New electric-field scaling law for swarm experiments

We generalize the familiar result that the drift velocity $V_d$ and the product $\mathrm{pD}$ of the pressure and the diffusion coefficient depend on pressure $p$ and electric field $E$ only through the ratio $\frac{E}{p}$ in swarm experiments. Our new scaling law applies to different systems to the extent that their elastic and inelastic cross sections are in the same ratio. We present model calculations of $V_d$ for electrons in gaseous C${\mathrm{H}}_4$-Ar and C${\mathrm{H}}_4$-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ mixtures predicting that the scaling is approximately obeyed if the C${\mathrm{H}}_4$ concentrations are appropriately related. We also examine $V_d$ and $D_{\perp }$ data for electrons in C${\mathrm{H}}_4$ and Si${\mathrm{H}}_4$ at low $E$ and find that the scaling is approximately obeyed with a factor of 6. This suggests strongly that the low energy (≲1 eV) effective elastic and inelastic electron cross sections for these molecules have approximately the same shape and differ by the same factor, which is approximately 6. Thus in particular we predict a Ramsauer minimum for Si${\mathrm{H}}_4$, which has been suggested previously.