  Collision strengths for electron-impact of fine-structure level excitation
within the ground term of Ne$^{+}$ and Ne$^{2+}$ are calculated using the
Breit-Pauli, Intermediate Coupling Frame Transformation, and DARC $R$-matrix
methods. Maxwellian-averaged effective collision strengths and excitation rate
coefficient qij are presented for each. The application of the current
calculations is to very low temperature astrophysical plasmas, thus we examine
the sensitivity of the effective collision strengths down to 10 K. The use of
the various theoretical methods allows us to place estimated uncertainties on
the recommended effective collision strengths. We also investigate the
sensitivity of the collision strengths to the resonance positions and
underlying atomic structure. Good agreement is found with previous R-matrix
calculations at higher temperature.
