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Kh1;2X-Ray Hypersatellite Line Broadening as a Signature of K-Shell Double Photoionization
Followed by Outer-Shell Ionization and Excitation
M. Polasik,
1,
*K. Słabkowska,
1
J. Rzadkiewicz,
2,3
K. Kozioł,
1
J. Starosta,
1
E. Wiatrowska-Kozioł,
1
J.-Cl. Dousse,
4
and J. Hoszowska
4
1
Faculty of Chemistry, Nicholas Copernicus University, 87-100 Torun
´, Poland
2
Soltan Institute for Nuclear Studies, 05-400 Otwock-S
´wierk, Poland
3
Institute of Plasma Physics and Laser Microfusion, Hery 23, 01-497 Warsaw, Poland
4
Physics Department, University of Fribourg, CH-1700 Fribourg, Switzerland
(Received 20 December 2010; revised manuscript received 7 March 2011; published 11 August 2011)
We propose a novel approach for the theoretical analysis of the photoinduced high-resolution Kh1;2x-
ray hypersatellite spectra, which allows us to obtain reliable values of lifetimes of the doubly K-shell
ionized states and fundamental information about the relative role of K-shell double photoionization (DPI)
mechanisms. It is demonstrated for the first time that the Kh1;2hypersatellite natural line broadening
observed for selected metal atoms with 20 Z30 can be well reproduced quantitatively by taking into
account the influences of the open-shell valence configuration (adopted from predictions of the band-
structure method) and the outer-shell ionization and excitation following the DPI process.
DOI: 10.1103/PhysRevLett.107.073001 PACS numbers: 32.30.Rj, 32.70.Cs, 32.70.Jz, 32.80.Fb
Observed for the first time by Charpak [1] and enlight-
ened by Briand et al. [2], the Kh1;2x-ray hypersatellite
lines originate from the 1s2!1s12p1transitions (i.e.,
from the radiative decay of initial K2states with two
holes in the Kshell). Thanks to the development of intense
energy-tunable x-ray synchrotron radiation sources, the
observation of photoinduced high-resolution Kh1;2hyper-
satellite spectra has become feasible [3–8]. From the in-
terpretation of these hypersatellite spectra, rich and
valuable information can then be obtained about the prop-
erties of K-shell hollow atoms (i.e., atoms with an empty K
shell and occupied outer shells) as well as about the double
photoionization (DPI) mechanisms.
At present, it is well established [3–7,9] that the absorp-
tion of a single photon can lead to K-shell DPI via two
different mechanisms: (i) a purely quantum mechanical
shakeoff (SO) and (ii) a (quasi)classical knockout (KO).
In the SO mechanism leading to DPI, the primary K-shell
photoelectron is ejected rapidly, and due to the sudden
change of the atomic potential the second K-shell electron
is ionized. In the KO process the outgoing first K-shell
photoelectron knocks out the second K-shell electron. Very
recently high-resolution measurements of Kh1;2hyper-
satellite x-ray spectra induced by photoionization were
reported by Hoszowska et al. [3,4] for several light ele-
ments with 12 Z23. From these measurements the
photon energy dependence of the K-shell DPI was deter-
mined and a semiempirical model to separate both DPI
mechanisms was proposed. In that work it was concluded
that near threshold and at intermediate photon energies the
K-shell DPI is dominated by the KO mechanism, the SO
mechanism being important only at high photon energies.
These findings support the conclusions of Kanter et al. [6]
and Huotari et al. [7] for medium-Zatoms.
