New cross sections for the rotational excitation of H3+ by electrons are
calculated {\it ab initio} at low impact energies. The validity of the
adiabatic-nuclei-rotation (ANR) approximation, combined with R-matrix
wavefunctions, is assessed by comparison with rovibrational quantum defect
theory calculations based on the treatment of Kokoouline and Greene ({\it Phys.
Rev. A} {\bf 68} 012703 2003). Pure ANR excitation cross sections are shown to
be accurate down to threshold, except in the presence of large oscillating
Rydberg resonances. These resonances occur for transitions with ΔJ=1
and are caused by closed channel effects. A simple analytic formula is derived
for averaging the rotational probabilities over such resonances in a 3-channel
problem. In accord with the Wigner law for an attractive Coulomb field,
rotational excitation cross sections are shown to be large and finite at
threshold, with a significant but moderate contribution from closed channels.Comment: 3 figures, a5 page