Sommerfeld parameter

The Sommerfeld parameter Template:Math, 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

$\eta =\frac{Z_1{Z}_2{e}^2}{4\pi {ϵ}_0\hslash v}=\alpha Z_1{Z}_2\sqrt{\frac{\mu c^2}{2E}}$,

where Template:Math is the elementary charge, Template:Math and Template:Math are the atomic numbers of two interacting nuclides, Template:Math is the magnitude of the relative incident velocity in the center-of-mass frame, Template:Math is the unitless fine-structure constant, Template:Math is the speed of light, and Template:Math is the reduced mass of the two nuclides of interest.

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

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

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.