
\sect{Chemical equilibrium for gamma==e+e}

%Baruch's  B22

Consider the reaction
\[\ \gamma+ \gamma\leftrightarrow     e^{+}+e^{-}\]
where the net charge of the system is fixed by the density
difference $n_0=n_+-n_-$; ${\gamma}$  is a photon and ${e^{\pm}}$
are the positron and electron, respectively.
\begin{itemize}
\item[(a)] Derive equations from which the densities $n_+$ and $n_-$ can
be determined in terms of $n_0$, temperature $T$, and the mass $m$
of either $e^+$ or $e^-$.
\item[(b)] Find the Fermi momentum $p_F$ at $T=0$ for
non-relativistic $e^+,\, e^-$ and the condition on $n_0$ that
allows a non-relativistic limit.
\item[(c)] Solve (a) for $p_F^2/2m<<k_BT<<mc^2$. (Hint: Find first
an expression for the product $n_+n_-$).\\
\end{itemize}

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