  The Configuration Interaction (CI) method using a large Laguerre basis
restricted to l = 0 orbitals is applied to the calculation of the He ground
state. The maximum number of orbitals included was 60. The numerical evidence
suggests that the energy converges as Delta E^N approx A/N^(7/2) + B/N^(8/2) +
>... where N is the number of Laguerre basis functions. The electron-electron
delta-function expectation converges as Delta delta^N approx A/N^(5/2) +
B/N^(6/2) + ... and the variational limit for the l = 0 basis is estimated as
0.1557637174(2) a_0^3. It was seen that extrapolation of the energy to the
variational limit is dependent upon the basis dimension at which the exponent
in the Laguerre basis was optimized. In effect, it may be best to choose a
non-optimal exponent if one wishes to extrapolate to the variational limit. An
investigation of the Natural Orbital asymptotics revealed the energy converged
as Delta E^N approx A/N^6 + B/N^7 + ... while the electron-electron
delta-function expectation converged as Delta delta^N approx A/N^4 + B/N^5 +
>... . The asymptotics of expectation values other than the energy showed
fluctuations that depended on whether $N$ was even or odd.
