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We calculate the Doppler broadening of the $W^-$ resonance produced in$\bar{\nu}_e e^-$ collisions of cosmic anti-neutrinos with $E_{\nu}\approx 6.3\ PeV$ with electrons in atoms up to Iron. Revisiting this issue is prompted byrecent observations of PeV neutrinos by Ice-Cube. Despite its poor energyresolution, the $20\%$ Doppler broadening of the resonance due to electronicmotions can produce observable effects via non-linear neutrino absorption nearthe resonance. The attendant suppression of the peak cross section allows$\bar{\nu}_e$ to travel correspondingly longer distances. While this effect isunlikely to be directly detected in the near future, it may facilitateterrestrial tomography at depths of $\sim 10 \ km$, complementing deeperexplorations using the more frequent nuclear interactions at lower energies.

The Effect of Doppler Broadening on the $6.3 \ PeV$ $W^-$ Resonance in $\bar{\nu}_e e^-$ Collisions