  The two electron configuration in the Helium atom is known to very high
precision. Yet, we tend to refer to this configuration as a $1s\uparrow
1s\downarrow$ singlet, where the designations refer to Hydrogen orbitals. The
high precision calculations utilize basis sets that are suited for high
accuracy and ease of calculation, but do not really aid in our understanding of
the electron configuration in terms of product states of Hydrogen orbitals.
Since undergraduate students are generally taught to think of Helium, and
indeed, the rest of the periodic table, in terms of Hydrogenic orbitals, we
present in this paper a detailed spectral decomposition of the two electron
ground state for Helium in terms of these basis states. The $1s\uparrow
1s\downarrow$ singlet contributes less than 93% to the ground state
configuration, with other contributions coming from both bound and continuum
Hydrogenic states.
