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nuclear physics Nuclear physics is the field of physics that studies atomic nuclei and their constituents and interactions, in addition to the study of other forms of nuclear matter. Nuclear physics should not be confused with atomic physics, which studies th ...
and
nuclear chemistry Nuclear chemistry is the sub-field of chemistry dealing with radioactivity, nuclear processes, and transformations in the nuclei of atoms, such as nuclear transmutation and nuclear properties. It is the chemistry of radioactive elements such as t ...
, the fission barrier is the
activation energy In the Arrhenius model of reaction rates, activation energy is the minimum amount of energy that must be available to reactants for a chemical reaction to occur. The activation energy (''E''a) of a reaction is measured in kilojoules per mole (k ...
required for a nucleus of an atom to undergo fission. This barrier may also be defined as the minimum amount of energy required to deform the nucleus to the point where it is irretrievably committed to the fission process. The energy to overcome this barrier can come from either
neutron The neutron is a subatomic particle, symbol or , that has no electric charge, and a mass slightly greater than that of a proton. The Discovery of the neutron, neutron was discovered by James Chadwick in 1932, leading to the discovery of nucle ...
bombardment of the nucleus, where the additional energy from the neutron brings the nucleus to an excited state and undergoes deformation, or through
spontaneous fission Spontaneous fission (SF) is a form of radioactive decay in which a heavy atomic nucleus splits into two or more lighter nuclei. In contrast to induced fission, there is no inciting particle to trigger the decay; it is a purely probabilistic proc ...
, where the nucleus is already in an excited and deformed state. Efforts to understand fission processes are ongoing and have been a very difficult problem since fission was first discovered by
Lise Meitner Elise Lise Meitner ( ; ; 7 November 1878 – 27 October 1968) was an Austrian-Swedish nuclear physicist who was instrumental in the discovery of nuclear fission. After completing her doctoral research in 1906, Meitner became the second woman ...
,
Otto Hahn Otto Hahn (; 8 March 1879 – 28 July 1968) was a German chemist who was a pioneer in the field of radiochemistry. He is referred to as the father of nuclear chemistry and discoverer of nuclear fission, the science behind nuclear reactors and ...
, and Fritz Strassmann in 1938. While nuclear physicists understand many aspects of the fission process, there is currently no encompassing theoretical framework that gives a satisfactory account of the basic observations.


Scission

The fission process can be understood when a nucleus with some equilibrium deformation absorbs energy (through
neutron capture Neutron capture is a nuclear reaction in which an atomic nucleus and one or more neutrons collide and merge to form a heavier nucleus. Since neutrons have no electric charge, they can enter a nucleus more easily than positively charged protons, wh ...
, for example), becomes excited and deforms to a configuration known as the "transition state" or "saddle point" configuration. As the nucleus deforms, the nuclear Coulomb energy decreases while the nuclear surface energy increases. At the saddle point, the rate of change of the Coulomb energy is equal to the rate of change of the nuclear surface energy. The formation and eventual decay of this transition state nucleus is the rate-determining step in the fission process and corresponds to the passage over an activation energy barrier to the fission reaction. When this occurs, the neck between the nascent fragments disappears and the nucleus divides into two fragments. The point at which this occurs is called the "scission point".


