Coulomb barrier

2025-10-06T13:56:17Z

2600:382:B1E0:3243:F408:98ED:1FD5:B069: specified what type of nuclear reaction the nuclei would undergo.

{{Short description|Electrostatic energy barrier that must be overcome for nuclear reactions to occur}}{{refimprove|date=December 2016}}
The '''Coulomb barrier''', named after [[Coulomb's law]], which is in turn named after physicist [[Charles-Augustin de Coulomb]], is the energy barrier due to [[electrostatic]] interaction that two [[Atomic nucleus|nuclei]] need to overcome so they can get close enough to undergo a [[nuclear reaction]] such as [[nuclear fusion]].

==Potential energy barrier==
This energy barrier is given by the [[electric potential energy]]:
:<math>U_\text{coulomb} = {1\over 4\pi\varepsilon_0} {q_1 q_2\over r}</math>
where
:''ε''0 is the [[permittivity of free space]];
:''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]]s (i.e. the number of protons) of the colliding nuclei:
:<math>U_\text{coulomb} = {{Z_1 Z_2 e^2}\over 4\pi \varepsilon_0 r}</math>
where ''e'' is the [[elementary charge]], and ''Zi'' 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]] to take place and bind them together.

According to the [[kinetic theory of gases#Temperature and kinetic energy|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 classical [[ideal gas]]es the velocity distribution of the gas particles is given by [[Maxwell–Boltzmann distribution|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 [[George Gamow|Gamow]]. The consideration of barrier-penetration through tunnelling and the speed distribution gives rise to a limited range of conditions where [[Nuclear fusion|fusion]] can take place, known as the [[Gamow window]].

The absence of the Coulomb barrier for uncharged particles enabled the [[discovery of the neutron]] by [[James Chadwick]] in 1932.<ref>{{cite journal|last1=Chadwick|first1=James|title=Possible existence of a neutron|journal=Nature|date=1932|volume=129|issue=3252|page=312|doi=10.1038/129312a0|bibcode = 1932Natur.129Q.312C |doi-access=free}}</ref><ref>{{cite journal|last1=Chadwick|first1=James|title=The existence of a neutron|journal=Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences|date=1932|volume=136|issue=830|pages=692–708|doi=10.1098/rspa.1932.0112|bibcode = 1932RSPSA.136..692C |doi-access=free}}</ref>

== Potential energy barrier models ==
There is keen interest in the mechanics and parameters of nuclear fusion, including methods of modeling the Coulomb barrier for scientific and educational purposes. The Coulomb barrier is a type of potential energy barrier, and is central to nuclear fusion. It results from the interplay of two fundamental interactions: the strong interaction at close-range within ≈ 1 [[femtometre]] (fm), and the [[Electromagnetism|electromagnetic interaction]] at far-range beyond the Coulomb barrier.

The microscopic range of the [[strong interaction]], as well as its odd behavior relative to other fundamental forces, present a challenge to model and no classical examples exist on the human scale. [[Gravity|Gravitational]] and [[Coulomb's law|electrostatic forces]] scale with the inverse of the square of the distance between them. But at short distances, the strong force is attractive and actually ''increases'' with distance (up to about 1 fm), beyond which the interaction transitions abruptly to repulsion. A visual and tactile classroom model of this strange behavior garnered first prize at the 2023 national apparatus competition of the American Academy of Physics Teachers in Sacramento, California. The apparatus uses circular arrays of alternating antiparallel double N and single S magnets to generate asymmetric alternating N/S magnetic fields that result in strong magnetic attraction within ≈ 1cm, and weaker repulsion at a distance beyond ≈ 1cm. Instructions for how to build an inexpensive 3D printed model of the magnetic "Coulomb" barrier apparatus are included in a follow-on ''Physics Education'' publication.<ref>{{Cite journal |last=Walsh |first=Ray |date=2023-11-01 |title=Magnetic 'Coulomb' barrier |url=https://iopscience.iop.org/article/10.1088/1361-6552/acede3 |journal=Physics Education |volume=58 |issue=6 |pages=063001 |doi=10.1088/1361-6552/acede3 |bibcode=2023PhyEd..58f3001W |issn=0031-9120|doi-access=free }}</ref>

Magnetic and electric forces were unified within the electromagnetic fundamental force by [[James Clerk Maxwell]] in 1873 in [[A Treatise on Electricity and Magnetism]]. In the case of the magnetic "Coulomb" barrier apparatus, a potential energy barrier arises between alternating/unequal asymmetric North/South ''magnetic'' poles, as described in a related magnetic potential energy barrier patent (US11,087,910 B2). An included method extends the phenomenon to further include the modelling of an electrostatic potential energy barrier, as well, using alternating/unequal positive and negative ''electrostatic'' charges. A potential energy barrier and fusion potential curve are shown to arise between a pair of deuterons, each modelled as a linear arrangement of six regularly-spaced up (+2/3) and down (-1/3) quark charges.<ref>{{Cite journal |last=Walsh |first=Ray |date=2025-02-01 |title=Symmetry/asymmetry within a cylindrical lattice model of nuclear structure predicts cosmic abundance/scarcity |url=https://iopscience.iop.org/article/10.1088/2399-6528/adb36f |journal=Journal of Physics Communications |volume=9 |issue=2 |pages=025002 |doi=10.1088/2399-6528/adb36f |bibcode=2025JPhCo...9b5002W |issn=2399-6528|doi-access=free }}</ref>

==References==
{{Reflist}}

{{DEFAULTSORT:Coulomb Barrier}}
[[Category:Nuclear physics]]
[[Category:Nuclear fusion]]
[[Category:Nuclear chemistry]]

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Coulomb barrier