12
A. Rouzée et al.
In the final (molecular ion + electron) state the symmetry of the wavefunction
is determined both by the electronic state of the ion and that of the continuum electron. The wave function of a photoelectron ejected by single photon ionization can
be expressed as a superposition of partial waves that are characterized by the angular momentum l of the photoelectron and a symmetry index λ that describes the
projection of this angular momentum on the molecular axis; for λ = 0 the states are
designated as σ and for λ = 1 as π . In practice, the partial-wave expansion converges at relatively small l (l < 4, or in usual notation s, p, d and f partial waves).
In addition, the dipolar u ←→ g selection rule restricts the electron in the continuum to ungerade symmetry for the final ionic states X 2 Σ g and C 2 Σ g (which implies
that only odd angular momenta appear in the partial wave expansion of the outgoing
electron) and to gerade symmetry for the final ionic states A 2 Π u and B 2 Σ u (which
means that only even angular momenta appear in the partial wave expansion of the
outgoing electron). One cannot extract the partial wave decomposition of the electronic wave packet from the experimental results due to the low degree of alignment.
The experimental result can only put constraints on the possible decomposition of
the electronic wavepacket into partial waves. For the ionization leading to the final
X 2 Σ g ground ionic state for instance, where the wave packet is mainly composed
of l = 1, 3 (p and f waves), the pronounced positive contribution along the laser polarization axis that is observed both theoretically and experimentally suggests that
the photoelectron partial wave decomposition contains a strong contribution from
the p-partial wave. The computational results support this notion, but also suggest
an important role for f-wave photo-emission.
One of the most significant results that follows from the experimental and theoretical contour plots shown in Fig. 1.4b–f is the fact that the differential photoelectron angular distributions clearly depend on the kinetic energy of the outgoing
electron. This may be interpreted as a manifestation of the onset of structural information in the photoelectron angular distributions. Although the photoelectron
kinetic energies are still too low to observe readily interpretable diffraction patterns,
and although the differential photoelectron angular distributions are heavily affected
by the extensive angular averaging that occurs as a result of the rather modest degree
of alignment and anti-alignment in the experiment, this result provides the rationalization for attempts to extend these results to higher photon energies. Extending
the use of HHG sources, this may become possible in the near future by the use
of different generating gasses with a higher cut-off (He or Ne, rather than Ar) in
the HHG process [36], and/or by performing HHG with a longer wavelength driver
wavelength [37] or making use of a multi-color field [38].
Alternatively, higher photon energies may be accessed by performing the experiment at one of the emerging XUV/X-ray FEL facilities, which moreover have the
advantage that they offer a peak brightness which exceeds that of HHG sources by
many orders of magnitude. FELs like FLASH and LCLS offer more than 10 12 photons/pulse at photon energies ranging from ca. 0.04 to 10 keV. However, the advantages of FELs over HHG come at the expense of a lack of coherence and the difficulty to synchronize other laser sources to the FEL. The former is not a serious problem in molecular pump-probe experiments aiming at femtosecond time resolution,
A. Rouzée et al.
In the final (molecular ion + electron) state the symmetry of the wavefunction
is determined both by the electronic state of the ion and that of the continuum electron. The wave function of a photoelectron ejected by single photon ionization can
be expressed as a superposition of partial waves that are characterized by the angular momentum l of the photoelectron and a symmetry index λ that describes the
projection of this angular momentum on the molecular axis; for λ = 0 the states are
designated as σ and for λ = 1 as π . In practice, the partial-wave expansion converges at relatively small l (l < 4, or in usual notation s, p, d and f partial waves).
In addition, the dipolar u ←→ g selection rule restricts the electron in the continuum to ungerade symmetry for the final ionic states X 2 Σ g and C 2 Σ g (which implies
that only odd angular momenta appear in the partial wave expansion of the outgoing
electron) and to gerade symmetry for the final ionic states A 2 Π u and B 2 Σ u (which
means that only even angular momenta appear in the partial wave expansion of the
outgoing electron). One cannot extract the partial wave decomposition of the electronic wave packet from the experimental results due to the low degree of alignment.
The experimental result can only put constraints on the possible decomposition of
the electronic wavepacket into partial waves. For the ionization leading to the final
X 2 Σ g ground ionic state for instance, where the wave packet is mainly composed
of l = 1, 3 (p and f waves), the pronounced positive contribution along the laser polarization axis that is observed both theoretically and experimentally suggests that
the photoelectron partial wave decomposition contains a strong contribution from
the p-partial wave. The computational results support this notion, but also suggest
an important role for f-wave photo-emission.
One of the most significant results that follows from the experimental and theoretical contour plots shown in Fig. 1.4b–f is the fact that the differential photoelectron angular distributions clearly depend on the kinetic energy of the outgoing
electron. This may be interpreted as a manifestation of the onset of structural information in the photoelectron angular distributions. Although the photoelectron
kinetic energies are still too low to observe readily interpretable diffraction patterns,
and although the differential photoelectron angular distributions are heavily affected
by the extensive angular averaging that occurs as a result of the rather modest degree
of alignment and anti-alignment in the experiment, this result provides the rationalization for attempts to extend these results to higher photon energies. Extending
the use of HHG sources, this may become possible in the near future by the use
of different generating gasses with a higher cut-off (He or Ne, rather than Ar) in
the HHG process [36], and/or by performing HHG with a longer wavelength driver
wavelength [37] or making use of a multi-color field [38].
Alternatively, higher photon energies may be accessed by performing the experiment at one of the emerging XUV/X-ray FEL facilities, which moreover have the
advantage that they offer a peak brightness which exceeds that of HHG sources by
many orders of magnitude. FELs like FLASH and LCLS offer more than 10 12 photons/pulse at photon energies ranging from ca. 0.04 to 10 keV. However, the advantages of FELs over HHG come at the expense of a lack of coherence and the difficulty to synchronize other laser sources to the FEL. The former is not a serious problem in molecular pump-probe experiments aiming at femtosecond time resolution,