The Sommerfeld parameter, 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]
η=
| Z1Z2e2 | |
| 4\pi\epsilon0\hbarv |
=\alphaZ1Z2\sqrt{
| \muc2 | |
| 2E |
where is the elementary charge, and are the atomic numbers of two interacting nuclides, is the magnitude of the relative incident velocity in the center-of-mass frame, is the unitless fine-structure constant, is the speed of light, and is the reduced mass of the two nuclides of interest.
One of its best-known applications is in the exponent of the Gamow factor (also known as the penetrability factor),
P=\exp(-2\piη)
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.[2]