  It has been claimed that the coherent scattering of relic neutrinos with the
Earth will result in a neutrino-antineutrino asymmetry of
$\mathcal{O}(10^{-4})$ on the Earth surface, which is five orders of magnitude
larger than the naive model expectation. In this work we show that this
overdensity was overestimated for the perfectly round Earth by solving the
exact solution with partial waves. The maximal asymmetry after summing over all
the angular modes is only around $10^{-8}$ above the ground. To achieve the
proposed asymmetry of $\mathcal{O}(10^{-4})$, a special geography may be needed
as the experimental site.
