Capturing transient core-to-core resonances in Kr in intense extreme-ultraviolet laser fields by electron-ion coincidence spectroscopy

概要

PHYSICAL REVIEW A 107, L021101 (2023)
Letter

Capturing transient core-to-core resonances in Kr in intense extreme-ultraviolet
laser fields by electron-ion coincidence spectroscopy
Mizuho Fushitani ,1,2,* Makoto Yamada,1 Hikaru Fujise,1 Shigeki Owada ,2,3 Tadashi Togashi ,2,3 Kyo Nakajima ,2,3
Makina Yabashi,2,3 Akitaka Matsuda ,1,2 Yasumasa Hikosaka ,4,2,† and Akiyoshi Hishikawa 1,2,5,‡
1

Department of Chemistry, Graduate School of Science, Nagoya University, Nagoya, Aichi 464-8602, Japan
2
RIKEN, SPring-8 Center, Sayo, Hyogo 679-5148, Japan
3
Japan Synchrotron Radiation Research Institute, Sayo, Hyogo 679-5198, Japan
4
Institute of Liberal Arts and Sciences, University of Toyama, Toyama 930-0194, Japan
5
Research Center for Materials Science, Nagoya University, Nagoya, Aichi 464-8602, Japan
(Received 12 October 2022; accepted 9 February 2023; published 23 February 2023)

Resonances between core-hole states have been long hypothesized to understand nonlinear responses of atoms
and molecules exposed to intense x-ray free-electron laser (XFEL) pulses, but evaded clear identification in
previous studies due to their transient nature. Here we report clear evidence of core-to-core resonances by stateof-the-art electron-ion coincidence spectroscopy on Kr atoms. The observed 3p-3d resonance manifested the
significance in multiple ionization to highly charged states against the ultrafast core-hole decay. The present
study, elucidating the role of the core-to-core resonance in electronic responses of matter to high-frequency laser
fields, will advance our understanding of nonlinear spectroscopy and ultrafast imaging by ultrashort intense EUV
and x-ray pulses.
DOI: 10.1103/PhysRevA.107.L021101

Resonances are of great importance in light-matter interaction in strong laser fields, which enhance particular nonlinear
processes by orders of magnitude. In extreme ultraviolet
(EUV) and x-ray laser fields, the nonlinear responses of matter
can be characterized by the participation of inner-shell or
core electrons (see, for example, Refs. [1–5]), which makes
a marked contrast to those in the visible and infrared regions.
It was shown that the resonant excitation of core electrons into
densely spaced Rydberg and valence states can enhance nonlinear photoionization to unexpectedly high charge states, as
demonstrated with Ne [6,7], Kr [8], Xe [9,10], and CH3 I [11].
Resonances involving core electrons can be further enhanced
by harnessing vacancies created in fully occupied orbitals
during the interaction with the laser fields. Such resonance
was identified with Ne [6], where ionization from the 1s core
orbital is enhanced by 1s → 2p resonance in singly ionized
Ne at hν = 848 eV. Since the transition is not open in the
neutral ground state, the resonance is often referred to as “hidden” resonances [6,12]. It is suggested that such resonances
also play a decisive role in ultrafast diffraction imaging of
nanoscale and biological systems using x-ray free-electron
lasers (FELs) [13].
In addition to the core-to-valence resonances mentioned
above, transient resonances can also occur between corehole states, which have been indeed hypothesized to interpret
the charge distribution of rare gas atoms, such as Kr and Xe
[14] as well as Ar [15], exposed to intense x-ray pulses. The

*

fusitani@chem.nagoya-u.ac.jp
hikosaka@las.u-toyama.ac.jp
‡
hishi@chem.nagoya-u.ac.jp
†

2469-9926/2023/107(2)/L021101(7)

core-to-core resonance has also been discussed in our previous
study [16] of two-photon ionization to 4d double core-hole
hν

hν

→ Xe+ (4d −1 ) + e− −
→ Xe2+ (4d −2 ) +
states of Xe, Xe −
−
2e . The photoionization cross section of Xe+ (4d −1 ) to
Xe2+ (4d −2 ) was found to be up to three times larger than the
typical cross section of 4d inner-shell ionization [17,18], indicating an additional contribution to the well-known 4d giant
resonance. To explain this unexpectedly large cross section,
core-to-core resonant transitions from 4d −1 to 4p−1 states in
Xe+ were proposed because the 4p−1 states couple strongly
with 4d −2 states. However, the broad spectral feature of the
4p−1 state spreading over 30 eV near the 4d −2 ionization
threshold [19,20] prevented the unambiguous identification of
resonances. Therefore, core-to-core resonant transitions have
yet to be verified to fully understand the complex responses
of matter in intense EUV and x-ray laser fields. Obviously,
such resonances, hidden in neutral species in their ground
states, require a transient core vacancy. The competition
with core-hole decay proceeding in an ultrashort timescale
(10 fs) makes the observation of the transient resonances
challenging.
Here we present clear identification of hidden core-tocore transitions with Kr in intense EUV-FEL fields by using
electron-ion coincidence spectroscopy [16,21]. In contrast to
the strongly perturbed Xe+ (4p−1 ) case, the 3p and 3d corehole states of Kr are well defined in energy [22,23]. The
optical transitions between the spin-orbit sublevels (3p1/2,3/2
and 3d3/2,5/2 ) should appear with three distinct spectral lines
around hν = 120 eV, which allows us to identify the 3p − 3d
resonances as a function of the central photon energy of
EUV-FEL. The 3p core-hole state formed in Kr + is detected
by the 3p Auger electrons [24–26]. The coincidence electron

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©2023 American Physical Society

MIZUHO FUSHITANI et al.