The theoretical evaluation of the Kh1;2natural line-
widths is based on the following formula:
Kh1;2
¼KK þKL3;2;(1)
where KK and KL3;2are the natural widths of the doubly
ionized K2and K1L1
3;2states which correspond to the
initial and final states of the Kh1;2hypersatellite transi-
tions, respectively. The width of the K1L1
3;2state can be
approximated by
KL2;3
’KþL3;2;(2)
where Kand L3;2are the natural widths of the singly
ionized K1and L1
3;2states, respectively. The first empiri-
cal estimation of the Kh1;2natural linewidths was pro-
posed by Mosse
´et al. [10] who employed Eq. (1),
assuming for the width of the K2state the following
approximation KK ¼2K. However, it was found later
that the Kh1;2linewidths derived from high-resolution
K-hypersatellite spectra induced by DPI [5,8] were sys-
tematically bigger than those obtained using Mosse
´’s
approximation. The modifications of Eq. (1) for the LS
and intermediate coupling regime (low- and medium-Z
regions) proposed by Rzadkiewicz et al. [11] lead to
even higher disagreement between theory and experiment.
The changes in the fluorescence yields considered by Chen
[12] were found to be relatively small and did not allow one
to eliminate the observed discrepancies. All these consid-
erations lead to the conclusion drawn by Diamant et al. [8]
that no good physical reason could be found to explain the
observed Kh1;2line broadenings nor the resulting reduced
lifetimes of the K2states.
In this Letter we propose a novel approach for the
theoretical analysis of the photoinduced high-resolution
PRL 107, 073001 (2011) PHYSICAL REVIEW LETTERS week ending
12 AUGUST 2011
0031-9007=11=107(7)=073001(5) 073001-1 Ó2011 American Physical Society
Kh1;2x-ray hypersatellite spectra measured for thin solid
targets. This approach permits us to explain the broadening
of the hypersatellite lines and allows us to obtain informa-
tion about the relative importance of the different K-shell
DPI mechanisms.
First, we determined the radiative natural widths of the
K2states, using multiconfiguration Dirac-Fock (MCDF)
calculations including the transverse (Breit) interaction
and QED corrections (see, e.g., [13] and references
therein). The total natural widths KK and the mean life-
times of K2states KK were then computed from the
following simple relations:
KK ¼rad
KK þnonrad
KK ;(3)
KK ¼
@
KK
;(4)
where rad
KK are the radiative natural widths and nonrad
KK the
nonradiative natural widths. For the nonradiative widths
the values of Chen [12] adopted directly for Cr and Zn and
interpolated for Ca, V, and Co, with 1% accuracy, were
employed. The Kh2and Kh1natural linewidths were
evaluated on the basis of the calculated [according to
Eq. (3)] total natural widths of the K2states and the total
widths of the K1,L1
2, and L1
3states tabulated by
Campbell and Papp [14].
Our theoretical predictions for the total natural widths of
the K2level and the Kh2and Kh1natural linewidths
for selected atoms with 20 Z30 are presented in
Table I. The calculated mean lifetimes of the K2doubly
ionized states are also listed (last column). For all elements
it is found that the latter are about 2.2 times shorter than
those of the K1singly ionized states. The comparison of
the theoretical linewidths derived from Eq. (1) with the
available experimental Kh2and Kh1values obtained
from photoinduced x-ray spectra [4,8] shows that our
‘‘basic procedure’’ results (columns 4 and 9 in Table I)
are much smaller than the experimental values, the
deviations being particularly pronounced for the open
outer-shell elements.
One of the reasons for the observed differences is the so-
called open-shell valence configuration (OVC) effect. The
latter is related to the fact that, in the case of open-shell
atoms, there are for each transition many initial and final
states. A transition consists then of numerous overlapping
components having slightly different energies and widths.
As a consequence of the OVC effect, the effective natural
Kh1;2linewidths are much larger than those predicted by
Eq. (1). In view of the fact that in the solid state the valence
configurations are different from those of free atoms, we
have adopted in our evaluation of the OVC effect valence
shell configurations that are as close as possible to the
ones predicted by the augmented plane-wave band-
structure calculations, i.e., 3d3:984s1:02 ,3d4:964s1:04 , and
3d7:874s1:13 for V, Cr, and Co, respectively [15,16]. We
have also checked that the modifications of the valence
configurations for Ca and Zn do not noticeably influence
the widths of the Kh1;2lines (differences were found to be
less than 0.02 eV). Therefore, for Ca and Zn, we present
results for closed-shell configurations.
