  The interacting model describing the Rabi transition is essential in studying
atom-photon interactions, where the kinetic energy term is often neglected for
the convenience of analysis. We first study the approximation through the
fidelity approach and verify its valid region in the parameter space of
detuning and momentum. We find that as the radiation field's momentum and the
absolute value of detuning decrease, the approximation becomes valid. We
further discover that the omission of the kinetic energy term will overestimate
the measuring accuracy of the Rabi frequency in some parameter regions and
underestimate the precision in other regimes with Fisher information tools'
help. Notably, a specific choice of the initial Gaussian state's variance in
position space will improve the measuring accuracy when we take the kinetic
energy term into account. We also study the realistic measurement of the Rabi
frequency for cases with and without the kinetic energy.
