Sommerfeld parameter

The Sommerfeld parameter η 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]

$\eta ={\frac {Z_{1}Z_{2}e^{2}}{4\pi \epsilon _{0}\hbar v}}$,

where e is the elementary charge, Z₁ and Z₂ are the atomic numbers of two interacting nuclides, and v is the magnitude of the relative incident velocity.

One of its best-known applications is in the exponent of the Gamow factor P,

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

which is the probability of an s-wave proton to penetrate the Coulomb barrier.

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. Retrieved January 30, 2015.
2. Breit, G. (1967). "Virtual Coulomb Excitation in Nucleon Transfer" (PDF). Proceedings of the National Academy of Sciences of the United States of America. 57 (4): 849. Bibcode:1967PNAS...57..849B. doi:10.1073/pnas.57.4.849. Retrieved 27 January 2015.