Liquid drop model

From the description of the beginning of the fission process to the "scission point," it is apparent that the change of the shape of the nucleus is associated with a change of energy of some kind. In fact, it is the change of two types of energies: (1) the macroscopic energy related to the nuclear bulk properties as given by the liquid drop model and (2) the quantum mechanical energy associated with filling the shell model orbitals. For the nuclear bulk properties with small distortions, the surface, E_s, and Coulomb, E_c, energies are given by: :E_s = E_s^0 \left(1 + \frac\alpha_2^2\right) :E_c = E_c^0 \left(1 - \frac\alpha_2^2\right) where E_s^0 and E_c^0 are the surface and Coulomb energies of the undistorted spherical drops, respectively, and \alpha_2 is the quadrupole distortion parameter. When the changes in the Coulomb and surface energies (\Delta E_c = E_c^0 - E_c, \Delta E_s = E_s^0 - E_s) are equal, the nucleus becomes unstable with respect to fission. At that point, the relationship between the undistorted surface and Coulomb energies becomes: :x = \frac where x is called the fissionability parameter. If x > 1, the liquid drop energy decreases with increasing \alpha_2, which leads to fission. If x < 1, then the liquid drop energy decreases with decreasing \alpha_2, which leads to spherical shapes of the nucleus. The Coulomb and surface energies of a uniformly charged sphere can be approximated by the following expressions: :E_c^0 = \frac \frac = a_c \frac :E_s^0 = 4 \pi R_0^2 S A^ = a_s A^ where Z is the
atomic number The atomic number or nuclear charge number (symbol ''Z'') of a chemical element is the charge number of its atomic nucleus. For ordinary nuclei composed of protons and neutrons, this is equal to the proton number (''n''p) or the number of pro ...
of the nucleus, A is the
mass number The mass number (symbol ''A'', from the German word: ''Atomgewicht'', "atomic weight"), also called atomic mass number or nucleon number, is the total number of protons and neutrons (together known as nucleons) in an atomic nucleus. It is appro ...
of the nucleus, e is the charge of an electron, R_0 is the radius of the undistorted spherical nucleus, S is the surface tension per unit area of the nucleus, a_c = 3e^2/5 R_0 and a_s = 4 \pi R_0^2 S. The equation for the fissionability parameter then becomes: :x = \left(\frac\right)\left(\frac\right) = \left(\frac\right)/\left(\frac\right)_ where the ratio of the constant \left(a_c/2 a_s\right)^ is referred to as \left(Z^2/A\right)_. The fissionability of a given nucleus can then be categorized relative to \left(Z^2/A\right). As an example,
plutonium-239 Plutonium-239 ( or Pu-239) is an isotope of plutonium. Plutonium-239 is the primary fissile isotope used for the production of nuclear weapons, although uranium-235 is also used for that purpose. Plutonium-239 is also one of the three main iso ...
has a \left(Z^2/A\right) value of 36.97, while less fissionable nuclei like
bismuth-209 Bismuth-209 (Bi) is an isotope of bismuth, with the longest known half-life of any radioisotope that undergoes α-decay (alpha decay). It has 83 protons and a magic number of 126 neutrons, and an atomic mass of 208.9803987 amu (atomic mass unit ...
have a \left(Z^2/A\right) value of 32.96. For all stable nuclei, x must be less than 1. In that case, the total deformation energy of nuclei undergoing fission will increase by an amount (1/5) \alpha_2^2 (2 E_s^0 - E_c^0), as the nucleus deforms towards fission. This increase in potential energy can be thought of as the activation energy barrier for the fission reaction. However, modern calculations of the potential energy of deformation for the liquid drop model involve many deformation coordinates aside from \alpha_2 and represent major computational tasks.


Shell corrections

In order to get more reasonable values for the nuclear masses in the liquid drop model, it is necessary to include shell effects. Soviet physicist Vilen Strutinsky proposed such a method using "shell correction" and corrections for nuclear pairing to the liquid drop model. In this method, the total energy of the nucleus is taken as the sum of the liquid drop model energy, E_, the shell, \delta S, and pairing, \delta P, corrections to this energy as: :E = E_ + \sum_(\delta S + \delta P) The shell corrections, just like the liquid drop energy, are functions of the nuclear deformation. The shell corrections tend to lower the ground state masses of spherical nuclei with magic or near-magic numbers of neutrons and
protons A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' ( elementary charge). Its mass is slightly less than the mass of a neutron and approximately times the mass of an electron (the pro ...
. They also tend to lower the ground state mass of mid shell nuclei at some finite deformation thus accounting for the deformed nature of the actinides. Without these shell effects, the heaviest nuclei could not be observed, as they would decay by spontaneous fission on a time scale much shorter than we can observe. This combination of macroscopic liquid drop and microscopic shell effects predicts that for nuclei in the U- Pu region, a double-humped fission barrier with equal barrier heights and a deep secondary minimum will occur. For heavier nuclei, like
californium Californium is a synthetic chemical element; it has symbol Cf and atomic number 98. It was first synthesized in 1950 at Lawrence Berkeley National Laboratory (then the University of California Radiation Laboratory) by bombarding curium with al ...
, the first barrier is predicted to be much larger than the second barrier and passage over the first barrier is rate determining. In general, there is ample experimental and theoretical evidence that the lowest energy path in the fission process corresponds to having the nucleus, initially in an axially symmetric and mass (reflection) symmetric shape pass over the first maximum in the fission barrier with an axially asymmetric but mass symmetric shape and then to pass over the second maximum in the barrier with an axially symmetric but mass (reflection) asymmetric shape. Because of the complicated multidimensional character of the fission process, there are no simple formulas for the fission barrier heights. However, there are extensive tabulations of experimental characterizations of the fission barrier heights for various nuclei.


See also

* Cold fission *
Nuclear fusion Nuclear fusion is a nuclear reaction, reaction in which two or more atomic nuclei combine to form a larger nuclei, nuclei/neutrons, neutron by-products. The difference in mass between the reactants and products is manifested as either the rele ...


References

{{Footer energy Nuclear physics Nuclear fission Nuclear chemistry Otto Hahn 1938 in science 1938 in Germany