VUV Spectroscopy of Atoms, Molecules and Surfaces

128 Chapter 6. Two-colour pump-probe experiments on He ...
matrix element connecting the initial- and final states of a given transition,
it provides, in addition, a sensitive test of atomic- and molecular structure
theory. In fact, the accuracy of laboratory measurements has reached a level
where electron correlation and—especially for larger systems—relativistic effects
can no longer be ignored. The many-body approaches are basically the
same as those discussed in chapter 2, i.e. relativistic MCHF [9, 10], variational
configuration interaction [11], many-body perturbation theory [12] and—for
two-electron systems—the hyperspherical-coordinate approach [13]. In fact,
the R-matrix method used in negative ion calculations was first applied in
connection with—and has thus been adopted from—the Opacity Project [14].
Although fairly accurate, theoretical calculations cannot always be trusted
and must be tested against experiments, especially when used in spectral
analysis where a higher precision is required [15]. Due to the increased experimental
difficulties associated with the UV and VUV regions, the lack of
accurately measured oscillator strengths is particularly severe in this wavelength
range where demands are increasing with the launches of the EUVE
(Extreme Ultraviolet Explorer) and FUSE (Far UltraViolet Spectroscopic Explorer)
satellites in 1992 and 1999, respectively [16]. The oscillator strength
can be determined either from a measurement of the radiative lifetime of the
upper level of the transition combined with a knowledge of the branching ratio
for decay to the specific lower level, or from a measurement of either the real
or imaginary part of the refractive index of the gas medium [17]. In the latter
case, knowing the column density (the volume density times unit length),
the oscillator strength can be inferred by exploiting its dependence on the
refractive index (i.e. the dispersion or absorption) [18]. In practice, one measures
either interferometrically the phase shift, or dispersion, of a (spectrally
white) light beam passing through the gas, or—with a spectrometer—the
absorption- or emission spectrum of the gas. The column density is, however,
not easily determined, and unless the medium is optically thin, the
absorption coefficient will depend on the line shape of the transition in a
non-trivial way [17]. As a consequence, oscillator strengths are most often
determined from lifetime measurements, the branching ratio being known
from emission- or absorption experiments using a grating spectrometer or
a so-called Fourier-transform spectrometer [19, 20]. The Fourier-transform
spectrometer is in essence a Michelson interferometer which, when used with
a spectrally (absorption-modulated) white light source gives an intensity variation
as a function of delay whose Fourier-transform is the spectral content
of the light source [21]. As opposed to a grating spectrometer this has the
advantage of using all of the available light for the measurement but due to
the presence of the tranmittive optics it cannot be applied below ∼120 nm.
Denoting by Wka and Wki the transition rates from the upper level k to the