In order to evaluate the influence of the OVC effect on
the Kh1;2natural linewidths, we have synthesized the
hypersatellite spectra using the ‘‘basic’’ natural linewidth
data quoted in Table I(columns 4 and 9). Results of this
evaluation procedure are illustrated for the open-shell Co
atom in Fig. 1. For both hypersatellite transitions the
theoretical stick spectra (MCDF component energies
with their relative intensities—red sticks in Fig. 1) and
the synthesized spectra corresponding to the sums of
the overlapping Lorentzians attached to each MCDF
component (red dashed line in Fig. 1) are depicted. The
synthesized spectra were then fitted using one Lorentz
profile for the Kh2line and one for the Kh1line (blue
solid lines in Fig. 1). In order to evaluate the broadening
arising from the OVC effect, the widths of these
fitted Lorentzians were compared to the widths determined
from Eq. (1) (the corresponding Lorentzians are
TABLE I. Theoretical MCDF-based predictions for the total widths and lifetimes of the K2states, the evaluated natural linewidths
of the Kh2and Kh1lines for selected metal atoms with 20 Z30, and the available experimental linewidths. Numbers in
parentheses are the uncertainties in the last digits of the numbers cited.
Atom
Confi-
gura-
tion
Width of
K2state
(eV)
Natural linewidths (eV) Lifetime of
K2state
(1016 s)
Kh2Kh1
Eq. (1)OVC
a
OIE1
b
OIE2
c
Exp. Eq. (1)OVC
a
OIE1
b
OIE2
c
Exp.
20Ca (4s2) 1.87 2.85 2.85 2.99 3.63 3.72(18)
d
2.85 3.52
23V(3d44s1) 2.24 3.53 5.20 5.28 5.46 5.5(1)
e
3.53 5.35 5.47 5.66 6.0(6)
e
2.94
5.54(19)
d
5.6(10)
d
24Cr (3d54s1) 2.39 3.73 5.41 5.59 5.77 5.7(1)
e
3.73 6.60 6.72 6.90 5.0(9)
e
2.75
27Co (3d84s1) 2.96 4.66 5.82 6.17 6.80 6.7(1)
e
4.67 6.19 6.52 6.94 7.1(6)
e
2.24
30Zn (3d10 4s2) 3.69 5.92 5.92 6.49 7.23 7.5(4)
e
5.93 5.93 6.06 6.59 6.4(7)
e
1.78
a
Effective linewidths including only the OVC effect.
b
Effective linewidths with the OIE1 and OVC broadenings.
c
Effective linewidths with the OIE2 and OVC broadenings.
d
Hoszowska et al. [4].
e
Diamant et al. [8].
PRL 107, 073001 (2011) PHYSICAL REVIEW LETTERS week ending
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073001-2
represented by the green dash-dotted line in Fig. 1). As
shown, the profiles including the OVC effect are signifi-
cantly broader than those without the OVC effect. This
procedure which was performed for all open-shell ele-
ments permits us to diminish substantially the differences
between the theoretical and experimental results (see
‘‘OVC’’ and ‘‘Exp.’’ columns in Table I).
Another reason for the significant broadening observed
experimentally for the Kh1;2x-ray lines can be attributed
(for all elements) to the outer-shell ionization and excita-
tion (OIE) effect. In order to evaluate the OIE broadening
we have performed calculations of the total shake proba-
bilities, i.e., SO and shakeup (SU), applying the sudden
approximation (SA) model [17] and using MCDF wave
functions [13]. Three theoretical scenarios were consid-
ered. In the first one (OIE1), the fast single K-shell ion-
ization is followed by shake processes that remove the
second 1selectron and some valence electrons. As the
shaken 1selectron is slow, the valence electron is assumed
to be affected only by the sudden atomic potential change
resulting from the removal of the fast 1sphotoelectron. In
the second scenario (OIE2), the outer-shell shake process
is due to the K-shell double ionization, assuming that the
two 1selectrons are removed quasisimultaneously and
escape both at high enough velocities. In the OIE2 case
the potential change is more pronounced and thus the shake
probability bigger. In the third scenario shake processes are
energetically forbidden so that no OIE broadening is ex-
pected. The subshell shake probabilities calculated for the
OIE1 and OIE2 scenarios are presented in Table II.As
shown, the OIE2 total shake probabilities are a few times
bigger than the OIE1 ones.
