Asymptotics of the Helium Bound States
An original method is proposed for searching the formal solution of the Hylleraas equation for the helium atom. A mathematically rigorous study confirms, in a unified and simpler manner, several results obtained earlier in the literature but not necessarily in the same contexts. We use an adequate transformation of the Schrödinger equation to identify three asymptotic channels. Two of these are considered in details as physical and are seen to differ from“traditional” ones. In particular, we demonstrate that there is no place for the widely used Hylleraas type exponent.
KeywordsHylleraas equation helium ground state
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