the temperature of a gas is just a measure of the average kinetic energy of the particles in that gas. For classical

ideal gas An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is a ...

es the velocity distribution of the gas particles is given by Maxwell–Boltzmann. From this distribution, the fraction of particles with a velocity high enough to overcome the Coulomb barrier can be determined. In practice, temperatures needed to overcome the Coulomb barrier turned out to be smaller than expected due to quantum mechanical tunnelling, as established by Gamow. The consideration of barrier-penetration through tunnelling and the speed distribution gives rise to a limited range of conditions where

fusion Fusion, or synthesis, is the process of combining two or more distinct entities into a new whole. Fusion may also refer to: Science and technology Physics *Nuclear fusion, multiple atomic nuclei combining to form one or more different atomic nucl ...

can take place, known as the Gamow window. The absence of the Coulomb barrier enabled the neutron's discovery by

James Chadwick Sir James Chadwick, (20 October 1891 – 24 July 1974) was an English physicist who was awarded the 1935 Nobel Prize in Physics for his discovery of the neutron in 1932. In 1941, he wrote the final draft of the MAUD Report, which inspi ...

in 1932.

References

{{DEFAULTSORT:Coulomb Barrier Nuclear physics Nuclear fusion Nuclear chemistry