Chromatic Weak Lensing of a Generic Spherical Spacetime Through Millicharged Dark Matter Media

We study photon scattering in a transparent dispersive medium around a spherical geometry whose lapse contains independent inverse-radius terms through the fifth order. Free millicharged particles and neutral dark atoms provide microscopic response models through cold-plasma dispersion and dynamical polarizability, respectively. A joint expansion to the second order in the metric and susceptibility amplitudes retains every pairwise gravitational contribution and every mixed term coupling gravity and dispersion. The mixed coefficients depend on the logarithmic frequency derivative of the response. We separately derive a complete expansion through the fifth order in the inverse impact parameter using a generating formula that retains all nonlinear contributions at each radial order. Explicit vacuum coefficients and coefficients for a medium with an inverse-radius susceptibility relate the two expansions while preserving their distinct order counting. For an inverse-radius susceptibility, a relation between the leading radial coefficients and their spectral variation isolates the inverse-square metric coefficient under specified material assumptions. Higher metric coefficients require additional radial information and control of nonlinear material response. Calculations using exact rays test the expansions, reproduce the coefficient bias from neglected refraction, and quantify the conditioning of frequency subtraction. The metric is a phenomenological exterior ansatz. The calculation provides a consistent framework for separating geometric and material contributions in weak dispersive lensing.