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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 nuclei need to overcome so they can get close enough to undergo a nuclear reaction.
This energy barrier is given by the electric potential energy:
where
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 numbers (i.e. the number of protons) of the colliding nuclei:
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, the temperature of a gas is just a measure of the average kinetic energy of the particles in that gas. For classical ideal gases 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 can take place, known as the Gamow window.
The absence of the Coulomb barrier enabled the discovery of the neutron by James Chadwick in 1932. [1] [2]
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 fm, and the electromagnetic interaction at far-range beyond the Coulomb barrier. The microscopic range of the strong interaction, on the order of one femtometre, makes it challenging to model and no classical examples exist on the human scale. A visual and tactile classroom model of strong close-range attraction and far-range repulsion characteristic of the fusion potential curve is modeled in the magnetic “Coulomb” barrier apparatus. [3] The apparatus won first place in the 2023 national apparatus competition of the American Academy of Physics Teachers in Sacramento, California. Essentially, a pair of opposing permanent magnet arrays generate asymmetric alternating N/S magnetic fields that result in repulsion at a distance and attraction within ≈ 1cm. A related patent method (US11,087,910 B2) further describes the apparatus and outlines criteria for more generally modeling an electromagnetic potential energy barrier. 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, the patent describes alternating/unequal or asymmetric North and South magnetic poles but the patent method language is broad enough to include positive and negative electrostatic poles as well. The implication is that regularly spaced opposite and unequal electrostatic point charges possess the capacity to model an electrostatic potential energy barrier as well.
Atoms are the basic particles of the chemical elements. An atom consists of a nucleus of protons and generally neutrons, surrounded by an electromagnetically bound swarm of electrons. The chemical elements are distinguished from each other by the number of protons that are in their atoms. For example, any atom that contains 11 protons is sodium, and any atom that contains 29 protons is copper. Atoms with the same number of protons but a different number of neutrons are called isotopes of the same element.
Alpha decay or α-decay is a type of radioactive decay in which an atomic nucleus emits an alpha particle and thereby transforms or "decays" into a different atomic nucleus, with a mass number that is reduced by four and an atomic number that is reduced by two. An alpha particle is identical to the nucleus of a helium-4 atom, which consists of two protons and two neutrons. It has a charge of +2 e and a mass of 4 Da. For example, uranium-238 decays to form thorium-234.
Nuclear fusion is a reaction in which two or more atomic nuclei, usually deuterium and tritium, combine to form one or more different atomic nuclei and subatomic particles. The difference in mass between the reactants and products is manifested as either the release or absorption of energy. This difference in mass arises due to the difference in nuclear binding energy between the atomic nuclei before and after the reaction. Nuclear fusion is the process that powers active or main-sequence stars and other high-magnitude stars, where large amounts of energy are released.
Nuclear fission is a reaction in which the nucleus of an atom splits into two or more smaller nuclei. The fission process often produces gamma photons, and releases a very large amount of energy even by the energetic standards of radioactive decay.
A fusor is a device that uses an electric field to heat ions to a temperature at which they undergo nuclear fusion. The machine induces a potential difference between two metal cages, inside a vacuum. Positive ions fall down this voltage drop, building up speed. If they collide in the center, they can fuse. This is one kind of an inertial electrostatic confinement device – a branch of fusion research.
A virtual particle is a theoretical transient particle that exhibits some of the characteristics of an ordinary particle, while having its existence limited by the uncertainty principle, which allows the virtual particles to spontaneously emerge from vacuum at short time and space ranges. The concept of virtual particles arises in the perturbation theory of quantum field theory (QFT) where interactions between ordinary particles are described in terms of exchanges of virtual particles. A process involving virtual particles can be described by a schematic representation known as a Feynman diagram, in which virtual particles are represented by internal lines.
Inertial electrostatic confinement, or IEC, is a class of fusion power devices that use electric fields to confine the plasma rather than the more common approach using magnetic fields found in magnetic confinement fusion (MCF) designs. Most IEC devices directly accelerate their fuel to fusion conditions, thereby avoiding energy losses seen during the longer heating stages of MCF devices. In theory, this makes them more suitable for using alternative aneutronic fusion fuels, which offer a number of major practical benefits and makes IEC devices one of the more widely studied approaches to fusion.
In nuclear physics, the semi-empirical mass formula (SEMF) is used to approximate the mass of an atomic nucleus from its number of protons and neutrons. As the name suggests, it is based partly on theory and partly on empirical measurements. The formula represents the liquid-drop model proposed by George Gamow, which can account for most of the terms in the formula and gives rough estimates for the values of the coefficients. It was first formulated in 1935 by German physicist Carl Friedrich von Weizsäcker, and although refinements have been made to the coefficients over the years, the structure of the formula remains the same today.
Elastic scattering is a form of particle scattering in scattering theory, nuclear physics and particle physics. In this process, the internal states of the particles involved stay the same. In the non-relativistic case, where the relative velocities of the particles are much less than the speed of light, elastic scattering simply means that the total kinetic energy of the system is conserved. At relativistic velocities, elastic scattering also requires the final state to have the same number of particles as the initial state and for them to be of the same kind.
