\begin{table}%t3
\caption {\label{table-reactions}Weak interaction coefficients in the Weinberg-Salam-Glashow
theory (in first order), where $\left< M \right>^{2}$ is the squared
and spin-averaged matrix element and $\theta_{\rm W}$ is the Weinberg
angle. $\vec{p}_{i}$ are the 4-momenta of the interacting
particles. For the calculation of the proper phase space integration
with the assumption of a homogeneous distribution as well as
various additional neutrino interaction processes, see for example
\citet{HannestadMadsen:1995}.}
%\centering
\par
\begin{tabular}{c c c c}
\hline \hline\\[-3mm]
Reaction & $\left< M \right>^{2}$ & $c_{V}$ & $c_{\rm A}$ \\
\hline\\[-3mm] 
$\nu_{i}+{\rm e}^{-}\leftrightarrows\nu'_{i}+{\rm e }'^{-}$
&
$32G_{F}^{2}((c_{\rm A}+c_{V})^{2}(\vec{p}_{\nu}\centerdot\vec{p}_{\rm e})
(\vec{p}_{\nu'}\centerdot\vec{p}_{\rm e'})$
&
$\frac{1}{2}+2\sin\theta_{\rm W}$
& 
$\frac{1}{2}$ \\ 
&
$~~~~~~~~~~~~~~+(c_{\rm A}-c_{V})^{2}
(\vec{p}_{\nu}\centerdot\vec{p}_{\rm e'})
(\vec{p}_{\rm e}\centerdot\vec{p}_{\nu'}))$
&
\par
& 
\\
&
$-(c_{V}^{2}-c_{\rm A}^{2})^{2}m_{\rm e}^{2}
(\vec{p}_{\nu}\centerdot\vec{p}_{\nu'}))$
&
\par
& 
\par
\\ 
& 
\par
& 
\par
& 
\par
\\
${\rm e}^{-}+{\rm e}^{+}\leftrightarrows\nu_{i}+\overline{\nu}_{i}$
&
$32G_{F}^{2}((c_{\rm A}+c_{V})^{2}
(\vec{p}_{\nu_{i}}\centerdot\vec{p}_{\rm e^{+}})
(\vec{p}_{\overline{\nu}_{i}}\centerdot\vec{p}_{\rm e^{-}})$
&
$\frac{1}{2}+2\sin\theta_{\rm W}$
& 
$\frac{1}{2}$
\\ 
& 
$~~~~~~~~~~~~~~+(c_{\rm A}-c_{V})^{2}
(\vec{p}_{\nu_{i}}\centerdot\vec{p}_{\rm e^{-}})
(\vec{p}_{\overline{\nu}_{i}}\centerdot\vec{p}_{\rm e^{+}})$
&
\par
& 
\par
\\ 
& 
$-(c_{V}^{2}-c_{\rm A}^{2})^{2}m_{\rm e}^{2}
(\vec{p}_{\nu_{i}}\centerdot\vec{p}_{\overline{\nu}_{i}}))$
&
\par
& 
\par
\\ 
&
\par
& 
\par
& 
\par
\\
$\nu_{\rm e}+\overline{\nu}_{\rm e}\leftrightarrows\nu_{\mu,\tau}+\overline{\nu}_{\nu,\tau}$
&
$32G_{F}^{2}
(\vec{p}_{\nu_{\mu,\tau}}\centerdot\vec{p}_{\overline{\nu}_{\rm e}})
(\vec{p}_{\overline{\nu}_{\mu,\tau}}\centerdot\vec{p}_{\nu_{\rm e}})$
&
$\frac{1}{2}$
& 
$\frac{1}{2}$ \\[1mm]
\hline
\end{tabular}
\end{table}