The evaluation procedure of the OIE effect (OIE2 sce-
nario) for the case of the Kh2transition of the closed-shell
Ca atom is illustrated in Fig. 2. Shown are the hypersatel-
lite transition (blue long-dashed line), the hypersatellite
satellites corresponding to 3p,4s, and 3p4sspectator holes
produced by the OIE effect, and the sum of all lines (red
solid line). The Lorentzian corresponding to the fit of
the sum is also depicted (black dash-dot-dot line). The
latter was used to determine the effective linewidth of the
hypersatellite transition. As can be seen, the distinct con-
tributions of the satellite groups of the hypersatellite
(which are shifted with respect to the ‘‘pure’’ hypersatel-
lite) result in an increase of the effective Kha2hypersatel-
lite linewidth. On the other hand, the effective line shape of
the hypersatellite is very similar for satellites resulting
from SO and SU processes (see also Ref. [18]). In the
case of open-shell atoms the procedure for the evaluation
of the OIE effect includes at the same time the OVC effect.
A similar analysis was performed for the other elements
and for the OIE1 case (see ‘‘OIE2’’ and ‘‘OIE1’’ columns
of Table I).
As can be seen in Table I, the large discrepancies be-
tween the experimental data and the linewidths evaluated
taking into account only the OVC effect indicate that the
third scenario is unlikely. We assign the third scenario (no
shake) to DPI via a slow KO mechanism, which can only
occur in the very narrow near DPI threshold energy range.
The discrepancies between the experimental data and the
Kh1;2linewidth predictions including the OIE1 and the
OVC effects (‘‘OIE1’’ columns in Table I) are only slightly
smaller. This indicates that the OIE1 scenario plays only a
minor role in the observed linewidth broadening. We as-
sign this scenario to the double K-shell ionization via a 1s
SO process. This mechanism is predominant at high
photon energies [3,4] because, due to the very fast 1s
photoelectron, shake processes may occur not only in the
outer shells but also in the Kshell.
For all considered elements there is a good agreement
between the experimental data and the effective Kh1;2
linewidths in the case of OIE2 broadening (‘‘OIE2’’ col-
umns in Table I). This agreement indicates that the OIE2
scenario (with a ‘‘strong’’ shake process) is dominant in the
production of the multivacancy states whose deexcitation
leads to the analyzed hypersatellite spectra. Note that the
experimental linewidths were obtained from hypersatellite
spectra measurements performed at photon energies where
FIG. 1 (color online). The OVC effect evaluation of the effec-
tive Kh1;2natural linewidth for the open-shell Co atom.
TABLE II. Total shake probabilities (in percent per subshell)
as a result of double K-shell ionization (the OIE2 scenario) for
selected atoms (calculated for the same valence configurations as
presented in Table I). Numbers in parentheses are the values for
single K-shell ionization (the OIE1 scenario).
