Parameters for neutrino-nucleon elastic scattering

It is shown that four parameters ${B}_{\ensuremath{\alpha}}$, linearly related to the usual form factors ${A}_{\ensuremath{\alpha}}({q}^{2})$, are especially convenient for discussing the experiments because the cross section is proportional to $\ensuremath{\Sigma}{({B}_{\ensuremath{\alpha}})}^{2}$ and the polarization of the recoil nucleon is given by ${\stackrel{\ensuremath{\rightarrow}}{l}}^{\ensuremath{'}}=\frac{2{B}_{4}({B}_{1}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{i}}}_{2}+{B}_{2}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{i}}}_{2}+{B}_{3}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{i}}}_{3})}{\ensuremath{\Sigma}{({B}_{\ensuremath{\alpha}})}^{2}}$. Here ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{i}}}_{1}$, ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{i}}}_{2}$, and ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{i}}}_{3}$ are unit vectors in the directions of ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{p}}}^{\ensuremath{'}}$, $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}\ifmmode\times\else\texttimes\fi{}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{p}}}^{\ensuremath{'}}$, and ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{i}}}_{1}\ifmmode\times\else\texttimes\fi{}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{i}}}_{2}$, where ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{p}}}^{\ensuremath{'}}$ is the momentum of the outgoing nucleon and $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$ that of the incident neutrino. A discussion of some possible experiments is given, as suggested by this parametrization.