Using data from NASA's Van Allen Probes, we have identified a synchronized exponential decay of electron flux in the outer zone, near L* = 5.0. Exponential decays strongly indicate the presence of a pure eigenmode of a diffusion operator acting in the synchronized dimension(s). The decay has a time scale of about 4 days with no dependence on pitch angle. While flux at nearby energies and L* is also decaying exponentially, the decay time varies in those dimensions. This suggests the primary decay mechanism is elastic pitch angle scattering, which itself depends on energy and L*. We invert the shape of the observed eigenmode to obtain an approximate shape of the pitch angle diffusion coefficient and show excellent agreement with diffusion by plasmaspheric hiss. Our results suggest that empirically derived eigenmodes provide a powerful diagnostic of the dynamic processes behind exponential decays.