K.J.Coakley

*Statistical Engineering Division, ITL*
C.Sansonetti and J.D.Gillaspy

*Atomic Physics Division, PL
*

By measuring the
binding energies of the low-lying levels of helium,
one can stringently test the accuracy of theoretical
calculations of two-electron quantum
electrodynamic (QED) effects in atoms.
In 1992, NIST reported a fully empirical determination of the 2^{1}S
ionization energy based on the representation of the long series of
transitions 2^{1}S - n^{1}P by a Ritz formula.
The NIST estimate
disagreed with an estimate from a Yale experiment.
In order to search for a possible resolution of the disagreement,
we have
improved our analysis of the NIST data.
First, we
correct the data for
systematic error due to
phase dispersion effects in our
Fabry-Perot interferometer.
Second, we use a improved physical model.
A model for the systematic error
is determined from
a calibration experiment.
In a two-stage bootstrap resampling scheme,
we estimate the total uncertainty of our
estimate of
the 2^{1}S ionization energy.
In the first stage, we simulate
a realization of
calibration data and get
a realization of
the wave number correction
model parameters.
In the second stage,
conditioned on the particular realization of the wave number correction
factors,
we simulate a bootstrap replication
of the observed helium wave number data.
Our new estimate of the ionization energy is
cm^{-1}.
Based on the old analysis,
the discrepancy
between the Yale and NIST estimates
was 2.8 sigma.
Based on our new analysis,
the discrepancy
is
reduced to 1.8 sigma.

We model the
*n*th quantum state
as

Above,
is the ionization energy,
*R* is the finite mass Rydberg constant and
is the quantum defect which we model as

where *B* and *C* are adjustable parameters
and

For helium, *Z*=2.
The finite mass Rydberg constant is
where
where the mass of the electron and the mass of the alpha particle (helium nucleus)
are *m* and *M*.
The constants are
1/137.0359895(61),
,
cm^{-1} .

Figure 15:
Upper left: residuals computed from observed data.
Upper right: a bootstrap replication of residuals.
Lower left: variability of ionization energy estimate
(about mean value) due to calibration experiment errors.
Lower right: variability of ionization energy estimate
(about mean value)
due to errors in both calibration and primary experiment.