The theory of the elastic scattering of a low velocity ion in a gas is examined in some detail. More precise measurements are reported on the elastic scattering of H+ and H3+ in hydrogen in the velocity range of 2 to 135 volts. The simple exponential form of a potential law is shown to change with the velocity of the ion, i.e., with distance of closest approach of the interacting particles. For H+ in H2 this is—V=−20.37×10−32r4from 2 to 24 volts (ra>1.74A)and V=−8.68×10−14r1.74from 24 to 135 volts (ra=1.74 to 1.5A).The interaction energy calculated on this basis is 3.0 electron volts instead of the 3.5 previously reported. For H3+ in H2 an average taken from 5.4 to 130 volts is V=−1.145×10−36r4.60(ra=2.12 to 1.07A);but between 10.5 and 28 volts (ra = 1.85 to 1.48A) V=−5.98×10−32r4.Both inverse fourth-power potential laws are compared with a similar law evaluated on the basis of the interaction being due solely to that of the charge on the ion interacting with the induced dipole of the hydrogen molecule. The H3+ law is seen to approximate this closely whereas the H+ law does not.

Simons, J. H., Fontana, C. M., Muschlitz, E. E., & Jackson, S. R. (1943). The Low Velocity Scattering of H+ and H3+ in Hydrogen. The Journal of Chemical Physics, 11(7), 307–312.