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The neutron transport equation is a balance statement that conserves neutrons. Each term represents a gain or a loss of a neutron, and the balance, in essence, claims that neutrons gained equals neutrons lost. It is formulated as follows: [1]
In the case of time-independent monochromatic radiation in an elastically scattering medium, the RTE is [1] (,) = (,) + (,) (, ′) ′where the first term on the RHS is the contribution of emission, the second term the contribution of absorption and the last term is the contribution from scattering in the medium.
This involves computing exact or approximate solutions of the transport equation, and there are various forms of the transport equation that have been studied. Common varieties include steady-state vs time-dependent, scalar vs vector (the latter including polarization), and monoenergetic vs multi-energy (multi-group).
Defining equation SI units Dimension Number of atoms N = Number of atoms remaining at time t. N 0 = Initial number of atoms at time t = 0 N D = Number of atoms decayed at time t = + dimensionless dimensionless Decay rate, activity of a radioisotope: A = Bq = Hz = s −1 [T] −1: Decay constant: λ
A continuity equation or transport equation is an equation that describes the transport of some quantity. It is particularly simple and powerful when applied to a conserved quantity , but it can be generalized to apply to any extensive quantity .
If k is greater than 1, the chain reaction is supercritical, and the neutron population will grow exponentially. If k is less than 1, the chain reaction is subcritical, and the neutron population will exponentially decay. If k = 1, the chain reaction is critical and the neutron population will remain constant.
Neutron flux in asymptotic giant branch stars and in supernovae is responsible for most of the natural nucleosynthesis producing elements heavier than iron.In stars there is a relatively low neutron flux on the order of 10 5 to 10 11 cm −2 s −1, resulting in nucleosynthesis by the s-process (slow neutron-capture process).
The momentum transfer plays an important role in the evaluation of neutron, X-ray, and electron diffraction for the investigation of condensed matter. Laue-Bragg diffraction occurs on the atomic crystal lattice, conserves the wave energy and thus is called elastic scattering, where the wave numbers final and incident particles, and , respectively, are equal and just the direction changes by a ...