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]

η=Z1Z2e24πϵ0ℏv=αZ1Z2μc22E,

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),

P=exp⁡(−2πη),

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]

## References

1. ↑ Rolfs, C.E.; Rodney, W.S. (1988). Cauldrons in the Cosmos. Chicago: University of Chicago press. p. 156. ISBN 0-226-72456-5. https://books.google.com/books?id=BHKLFPUS1RcC&pg=PA156.
2. ↑ Breit, G. (1967). "Virtual Coulomb Excitation in Nucleon Transfer". Proceedings of the National Academy of Sciences of the United States of America 57 (4): 849–855. doi:10.1073/pnas.57.4.849. PMID 16591541. PMC 224623. Bibcode: 1967PNAS...57..849B. http://www.pnas.org/content/57/4/849.full.pdf. Retrieved 27 January 2015.

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