The energy associated with giant impacts is large enough to generate global magma oceans during Earths accretion. However, geochemical evidence requiring a terrestrial magma ocean is scarce. Here we present evidence for at least two separate magma oc
ean outgassing episodes on Earth based on the ratio of primordial 3He to 22Ne in the present-day mantle. We demonstrate that the depleted mantle 3He/22Ne ratio is at least 10 while a more primitive mantle reservoir has a 3He/22Ne ratio of 2.3 to 3. The 3He/22Ne ratios of the mantle reservoirs are higher than possible sources of terrestrial volatiles, including the solar nebula ratio of 1.5. Therefore, a planetary process must have raised the mantles 3He/22Ne ratio. We show that long-term plate tectonic cycling is incapable of raising the mantle 3He/22Ne ratio and may even lower it. However, ingassing of a gravitationally accreted nebular atmosphere into a magma ocean on the proto-Earth explains the 3He/22Ne and 20Ne/22Ne ratios of the primitive mantle reservoir. Increasing the mantle 3He/22Ne ratio to a value of 10 in the depleted mantle requires at least two episodes of atmospheric blow-off and magma ocean outgassing associated with giant impacts during subsequent terrestrial accretion. The preservation of a low 3He/22Ne ratio in a primitive reservoir sampled by plumes suggests that the later giant impacts, including the Moon-forming giant impact, did not generate a whole mantle magma ocean. Atmospheric loss episodes associated with giant impacts provide an explanation for Earths subchondritic C/H, N/H, and Cl/F elemental ratios while preserving chondritic isotopic ratios. If so, a significant proportion of terrestrial water and potentially other major volatiles were accreted prior to the last giant impact, otherwise the fractionated elemental ratios would have been overprinted by the late veneer.
I summarize recent progress in the treatment of the Poincare three-nucleon problem at intermediate energies
