Exceptional Points in the Scattering Resonances of a Sphere Dimer

We investigate exceptional points of degeneracy (EPDs) in electromagnetic scattering of a sphere dimer from the electroquasistatic limit to the fully retarded regime. In the quasistatic limit, we prove that $\text{parity}\text{trev}$-symmetric configurations, realized by spheres with complex-conjugate susceptibilities, host EPDs. Beyond this limit, retardation breaks $\mathcal{P}\mathcal{T}$-symmetry; nevertheless, by jointly tuning the material dispersion of the two spheres, we derive analytic synthesis conditions for realizing EPDs at $\mathit{\text{real}}\mathit{\text{frequencies}}$. Near an EPD, we show that single-parameter perturbations yield the characteristic square-root splitting of the eigenfrequencies, and we quantify its impact on scattering, extinction, and absorption, clarifying sensing implications.