A Trichotomy for Modified Scattering Across the Yukawa-Coulomb Transition

Yonggeun Cho, Jinyeop Lee

We study the long-time asymptotics of the three-dimensional Hartree equation with Yukawa potential \[ V_μ(x)=\frac{e^{-μ|x|}}{|x|}, \qquad 0\leqμ\leq1. \] The Coulomb case corre…