Aneutronic fusion is any form of fusion power in which very little of the energy released is carried by neutrons. While the lowest-threshold nuclear fusion reactions release up to 80% of their energy in the form of neutrons, aneutronic reactions release energy in the form of charged particles, typically protons or alpha particles. Successful aneutronic fusion would greatly reduce problems associated with neutron radiation such as damaging ionizing radiation, neutron activation, reactor maintenance, and requirements for biological shielding, remote handling and safety.
The nuclear force is a force that acts between hadrons, most commonly observed between protons and neutrons of atoms. Neutrons and protons, both nucleons, are affected by the nuclear force almost identically. Since protons have charge +1 e, they experience an electric force that tends to push them apart, but at short range the attractive nuclear force is strong enough to overcome the electrostatic force. The nuclear force binds nucleons into atomic nuclei.
Superheavy elements, also known as transactinide elements, transactinides, or super-heavy elements, or superheavies for short, are the chemical elements with atomic number greater than 104. The superheavy elements are those beyond the actinides in the periodic table; the last actinide is lawrencium. By definition, superheavy elements are also transuranium elements, i.e., having atomic numbers greater than that of uranium (92). Depending on the definition of group 3 adopted by authors, lawrencium may also be included to complete the 6d series.
Nuclear binding energy in experimental physics is the minimum energy that is required to disassemble the nucleus of an atom into its constituent protons and neutrons, known collectively as nucleons. The binding energy for stable nuclei is always a positive number, as the nucleus must gain energy for the nucleons to move apart from each other. Nucleons are attracted to each other by the strong nuclear force. In theoretical nuclear physics, the nuclear binding energy is considered a negative number. In this context it represents the energy of the nucleus relative to the energy of the constituent nucleons when they are infinitely far apart. Both the experimental and theoretical views are equivalent, with slightly different emphasis on what the binding energy means.
The beta of a plasma, symbolized by β, is the ratio of the plasma pressure (p = nkBT) to the magnetic pressure (pmag = B2/2μ0). The term is commonly used in studies of the Sun and Earth's magnetic field, and in the field of fusion power designs.
In atomic, molecular, and optical physics and quantum chemistry, the molecular Hamiltonian is the Hamiltonian operator representing the energy of the electrons and nuclei in a molecule. This operator and the associated Schrödinger equation play a central role in computational chemistry and physics for computing properties of molecules and aggregates of molecules, such as thermal conductivity, specific heat, electrical conductivity, optical, and magnetic properties, and reactivity.
This glossary of physics is a list of definitions of terms and concepts relevant to physics, its sub-disciplines, and related fields, including mechanics, materials science, nuclear physics, particle physics, and thermodynamics. For more inclusive glossaries concerning related fields of science and technology, see Glossary of chemistry terms, Glossary of astronomy, Glossary of areas of mathematics, and Glossary of engineering.
The discovery of the neutron and its properties was central to the extraordinary developments in atomic physics in the first half of the 20th century. Early in the century, Ernest Rutherford developed a crude model of the atom, based on the gold foil experiment of Hans Geiger and Ernest Marsden. In this model, atoms had their mass and positive electric charge concentrated in a very small nucleus. By 1920, isotopes of chemical elements had been discovered, the atomic masses had been determined to be (approximately) integer multiples of the mass of the hydrogen atom, and the atomic number had been identified as the charge on the nucleus. Throughout the 1920s, the nucleus was viewed as composed of combinations of protons and electrons, the two elementary particles known at the time, but that model presented several experimental and theoretical contradictions.
Unbiunium, also known as eka-actinium or element 121, is a hypothetical chemical element; it has symbol Ubu and atomic number 121. Unbiunium and Ubu are the temporary systematic IUPAC name and symbol respectively, which are used until the element is discovered, confirmed, and a permanent name is decided upon. In the periodic table of the elements, it is expected to be the first of the superactinides, and the third element in the eighth period. It has attracted attention because of some predictions that it may be in the island of stability. It is also likely to be the first of a new g-block of elements.
Colliding beam fusion (CBF), or colliding beam fusion reactor (CBFR), is a class of fusion power concepts that are based on two or more intersecting beams of fusion fuel ions that are independently accelerated to fusion energies using a variety of particle accelerator designs or other means. One of the beams may be replaced by a static target, in which case the approach is termed accelerator based fusion or beam-target fusion, but the physics is the same as colliding beams.
Pycnonuclear fusion is a type of nuclear fusion reaction which occurs due to zero-point oscillations of nuclei around their equilibrium point bound in their crystal lattice. In quantum physics, the phenomenon can be interpreted as overlap of the wave functions of neighboring ions, and is proportional to the overlapping amplitude. Under the conditions of above-threshold ionization, the reactions of neutronization and pycnonuclear fusion can lead to the creation of absolutely stable environments in superdense substances.
