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The following apply for the nuclear reaction: a + b ↔ R → c. in the centre of mass frame, where a and b are the initial species about to collide, c is the final species, and R is the resonant state.
The multiplication factor, k, is defined as (see nuclear chain reaction): k = number of neutrons in one generation / number of neutrons in preceding generation If k is greater than 1, the chain reaction is supercritical, and the neutron population will grow exponentially.
Nuclear reactions may be shown in a form similar to chemical equations, for which invariant mass must balance for each side of the equation, and in which transformations of particles must follow certain conservation laws, such as conservation of charge and baryon number (total atomic mass number). An example of this notation follows:
The four-factor formula, also known as Fermi's four factor formula is used in nuclear engineering to determine the multiplication of a nuclear chain reaction in an infinite medium. Four-factor formula: k ∞ = η f p ε {\displaystyle k_{\infty }=\eta fp\varepsilon } [ 1 ]
In nuclear physics, the Bateman equation is a mathematical model describing abundances and activities in a decay chain as a function of time, based on the decay rates and initial abundances. The model was formulated by Ernest Rutherford in 1905 [ 1 ] and the analytical solution was provided by Harry Bateman in 1910.
A reaction with a negative Q value is endothermic, i.e. requires a net energy input, since the kinetic energy of the final state is less than the kinetic energy of the initial state. [1] Observe that a chemical reaction is exothermic when it has a negative enthalpy of reaction, in contrast a positive Q value in a nuclear reaction.
Excitation function (a.k.a. yield curve) is a term used in nuclear physics to describe a graphical plot of the yield of a radionuclide or reaction channel as a function of the bombarding projectile energy or the calculated excitation energy of the compound nucleus. [1] The yield is the measured intensity of a particular transition. [2]
Strictly speaking the above equation holds also for systems with chemical reactions if the terms in the balance equation are taken to refer to total mass, i.e. the sum of all the chemical species of the system. In the absence of a chemical reaction the amount of any chemical species flowing in and out will be the same; this gives rise to an ...