Fock’s expansion, Kato’s cusp conditions, and the exponential ansatz

We have examined the recent solution of the Fock expansion through O(${\mathit{r}}^2$) for the ground state of the helium atom and have verified that it correctly treats the discontinuity in the local energy characteristic of the triple-collision point. We have also developed an exponential representation of the Fock expansion that satisfies Kato’s cusp conditions for two-particle collisions even when the expansion is truncated at a finite order.