VOLUME 76, NUMBER 17 PHYSICAL REVIEW LETTERS 22 APRIL 1996
Raman versus Non-Raman Behavior in Resonant Auger Spectra of HCl
E. Kukk, H. Aksela, and S. Aksela
Department of Physical Sciences, University of Oulu, FIN-90570 Oulu, Finland
F. Gel’mukhanov and H. Ågren
Institute of Physics and Measurement Technology, Linköping University, S-58183 Linköping, Sweden
S. Svensson
Department of Physics, Uppsala University, Box 530, S-75121 Uppsala, Sweden
(Received 13 July 1995)
Two different types of Auger processes are shown to constitute the resonant Auger spectra
of HCl: one which does and one which does not show Raman narrowing with the decrease of
the spectral width of the exciting radiation. An analytical explanation for this phenomenon is
given. [S0031-9007(96)00044-0]
PACS numbers: 33.20.Fb, 33.20.–t
The Cl 2p absorption spectrum of the HCl molecule
exhibits an intense well-defined pre-edge structure [1–3].
It consists of a broad feature around hn 200 203 eV,
known to be due to the excitations to the first unoccupied
molecular orbital s
. This structure is accompanied
by a series of sharp peaks at higher photon energies,
corresponding to the excitations to s and d Rydberg
orbitals. The relaxation of the core excitations can,
in general, take place (i) through the resonant Auger
decay in the molecular environment and (ii) through
fast dissociation of the molecule, followed by atomic
Auger decay. The character of the core-excited state
determines the relaxation path and is therefore reflected
in the structure and line shapes of the Auger electron
spectrum.
The sharp absorption peaks correspond to the core-to-
Rydberg excitations populating only a single energy state.
The distribution of the exciting photons with energy v
is described by spectral function Fv2v
c
, g, which is
centered at energy v
c
and has the width g. If g is so
large that Fv2v
c
, g can be taken as constant over
the lifetime width G of the excited state, then the Auger
electron lines reflect the lifetime broadening of the excited
state [4]. The progress in the experimental techniques
utilizing synchrotron radiation has made it possible to
observe the Auger resonance Raman effect (ARRE) [5,6]
in the vacuum ultraviolet range for free atoms [7] and
recently also for molecules [8].
Resonant Auger constitutes a nonradiative x-ray scat-
tering process in which the incoming x-ray photon with
energy v excites through dipole interaction D the mole-
cule which then decays nonradiatively with emission of
the Auger electron e
2
due to Coulomb interaction Q.
The amplitude of this process is given by the generalized
Kramers-Heisenberg formula [6]:
F
of
v ~
X
i
0j D ji i j Q jf
v2 E
i
2 E
0
1 i G2
, (1)
where G is the lifetime width of the core excited state. We
use here atomic units. The cross section of this process
reads
se, v
X
f
j F
of
v j
2
d v2e2 E
f
2 E
0
,
(2)
where E
0
and E
i
are total molecular energies of ground
and intermediate states, E
f
is the total energy of the fi-
nal state molecular ion, and e is the energy of the Auger
electron. A negligible lifetime width of the final state in
the Auger process is then assumed. To describe a real-
istic experimental situation we must use the convolution
se, v
c
of the cross section (2) with the incoming x-ray
photon spectral function Fv2v
c
, g. The presence of
the Dirac d-energy function in Eq. (2) implies that the
ARRE becomes observable if g is comparable with G.
Under such experimental conditions, the Auger line shape
is properly given by the product of the Lorentzian distri-
bution of the lifetime broadening and the spectral func-
tion, which leads to the distorted shape and narrowing of
the resonant Auger electron lines [4,9,10]. Obviously, if
g is much narrower than G, then the width of the Auger
electron lines is practically determined by g and linear
dispersion of the Auger electron energy e with v
c
can be
observed.
The broadness of the molecular resonance features can
be, in principle, a result of the repulsive nature of the
excited state [11], or it can be due to the excitations to a
manifold of close-lying vibronic levels of a bonding state.
If the Auger decay of this manifold of states populates
a single final state, then, just due to energy conservation,
the Auger linewidth and energy e must follow the spectral
width g and energy v
c
, even when g.G.
The line-shape narrowing and linear dispersion, charac-
teristic to the ARRE, have been observed by Liu et al. [8]
for the Auger decay of the 3d
21
5pp Rydberg states in
the HBr molecule. On the other hand, the Auger decay
3100 0031-9007 96 76(17) 3100(4)$10.00 © 1996 The American Physical Society