VUV Spectroscopy of Atoms, Molecules and Surfaces

140 Chapter 6. Two-colour pump-probe experiments on He ...
momentum, single-photon ionization from the He 1s2p 1P1 state, leaving the
He + ioninthe1s2S1/2 ground state, leads to the emission of either an sor
d-wave electron, corresponding to a total final-state momentum of 1S0 or
1D2, respectively. The total cross section can be shown theoretically to be
given by
�
σ(θ) = σs + σd +2 σs + 1
10 σd
�
P2(cosθ) (6.6)
or
σ(θ) = 9
10 σd
�
3
+
10 σd
�
+3σs cos 2 θ (6.7)
= A + Bcos 2 θ, (6.8)
with A = 9
10σd and B = 3
10σd +3σs [57, 58]. Here P2(cos θ) = 1
2 (3cos2θ−1) is
the second-order Legendre polynomium, θ the angle between the polarization
vectors of the pump and the probe and σs (σd) the partial cross sections for
s(d)-electron emission. Thus, by measuring (relatively) σ as a function of
angle and fitting to the above expression to yield A and B, avalueforthe
ratio σd/σs =10A/(3B − A) can be deduced. In principle, it suffices to
measure the ion signal for two different angles, e.g. σ� = σ(θ =0◦ )andσ⊥
= σ(θ =90◦ ), corresponding to parallel- and perpendicular polarizations,
respectively. The ion signal Ni can be expressed in terms of the cross section
as [36]
�
Ni ∝ (1 − exp (−σjRprobe)) dV, (6.9)
where Rprobe is the space-dependent number of probe photons per cm 2 and
σj = σ � or σ⊥. When measuring Ni as a function of angle, the cross section
is most easily deduced if the probe-pulse energy is kept well below saturation
such that Ni ∝ σ(θ), assuming Rprobe to be spatially constant across the interaction
region. Due to the crossed-beam configuration the latter condition
was, however, not fulfilled in the present experiment and, more importantly,
the σ(θ) measurements were performed with a saturated probe-pulse energy.
In spite of this, an attempt has been made in figure 6.7 to compare the measured
angle-dependent ion signal with the theoretical curve given by equation
6.6, using the theoretically calculated ratio σd/σs = 13/1 [59]. The agreement
is seen to be reasonable but the scatter among the data points does
not allow a precise value for σd/σs to be extracted from a fit to equation 6.6;