  Partitioning of helium atom's correlation energy into radial and angular
contributions, although of fundamental interest, has eluded critical scrutiny.
Conventionally, radial and angular correlation energies of helium atom are
defined for its ground state as deviations, from Hartree--Fock and exact
values, of the energy obtained using a purely radial wavefunction devoid of any
explicit dependence on the interelectronic distance. Here, we show this
rationale to associate the contribution from radial-angular coupling entirely
to the angular part underestimating the radial one, thereby also incorrectly
predict non-vanishing residual radial probability densities. We derive analytic
matrix elements for the high-precision Hylleraas basis set framework to
seamlessly uncouple the angular correlation energy from its radial counterpart.
The resulting formula agrees with numerical cubature yielding precise purely
angular correlation energies for the ground as well as excited states. Our
calculations indicate 60.2% of helium's correlation energy to arise from
strictly radial interactions; when excluding the contribution from the
radial-angular coupling, this value drops to 41.3%.
