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Under in-plane uniaxial stress, the largest Fermi surface sheet of thecorrelated metal Sr$_2$RuO$_4$ undergoes a Lifshitz transition from anelectron-like to an open geometry. We investigate the effects of thistransition on transport through measurement of the longitudinal resistivity$\rho_{xx}$ and the Hall coefficient $R_\text{H}$. At temperatures wherescattering is dominated by electron-electron scattering, $R_\text{H}$ becomesmore negative across the Lifshitz transition, opposite to expectations from thechange in Fermi surface topology. We show that this change in $R_\text{H}$ isexplainable only if scattering changes throughout the Brillouin zone, not justat the point in $k$-space where the Lifshitz transition occurs. In a model oforbital-dependent scattering, the electron-electron scattering rate on sectionsof Fermi surface with $xy$ orbital weight decreases dramatically. On the otherhand, at temperatures where defect scattering dominates $\rho_{xx}$ and$R_\text{H}$ are essentially constant across the Lifshitz transition.

Probing momentum-dependent scattering in uniaxially stressed Sr$_2$RuO$_4$ through the Hall effect