Why polar excitons stay sharp: parity protection of the center-of-mass recoil channel in exciton-phonon scattering

Abstract: In polar semiconductors the Fröhlich interaction is the dominant electron--phonon coupling, yet excitonic resonances in materials such as halide perovskites remain anomalously sharp. We show that standard frozen-center-of-mass treatments of the exciton--phonon problem miss the decisive kinematic degree of freedom: restoring the exact center-of-mass (COM) recoil reveals a universally open, parameter-free $1s\to1s$ absorption channel at recoil momentum $q_<em>=\sqrt{2M_{\rm ex}\hbarω<em>{\rm LO}}/\hbar$, whose rate scales as $N</em>{\rm LO}(T)$. We prove that this recoil channel is controlled by destructive electron--hole interference: the recoil linewidth vanishes with the mass asymmetry as $$γ<em>{\rm LO}^{\rm recoil}\propto\mathcal{F}</em>{1s,1s}(q_</em>)<sup>2$$, and the elastic dressing obeys the exact suppression law $S_X/S_{\rm ind}=η<sup>2(6-η<sup>2)/5$ within the hydrogenic Fröhlich model. The theory establishes a hierarchy of scattering regimes. In mass-asymmetric materials (GaAs, $η=-0.74$) the recoil channel is active ($γ<em>{\rm LO}^{\rm recoil}=2.2$~meV); in mass-symmetric materials (FAPbI$_3$, $η=0$; MAPbI$_3$, $η=-0.11$) it is killed by interference (0.00 and 0.12 meV), showing that the observed 27--40 meV perovskite linewidths cannot be accounted for by COM recoil and therefore require internal-state-changing and other inelastic channels, of which the constructive, $η$-robust $1s\to np$ resonance is the leading candidate within the present model. The Fröhlich constant $α$ alone is therefore insufficient as a figure of merit: after projection onto the correlated exciton, the controlling parameters are $η$, $q</em>*a_X$, and the Rydberg detuning.