Constants of nature, atomic masses and some definitions...

Constants of nature
Energy factors
Table of Atomic masses
Astrophysical S-factor
Gamow energy
References

Constants of nature

The constants of nature used in this compilation are those provided by the latest published report of  the Particle Data Group [PA96]:

Energy factors

Some useful energy equivalent factors:

Atomic masses

For the reaction rate calculations, atomic masses have been taken from the 1997 compilation by G. Audi et al. [AU97]. The table below gives the recommended values for some of the atomic masses involved in the present compilation.

Astrophysical S-factor

At low energies where E<<E_Cou, the probability that incoming particles penetrate the Coulomb barrier can be approximated by the simple expression:
P = exp(-2ph).

The quantity h is called the Sommerfeld parameter.

In numerical units the exponent is 2ph = 0.9895 Z¹Z²(A/E)^1/2, where the center of mass energy E is given in MeV and the reduced mass A is in amu. This approximate expression for the tunneling probability is commonly referred to as the Gamow factor.Due to the exponential behaviour for tunneling, P, the cross section of charged-particle-induced nuclear reactions drops rapidly for energies E<<E_Cou (astrophysical energy range). As a quantum-mechanical interaction between particles, the nuclear reaction probability is proportional to a geometrical factor pl², which is proportional to E^-1. The two factors, P and E^-1, represent explicitely well-known energy dependences of non-nuclear nature. The cross section can be then described as:

s(E) = S(E) exp(2ph(E))/E.

The intrinsic nuclear part of the reaction probability is the so-called astrophysical S-factor, S(E), defined by this equation.The extrapolation of experimental data to the energies of astrophysical interest, the S-factor is a much more convenient function than the cross section. This is, for example, the case of reaction involving light nuclides, when no resonances are present in the stellar energy range [CL68, RO88]..

 Gamow window and Gamow energy

For a given stellar temperature T, nuclear reactions take place in a relative narrow window  DE₀ around the effective burning energy E₀. In numerical units these quantities are given by:

  E₀ = 0.1220 (Z₁²Z₂²AT₉²)^1/3 MeV

and

DE₀ = 0.2368(Z₁²Z₂²AT₉⁵)^1/6 MeV,

where the symbol T₉ represents the temperature T in units of 10⁹ K [CL68, RO88].

 References

[CL68]: D. D. Clayton, Principles of Stellar Evolution and Nucleosynthesis, New York, MacGraw-Hill, 1968.

[RO88]: C. E. Rolfs and W. S. Rodney, Cauldrons in the Cosmos, The University of Chicago Press, Chicago and London, 1988.

[PA92]: Particle Data Group, Review of Particle Properties, Phys. Rev. D45, (1992) 1.

[AU97]: G. Audi, O. Bersillon, J. Blachot, and A.H. Wapstra, Nucl. Phys. A624, 1 (1997).