Probabilities per subshell (%)
Atom 2s2p3s3p3d4s
20Ca 0.75 4.12 3.81 36.14 49.03
(0.21) (1.26) (1.31) (10.74) (20.23)
23V0.59 3.06 2.97 18.96 47.82 25.50
(0.16) (0.89) (0.78) (4.89) (18.25) (9.35)
24Cr 0.54 2.77 2.59 16.48 47.76 24.74
(0.15) (0.80) (0.68) (4.22) (18.29) (9.18)
27Co 0.42 2.11 1.82 11.44 45.99 23.24
(0.11) (0.59) (0.47) (2.89) (15.25) (8.88)
30Zn 0.32 1.65 1.23 9.16 34.49 31.07
(0.09) (0.46) (0.34) (2.34) (10.45) (11.70)
PRL 107, 073001 (2011) PHYSICAL REVIEW LETTERS week ending
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073001-3
the KO mechanism is dominant, i.e., in the wide energy
range around the maximum of the DPI cross section [4]or
significantly above threshold for K-shell DPI [8]. Further,
it was reported that the KO process proceeds very fast
(1018 s)[9] and for this process the energy sharing
between the first and second electron is nearly symmetric
[19,20]. Therefore, the ‘‘billiardlike’’ production of the
second K-shell hole should be sudden enough in the time
scale of the outer shell to treat the ejection or excitation of
outer-shell electrons (via SO and SU processes) in the SA
model. We assign thus the OIE2 scenario to the ionization
and excitation processes following the K-shell DPI via a
fast KO mechanism.
It is worth underlining that the completely different
nature of the K-shell DPI via the SO and via the KO
mechanisms [19,20] implicates that the strong (OIE2)
shake process should be excluded in the SO case.
Moreover, in the SO mechanism the shaken K-shell elec-
tron seems to be too slow [19,20] to make a sudden
potential change, even for an outer-shell electron and the
possibility of broadening as a result of the shake cascade
seems to be negligible. It is worth noting that there is a lack
of experimental data for the Kh1;2linewidths in the very
high photon energy range. Our theoretical predictions for
the OIE1 case can be treated as a lower limit for linewidths
measured at high photon energies because contributions of
the fast KO and other processes cannot be neglected. Since
the magnitude of the linewidth broadening depends on the
K-shell DPI mechanism followed by OIE processes, the
experimental values of Kh1;2linewidths can be used to
probe the relative role of the K-shell DPI mechanisms.
In conclusion, we propose a novel approach for the
theoretical analysis of high-resolution Kh1;2x-ray hyper-
satellite spectra induced by photons at different energies.
For the first time, predictions for the effective natural
Kh1;2linewidths taking into account the OVC effect
(including predictions of the band-structure method) and
the OIE effect (based on shake probability calculations)
allowed us to reproduce quantitatively the Kh1;2
linewidths observed in experiments using thin solid targets.
Since the OIE effect is specific to KO and SO processes,
from the measured linewidths’ analysis it was possible to
obtain fundamental information about the relative role of
the K-shell DPI mechanisms. On the basis of a detailed
theoretical analysis it was found that, in the considered
cases, the fast KO process plays a dominant role in the
K-shell DPI, as indicated by the large broadening of the
observed Kh1;2lines. This finding confirms the conclu-
sions of Hoszowska et al. [3,4], Huotari et al. [7], and
Diamant et al. [8]. Moreover, a good agreement between
the experimental data and the effective Kh1;2linewidths
indicates that the lifetimes of the K2states (about
2.2 times shorter than those of the K1states) for selected
atoms with 20 Z30 are reliable. This fact enables us
to reject the hypothesis reported in Ref. [8] that the large
broadening of the Kh1;2x-ray hypersatellite lines ob-
served in the experiment originates from a sizable (i.e.,
more than 2:2times) reduction of the lifetimes of the
K2states.
We believe that the results of this Letter may be helpful
to better understand the relative role of the K-shell DPI
mechanisms and the OIE processes leading to the complex
line shapes of hypersatellite transitions decaying hollow
K-shell atoms. We also hope that this work will inspire
experimental research concerning the excitation photon
energy dependence of the Kh1;2linewidths for low- and
medium-Zatoms (especially in the high photon energy
range).
This work was supported by the Polish Ministry
of Science and Higher Education under Grant
No. N N202 1465 33 and the Swiss National Science
Foundation.
*mpolasik@uni.torun.pl
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FIG. 2 (color online). Evaluation of the OIE2 broadening in
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PRL 107, 073001 (2011) PHYSICAL REVIEW LETTERS week ending
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073001-4
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