  The combination of the H I Ly{\alpha} (121.6 nm) line formation mechanism
with ultraviolet (UV) Ly{\alpha} and white-light (WL) observations provides an
effective method for determining the electron temperature of coronal mass
ejections (CMEs). A key to ensuring the accuracy of this diagnostic technique
is the precise calculation of theoretical Ly{\alpha} intensities. This study
performs a modelled CME and its driven shock via the 3D MHD simulation. We
generate synthetic UV and WL images of the CME and shock to quantify the impact
of different assumptions on theoretical Ly{\alpha} intensities, such as the
incident intensity of the Ly{\alpha} line (Idisk), the geometric scattering
function (p({\theta})), and the kinetic temperature (Tn) assumed to be equal to
the proton (Tp) or electron (Te) temperatures. By comparing differences of the
Ly{\alpha} intensities under these assumptions, we find that: (1) Using the
uniform or Carrington maps of the disk Ly{\alpha} emission underestimates the
corona Ly{\alpha} intensity (< 10%) compared to the synchronic map, except for
a slight overestimate (< 4%) in the partial CME core. The Carrington map yields
lower uncertainties than the uniform disk. (2) The geometric scattering process
has a minor impact on the Ly{\alpha} intensity, with a maximum relative
uncertainty of < 5%. The Ly{\alpha} intensity is underestimated for the most
part but overestimated in the CME core. (3) Compared to the assumption Tn = Tp,
using Tn = Te leads to more complex relative uncertainties in CME Ly{\alpha}
intensity. The CME core and void are both overestimated, with the maximum
uncertainty in the core exceeding 50% and the void remaining below 35%. In the
CME front, both over- and under-estimates exist with relative uncertainties of
< 35%. The electron temperature assumption has a smaller impact on the shock,
with an underestimated relative uncertainty of less than 20%.
