  Over the past decades, many authors advertised models on complexified
spacetime algebras for use in describing gravity. This work aims at providing
phenomenological support to such claims, by introducing a one-parameter real
phase $\alpha$ to the conventional Dirac equation with $\frac{1}{r}$-type
potential. This phase allows to transition between Euclidean
($\alpha=0,\pm\pi,\pm2\pi,\ldots$) and Minkowskian
($\alpha=\pm\frac{\pi}{2},\pm\frac{3\pi}{2},\ldots$) geometry, as two distinct
cases that one may expect from some complexified spacetime. The configuration
space is modeled on $4\times4$ matrix algebra over the bicomplex numbers,
$\mathbb{C}\oplus\mathbb{C}$. Spin-$\frac{1}{2}$ Coulomb scattering (Rutherford
scattering) in Born approximation is then executed. All calculations are done
``from scratch'', as they could have been done some 85 years ago. By removing
elegance from field theory that has since become customary, this paper aims at
remaining as generally applicable as possible, for a wide range of candidate
models that contain such a phase $\alpha$ in one way or another. Results for
backscattering and cross section at high energies are compared with results
from General Relativity calculations. Effects on intergalactic gas distribution
and momentum transfer from scattering high-energy leptons are sketched.
