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We propose a novel approach for the theoretical analysis of the photoinduced high-resolution K(h)α(1,2) x-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 K(h)α(1,2) hypersatellite natural line broadening observed for selected metal atoms with 20 ≤ Z ≤ 30 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.
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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,
*K. Słabkowska,
J. Rzadkiewicz,
K. Kozioł,
J. Starosta,
E. Wiatrowska-Kozioł,
J.-Cl. Dousse,
and J. Hoszowska
Faculty of Chemistry, Nicholas Copernicus University, 87-100 Torun
´, Poland
Soltan Institute for Nuclear Studies, 05-400 Otwock-S
´wierk, Poland
Institute of Plasma Physics and Laser Microfusion, Hery 23, 01-497 Warsaw, Poland
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 [38]. 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 [37,9] 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:
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
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 ¼2K. 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
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
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.
Width of
Natural linewidths (eV) Lifetime of
(1016 s)
Eq. (1)OVC
Exp. Eq. (1)OVC
20Ca (4s2) 1.87 2.85 2.85 2.99 3.63 3.72(18)
2.85     3.52
23V(3d44s1) 2.24 3.53 5.20 5.28 5.46 5.5(1)
3.53 5.35 5.47 5.66 6.0(6)
24Cr (3d54s1) 2.39 3.73 5.41 5.59 5.77 5.7(1)
3.73 6.60 6.72 6.90 5.0(9)
27Co (3d84s1) 2.96 4.66 5.82 6.17 6.80 6.7(1)
4.67 6.19 6.52 6.94 7.1(6)
30Zn (3d10 4s2) 3.69 5.92 5.92 6.49 7.23 7.5(4)
5.93 5.93 6.06 6.59 6.4(7)
Effective linewidths including only the OVC effect.
Effective linewidths with the OIE1 and OVC broadenings.
Effective linewidths with the OIE2 and OVC broadenings.
Hoszowska et al. [4].
Diamant et al. [8].
PRL 107, 073001 (2011) PHYSICAL REVIEW LETTERS week ending
12 AUGUST 2011
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)
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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
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
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
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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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... The mean equilibrium charge states (q mean ) of the 242m Am ions as a function of the kinetic energy were predicted by means of Schiwietz and Grande formulas [22]. Figure 5 presents this dependence for three stopping media, namely, 7 Li, 12 C, and 27 Al targets. As can be seen, for C and Al targets, the q mean of the 242m Am ions is slightly lower than for a Li target by ≈0.4 and ≈0.9, respectively. ...
... As can be seen, for C and Al targets, the q mean of the 242m Am ions is slightly lower than for a Li target by ≈0.4 and ≈0.9, respectively. The uncertainties of the q mean obtained from Ref. [22] as a deviation of the Am projectile as a function of its kinetic energy for 7 Li (green dotted line), 12 C (red solid line), and 27 Al (purple dash-dotted line) stopping media. The vertical bars present the potential positions of the 242m Am ion NEEC resonance kinetic energy for ns 1/2 , np 1/2,3/2 , nd 3/2,5/2 , and n f 5/2,7/2 subshells with n = 5 (blue bars), n = 6 (black bars), and n = 7 (orange bars) for the charge states (vertical axis) indicated by specific symbols at the tops of the bars. ...
... The code is based on the modified Dirac-Fock-Slater method that takes into account the Breit and QED corrections. In addition, we verified the obtained values with the multiconfigurational Dirac-Fock (MCDF) method [24][25][26][27], which gives almost identical level energies for 242 Am ions. ...
Following the first experimental observation of Mo93m isomer depletion via nuclear excitation by electron capture (NEEC), we consider another experimental scenario related to the Am242m isomer for which the probability of the NEEC process is expected to be even higher than for the Mo93m isomer. The optimum experimental conditions for the production and depletion of the Am242m isomer in a beam-based scenario are discussed. The relevant beam-target reaction cross sections have been calculated striving to ensure effective production of the Am242m isomer. Kinetic energies required for the NEEC process to occur have been predicted for the n=5, 6, and 7 subshells of Am242m ions and combined with available ion charge states at subsequent stages of the ion stopping process. The NEEC resonance strengths have been estimated for the partial contributions of individual subshells to the whole NEEC process.
