VUV Spectroscopy of Atoms, Molecules and Surfaces

6.3 Results and discussion 137
Ion signal (arb. units)
20
15
10
5
58.41 58.42 58.43 58.44
Wavelength (nm)
Figure 6.5: The apparent harmonic spectral profile on- (black) and off-spike (grey), respectively,
for a He pressure of 6×10 −4 mB.
(by saturating the ionization) and (ii) a significant absorption of the harmonic
by the He gas medium.
The observations can be qualitatively accounted for by a rate-equation
model where the He + signal Ni(t) is calculated as a function of time delay t
from a knowledge of the time-dependent population Nr(t) ofthe1s2p resonant
level [54]. Rate equations are well known in atomic physics [18] and have
previously been applied in studies of resonant two-photon ionization [55, 56]
but without including the absorption, which plays the key role in the present
context. Nr(t) can be expressed in terms of the excitation rate Ω(t) fromthe
ground state to the resonant level [52] which is assumed to be proportional
to the ”area” of the Lorentzian profile of the Stark-brodened atomic transition.
The absorption from the harmonic during its propagation towards the
interaction region is accounted for in a phenomenological way by multiplying
the Stark-broadened Lorentzian profile with the exponential absorption factor
of the Lambert-Beer law [24], using the wavelength-dependent field-free
Lorentzian absorption cross section in the exponent. In this manner the time
dependence of the Stark-broadening, following the time-dependent overlap
between the harmonic and the probe, is transferred into a time-dependence
of Ω(t). Neglecting the contribution to the ground-state population from the
radiative decay, the rate equations to be solved are
dNg
dt = − Ω(t)Ng, (6.3)