Sommerfeld parameter

The Sommerfeld parameter η, named after Arnold Sommerfeld, is a dimensionless quantity used in nuclear astrophysics in the calculation of reaction rates between two nuclei and also appears in the definition of the astrophysical S-factor. It is defined as^[1]

${\displaystyle \eta ={\frac {Z_{1}Z_{2}e^{2}}{4\pi \epsilon _{0}\hbar v}}=\alpha Z_{1}Z_{2}{\sqrt {\frac {\mu c^{2}}{2E}}}}$,

where e is the elementary charge, Z₁ and Z₂ are the atomic numbers of two interacting nuclides, v is the magnitude of the relative incident velocity in the center-of-mass frame, α is the unitless fine-structure constant, c is the speed of light, and μ is the reduced mass of the two nuclides of interest.

One of its best-known applications is in the exponent of the Gamow factor P (also known as the penetrability factor),

${\displaystyle P=\exp(-2\pi \eta )}$,

which is the probability of an s-wave nuclide to penetrate the Coulomb barrier, according to the WKB approximation. This factor is particularly helpful in characterizing the nuclear contribution to low-energy nucleon-scattering cross-sections - namely, through the astrophysical S-factor.

One of the first articles in which the Sommerfeld parameter appeared was published in 1967. 

This article uses material from the Wikipedia article  Metasyntactic variable, which is released under the  Creative Commons Attribution-ShareAlike 3.0 Unported License.