... On the other hand, the shifts predicted by the multiconfiguration Dirac-Fock (MCDF) calculations of Costa [47,48] are systematically smaller than present experimental values (in average −1.8 eV for Ca, −1.9 eV for V, −0.7 eV for Fe, and −0.8 eV for Cu). It seems, however, that the theoretical predictions are improved when the open-shell valence configuration (OVC) and outer-shell ionization and excitation (OIE) effects discussed in [49] are included in the MCDF calculations. For instance, for Ca the energy shift α 2 we have obtained using such upgraded MCDF calculations is 199.3 eV, a value in good agreement with our result and the one reported in [10]. ...
... The theoretical predictions listed in the fifth column were taken from [49]. In these calculations whose results are in general in satisfactory agreement with the experimental values from [10,16] but again somewhat smaller than present results, the influences of the OVC and OIE effects were taken into consideration. ...
We report on the radiative decay of double K-shell vacancy states produced in solid Ca, V, Fe, and Cu targets by impact with about 10 MeV/amu C and Ne ions. The resulting K hypersatellite x-ray emission spectra were measured by means of high-energy-resolution spectroscopy using a von Hamos bent crystal spectrometer. The experiment was carried out at the Philips variable energy cyclotron of the Paul Scherrer Institute. From the fits of the x-ray spectra the energies, line widths, and relative intensities of the hypersatellite x-ray lines could be determined. The fitted intensities were corrected to account for the energy-dependent solid angle of the spectrometer, effective source size, target self-absorption, crystal reflectivity, and detector efficiency. The single-to-double K-shell ionization cross-section ratios were deduced from the corrected relative intensities of the hypersatellites and compared to theoretical predictions from the semiclassical approximation model using hydrogenlike and Dirac-Hartree-Fock wave functions and from classical trajectory Monte Carlo calculations.
... The systematic theoretical study realized in this paper was performed using the multiconfigurational Dirac-Fock (MCDF) method in two approaches: the General-purpose Relativistic Atomic Structure Package (GRASP), and the MCDFGME code. The GRASP approach was mainly developed by Grant and co-workers and is described in detail in many papers [34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49]. Moreover, all basic ideas of the alternative Special Average Level (SAL) version of MCDF calculations, which is used in this work, were presented by Polasik [48]. ...
Full-text available
Kα,β X-ray lines from photon excitation were measured in selected elements from Mg to Cu using a high-resolution double-crystal X-ray spectrometer with a proportional counter, and the Kβ/Kα intensity ratio for each element was obtained, after correcting for self-absorption, detection efficiency, and crystal reflectance. This intensity ratio increases rapidly from Mg to Ca but, in the 3d elements region, the increase becomes slower. This is related to the intensity of the Kβ line involving valence electrons. The slow increase of this ratio in the 3d elements region is thought to be due to the correlation between 3d and 4s electrons. Moreover, the chemical shifts, FWHM, asymmetry indices, and Kβ/Kα intensity ratios of the Cr compounds, due to different valences, were also investigated using the same double-crystal X-ray spectrometer. The chemical effects were clearly observed, and the Kβ/Kα intensity ratio was found to be compound-dependent for Cr.
... The coefficients for 93m Mo ions (up to q ¼ 40) were obtained from the linear (quadratic for ns 1=2 orbitals) scaling dependence between ICCs and binding energies of a specific subshell nl j for ions and neutral atoms. The binding energies for neutral atoms were taken from tables [37], while those for ions were calculated by means of the multiconfigurational Dirac-Fock method [38][39][40][41]. The final α q;nl j IC ðDS → ISÞ obtained in this way can only be used for a fully ionized subshell. ...
A novel approach for isomer depletion in ion-atom collisions is proposed and considered theoretically. Analyses are performed for the depletion of the ^{93m}Mo isomer for which an unexpectedly large probability was measured in the beam-based experiment of Chiara et al. [Nature (London) 554, 216 (2018)NATUAS0028-083610.1038/nature25483]. The subsequent attempt at a theoretical description based on state-of-the-art atomic theory did not reproduce the experimental result [Wu et al., Phys. Rev. Lett. 122, 212501 (2019)PRLTAO0031-900710.1103/PhysRevLett.122.212501] and showed a dramatic disagreement with the experiment (by many orders of magnitude). This conflict calls for further research on the nature of isomer depletion mechanisms occurring in atomic processes. Here, we propose to consider the ^{93m}Mo isomer depletion as the nuclear excitation by electron capture in resonant transfer process taking into account the momentum distribution of the target electrons. Although our results only slightly shift the upper theoretical limit for the total ^{93m}Mo isomer depletion probability toward the experimental value, they show the importance of considering the Compton profile in the theoretical description, in particular for the L shell, for which the depletion probability increases by many orders of magnitude.
