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| {{Unreferenced|date=December 2009}}
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| The '''Coulomb barrier''', named after [[Coulomb's law]], which is named after physicist [[Charles-Augustin de Coulomb]] (1736–1806), is the energy barrier due to [[electrostatic]] interaction that two nuclei need to overcome so they can get close enough to undergo a [[nuclear reaction]]. This energy barrier is given by the [[electrostatic potential energy]]:
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| :<math>U_{coul} = k {{q_1\,q_2} \over r}={1 \over {4 \pi \epsilon_0}}{{q_1 \, q_2} \over r}</math>
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| where
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| :''k'' is the Coulomb's constant = 8.9876×10<sup>9</sup> N m² C<sup>−2</sup>;
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| :''ε''<sub>0</sub> is the [[Vacuum permittivity|permittivity of free space]];
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| :''q<sub>1</sub>'', ''q<sub>2</sub>'' are the charges of the interacting particles;
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| :''r'' is the interaction radius.
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| 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).
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| Coulomb's barrier increases with the [[atomic number]]s (i.e. the number of protons) of the colliding nuclei:
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| :<math>U_{coul}={{k \, Z_1 \, Z_2 \, e^2} \over r}</math> | |
| where ''e'' is the [[elementary charge]], 1.602 176 53×10<sup>−19</sup> C, and ''Z<sub>i</sub>'' the corresponding atomic numbers.
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| To overcome this barrier, nuclei have to collide at high velocities, so their kinetic energies drive them close enough for the [[strong interaction]] to take place and bind them together.
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| According to the [[kinetic theory of gases]], the temperature of a gas is just a measure of the average kinetic energy of the particles in that gas. For normal gases,{{Clarify|reason = "normal" in what sense?|date=January 2012}} the [[Maxwell-Boltzmann distribution]] gives the fraction of particles moving at a given velocity as a function of gas temperature, and thus the fraction of particles moving at velocities high enough to overcome the Coulomb's barrier can be derived.
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| In practice, temperatures needed to overcome Coulomb's barrier turn out to be smaller than expected due to quantum-mechanical [[quantum tunnelling|tunnelling]], as established by [[George Gamow|Gamow]]. The consideration of barrier-penetration through tunnelling and the speed distribution gives rise to a limited range of conditions where the fusion can take place, known as the [[Gamow window]].
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| It was the absence of a Coulomb barrier for the neutron that enabled [[James Chadwick]] to discover the neutron.
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| == See also ==
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| * [[Quantum tunnelling]]
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| {{DEFAULTSORT:Coulomb Barrier}}
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| [[Category:Nuclear physics]]
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| [[Category:Nuclear fusion]]
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| [[Category:Nuclear chemistry]]
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