against abundant charged particles, which is
crucial because competing processes such as
multiphoton ionization populate highly charged
ions at these pulse energies. Whereas the well-
established cold target recoil-ion momentum
spectroscopy (COLTRIMS)/reaction microscope
technique monitors recoil momentum of
charged particles in photoionization or frag-
mentation processes ( 19 – 21 ), PRI focuses on
neutral species.
The experiment was performed at the Small
Quantum Systems (SQS) instrument at the
SASE3 undulator beam line of the European
XFEL ( 22 , 23 ). We used the core resonances
of neon as a showcase to demonstrate that
PRI indeed can be used to monitor SXRS on
the single-atom level and showed that the
results are quantitatively described within the
framework of the density matrix formalism
using realistically simulated XFEL pulses. In
PRI, a position-sensitive microchannel plate
(MCP) detector is placed downstream of a
collimated pulsed atomic beam (Fig. 1B). In
an interaction region where a photon beam
crosses this atomic beam, energy and momen-
tum are transferred to the atoms in a scatter-
ing process. The detector is sensitive to atoms
with internal energy only, and the momentum
transfer is reflected in the deflection of the
atomic path ( 24 , 25 ).
In a simplifying two-step picture, an x-ray
photon excited the Ne atom in the vicinity of
the 1s→3p inner-shell resonance at a photon
energy ofħwL= 867.3 eV ( 26 ) (Fig. 1A). The
lifetime of this state is ~2.5 fs ( 26 ), the decay
being dominated by Auger transitions. About
2% of the excited atoms decayed radiatively,
predominantlybythe2p→1s transition at
~849 eV ( 18 , 27 ). This process left the Ne atom
in bound [2p–^1 3p]Jstates with excitation en-
ergies of ~18.5 eV ( 28 ). These states to a large
extent decayed to metastable Ne [2p–^1 3s]J=2
on the nanosecond time scale, long after the
interaction with the XFEL pulse. Although the
latter step was irrelevant for the SXRS process,
it was essential for the measurement method
because metastable Ne atoms were detected
in the downstream MCP detector ( 24 , 29 , 30 ).
If atoms were excited without momentum
transfer, they would continue toward the de-
tector with their original velocity, and the in-
teraction region where the atom and photon
beamscrosswouldbedirectlyimagedonthe
detector. Because the photon beam was nar-
row relative to the atomic beam, it was ex-
pected that a line appeared, with length and
thickness corresponding to the cross sections
of the atom and photon beams, respectively
(Fig. 1C). The atom did, however, acquire mo-
mentum in the scattering process. In the first
absorption step, this momentum transfer cor-
responded to a recoil velocity of ~14 m s–^1
along the direction perpendicular to its orig-
inal velocity. In our case, this fact led to a
clearly visible displacement of ~5 mm on the
detector. Because spontaneous emission in
the second step of the process was quasi-
isotropic, a randomly oriented recoil of sim-
ilar magnitude as in the first step resulted
in a large spread (Fig. 1C) of velocities, and
consequently the momentum transfer in the
spontaneous scattering process was expected
to give a shifted and blurred image of the
interaction region. Maintaining the simpli-
fying two-step picture of the SXRS process,
the second step of the scattering process was
now due to stimulated emission. In this case
the emitted photon had almost the same mo-
mentum as the photon absorbed in the first
step, and a clear image of the interaction re-
gion was retrieved.
In Fig. 2A, the total number of detected
metastable Ne* atoms is plotted on a loga-
rithmic scale over more than three orders of
magnitude as a function of the photon en-
ergy. Note that metastable Ne* atoms were
observed at incident photon energies downto 840 eV (i.e., as far as 28 eV below the 1s→
3p resonance). In Fig. 2B, the detector image
resulting from excitation at 860 eV is shown.
A broad distribution, as expected from a spon-
taneous scattering process, is observed. When
the incident energy was centered at 855 eV
(Fig.2C),closetotheenergyfor2p→1s tran-
sition, an additional sharp line appeared, which
indeed corresponded to a sharp image of
the interaction region. As described above, this
observation is precisely what was expected
for the SXRS process. The additional sharp
line was visible for incident photon energies
in the range between 845 and 857.5 eV (see
also fig. S3).
We carried out a rigorous theoretical treat-
ment of the process within the density matrix
formalism using simulated XFEL pulses ( 23 ).
In Fig. 3A, we show the results for the yield of
metastable Ne* atoms produced by the spon-
taneous Raman scattering (Ne*spon) and by
SXRS (Ne*stim). The Ne*sponyield (black curve)
displayed the resonance and compared wellSCIENCEsciencemag.org 25 SEPTEMBER 2020•VOL 369 ISSUE 6511 1631
Fig. 2. Total and
position-resolved
Ne* yields after
interaction of Ne
atoms with XFEL
radiation.(A) Scan of
the incident XFEL
photon energy in the
vicinity of the Ne 1s→
3p transition. Red
points: Measured
Ne* yield produced
via spontaneous
Raman scattering; the
statistical error bars
of the data points
are within the point
size. Dashed black
curve: Simulated Ne*
yield via spontaneous
Raman scattering
using a Gaussian XFEL
pulse with a bandwidth
of 8 eV full width half
maximum ( 23 ) con-
volved with the natural
Lorentzian line shape
of the resonance.
Green curve: Result
of a density matrix
calculation averaged
over 30 theoretically
derived chirped XFEL pulses. Blue bar: Energy of the 2p→1s transition used in the calculation; Black bars:
1s→3p and 4p transition energies and the ionization limitep. (B) Distribution of Ne* atoms deflected as
a result of momentum transfer in the spontaneous x-ray Raman scattering at an incident photon energy
of 860 eV. The upper panel displays the projection of the Ne* yield onto thezaxis. (C) Same as (B), but
recorded at 855 eV incident photon energy. Additionally, a narrow stripe of enhanced Ne* yield appears,
which has its origin in the recoilless stimulated Raman scattering as explained in the text and in Fig. 1.
The projection in the upper panel clearly shows a peak due to the stimulated x-ray Raman scattering.RESEARCH | REPORTS