PHYSICAL REVIEW A 107, L021101 (2023)

FIG. 1. (a) Schematic of transient core-to-core resonance at the 3p−1 − 3d −1 transition in the two-photon ionization of Kr, competing with
ultrafast 3d core-hole decay. (b) Energy level diagram of Kr z+ (z = 0–4) [24,26–28] relevant to the present study. Possible multiple ionization
pathways are shown by arrows representing photoabsorption and electron emission (black: single-photon process; purple: multiphoton process).
(c) Time-of-flight spectrum of Kr in intense EUV-FEL laser fields (121.5 eV, 1.2 × 1014 W/cm2 ).

spectroscopy with the counterpart Kr 3+ and Kr 4+ ions, the
major products via 3p core-hole decay [26] [see Fig. 1(b)],
securely identifies the formation of the 3p core hole and the
dependence of the FEL photon energy with minimal contamination from strong single-photon processes.
The experiments were conducted at the soft x-ray beam
line (BL1) of SACLA [29]. Intense ultrashort EUV laser
pulses (hν = 118–128 eV, bandwidth ∼1–2 eV, pulse duration ∼30 fs, repetition rate 60 Hz) [29,30] were focused by
Kirkpatric-Baez (KB) mirrors to gaseous Kr. Electrons and
ions produced by the interaction with intense EUV pulses
were detected by using a magnetic-bottle multielectron-ion
coincidence spectrometer [16,21]. Briefly, the electrons are
guided by a magnetic field toward a multichannel plate (MCP)
detector placed at the end of the time-of-flight tube [31,32].
The counterpart ions were then collected by pulsed voltages
applied approximately 1 μs after the laser irradiation to repeller (+4.0 kV) and extractor (+3.1 kV) electrodes, to be
detected by the same MCP detector. In coincidence measurements, the sample pressure was kept at ∼4 × 10−8 Pa.
A Zr filter (0.1 μm) was used to suppress the harmonics of the FEL. The average event rate was 0.32 per laser
shot. The typical energy resolution E of the spectrometer
can be given as E /E = 33 at the electron energy E 
200 eV. Electrons were decelerated by retarding electrodes
to observe Kr 3p Auger peaks [24–26] with a high-energy
resolution.
Figure 1(c) presents the ion time-of-flight mass spectrum
of Kr in intense EUV-FEL fields (1.2 × 1014 W/cm2 ). The
photon energy was tuned at 121.5 eV near the resonance
(120.7 eV) expected from the difference between the 3p−1
3/2
−1
and 3d5/2
states [22]. Multiply charged Kr z+ ions up to z = 4
were observed in the spectrum. The lower charged ions (z =
1–3) were mainly produced by one-photon ionization to the
3d core-hole states followed by the Auger decay, while the
formation of Kr 4+ needs absorption of at least two photons.
The electron spectrum recorded at a field intensity of 5.5 ×
1014 W/cm2 is shown in Fig. 2, which exhibits distinct peaks

at 108 and 93 eV corresponding to photoionization (P1 ) to the
4p−1 , 4s−1 and satellite states of Kr + [33,34] [see Fig. 1(b)].
Furthermore, the spectrum reveals an additional shoulderlike
component at 92 eV and weak broad features below 100 eV,
both of which become suppressed in the spectrum recorded at
a lower laser field intensity (1.9 × 1013 W/cm2 ).
To understand how the peaks in the electron spectra that are
nonlinearly proportional to the FEL intensity are correlated
with the formation of Kr z+ ions (z = 1 − 4), the electronion coincidence events are collected and processed further
by covariance analysis [35–37] to suppress the contributions
from false coincidence events. The electron-ion covariance
may be expressed as Cov(X, Y ) = (X − X )(Y − Y ) =
XY  − X Y , where X and Y are electron and ion signals,
respectively, and the bracket denotes an average per laser
shot. The second term corresponds to the contributions from
false events, which is not negligible in the measurements
recorded at the present event rate. Figure 3(a) shows the
electron spectrum correlated with Kr + , exhibiting the peaks
(P1 ) associated with valence ionization of Kr. These peaks also

FIG. 2. Total electron spectra of Kr at hν = 121.5 eV, recorded
with a retarding voltage of −57 V. The laser field intensities of
1.9 × 1013 W/cm2 (gray) and 5.5 ×1014 W/cm2 (red). Sticks represent energies of photoelectrons (P1 ) to the 4p−1 , 4s−1 and satellite
states of Kr + . The spectra are normalized at the 4p photoelectron
peak.

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CAPTURING TRANSIENT CORE-TO-CORE RESONANCES …

PHYSICAL REVIEW A 107, L021101 (2023)

FIG. 4. (a) Auger electron yields from the Kr + core-hole states,
2+
−1
−1
(red) and 3p−1
1/2 (blue), decaying to Kr (3d 4p ), as a
function of the FEL photon energy. ...

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