Degeneracy parameter

Using the parameters for the centre of the Sun given in Problem 3, estimate the degeneracy parameter from Eq. (5.41). 

Figure 16. Isoabundance contours for D, 4He, and 7Li in the ANv - rjio plane for four choices of the degeneracy parameter e. The shaded areas identify the ranges of parameters consistent with the abundances indicated (see the text).

However, electron-type neutrinos play a unique role in BBN, mediating the neutron-proton transformations via the weak interactions (see eq. 3.24). Suppose, for example, there are more ve than ve. If p,e is the ue chemical potential, then e = /j,e/kT is the neutrino degeneracy parameter in this case, e > 0. The excess of z/e will drive down... 

The constant a, or more usually A = e is called the degeneracy parameter, the reason for the name being as follows. If a is very great, and therefore A very small (compared to 1), we can neglect the 1 in the denominator in comparison with = e jA (since of course ySe is always positive) thus in this case we obtain... 

The degeneracy parameter is determined as before from the first subsidiary condition ... 

The Bolution of this difficulty is due to Pauli and Sommerfeld (1927), who pointed out that the laws of classical statistics ought not to be applied to the electron gas within a metal, since it is bound to behave as a degenerate gas. Thus, since the mass of the electron is 1840 times smaller than that of the hydrogen atom, it follows that, at room temperature T = 300°) and an electronic density oi n 3T0 , corresponding to a gas density at a pressure of 1 atmosphere, the value of the degeneracy parameter for the electron is... 

For the best thermal sources, the mean number of photons in the coherence volume (i.e., the degeneracy parameter ) is less than 10 . ... 

The mean number n of photons per mode is often called the degeneracy parameter of the radiation field. This example shows that the coherence volume is related to the modes of the radiation field. This relation can be also illustrated in the following way ... 

---