... Theoretical predictions of the Gd L and M x-ray diagram line positions have been performed using the multiconfiguration Dirac-Fock (MCDF) method, which is the primary theoretical tool applied in atomic physics, allowing for the determination of many of the significant atomic parameters. The MCDF method is described in detail in many papers [58][59][60][61][62][63][64][65][66][67][68][69][70] . Thanks to the ease of performing high-precision large-scale calculations, it is even possible to include electron correlations to a large extent. ...
We combined different experimental techniques with a theoretical approach to determine a consistent set of diagram lines energies and binding energies. We propose an original approach consisting in deter- mining the mass attenuation coefficients in an energy range covering the L-, M- and N- absorption edges, including a detailed evaluation of the associated uncertainties, to derive precisely the binding energies. We investigated the Lα, Lβ and M spectra of Gd with an independantly calibrated high-resolution anti- parallel double-crystal x-ray spectrometer. All the lines were identified and found in excellent agreement with the binding energies previously derived. Morever, we identified for the first time M5 − O2 , M4 − O2,3 and M4 − N2,3 diagram lines.
... However, practical calculations show that the ratio deviates from the simple estimation and the difference can be qualitatively understood from the effective charge seen by the electrons. Such a conclusion is in agreement with (14) 1.81 (14) 5.91(10) 113 s p 1 2 3 P 3 1.19 (14) 1.17 (14) 4.24(10) 79 s p 1 2 3 P 1 1.08 (14) 1.17 (14) 4.00(10) 72 recent experimental measurements [38][39][40][41]. Zitnik et al [39] reported a value of 2.8(±0.2) for the ratio of natural lifetime width of Ar 2+ p 2 2 to Ar + p 2 1 -. ...
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The Auger decay of single and double K-shell hole and hollow states of Al⁴⁺-Al¹¹⁺ was theoretically investigated in the framework of perturbation theory implemented by the distorted wave approximation. The natural lifetime widths of the hollow states (1s⁰2sx2py, x + y = 2,3, ⋯ 8) are found to be 1.3-1.9 times larger than those of corresponding hole states (1s2sx2pyx + y =2,3⋯,8. The maximal ratio is found originating from the hollow states of 1s⁰2s²2p³, which is ∼2.9 times as large as the hole states of . The calculated energy levels and natural lifetime widths are compared with the experimental and other theoretical results wherever available in the literature. The Auger decay rates and natural lifetime widths presented in this work are useful in the modeling of ultra-intensive x-ray laser interaction with aluminum.
... Much more complicated is the case of Mn Kβ 1,3 x-ray spectra, presented in Fig. 10, where the so called open-shell valence configuration (OVC) effect [45,47] exists. This figure shows the predicted Kβ 1,3 diagram lines and the satellite lines presented in different colors, obtained on the basis of the shake-process probabilities, together with the observed ones. ...
The Kβ x-ray spectra of the elements from Ca to Ge have been systematically investigated using a high-resolution antiparallel double-crystal x-ray spectrometer. Each Kβ1,3 natural linewidth has been corrected using the instrumental function of this type of x-ray spectrometer, and the spin doublet energies have been obtained from the peak position values in Kβ1,3 x-ray spectra. For all studied elements the corrected Kβ1 x-ray lines FWHM increase linearly as a function of Z. However, for Kβ3 x-ray lines this dependence is generally not linear in the case of 3d elements but increases from Sc to Co elements. It has been found that the contributions of satellite lines are considered to be [KM] shake processes. Our theoretically predicted synthetic spectra of Ca, Mn, Cu, and Zn are in very good agreement with our high-resolution measurements, except in the case of Mn, due to the open-shell valence configuration effect (more than 7000 transitions for diagram lines and more than 100000 transitions for satellite lines) and the influence of the complicated structure of the metallic Mn.
We report on the nature of Mo93m isomer depletion as a result of nuclear excitation by electron capture in a resonant transfer process, accounting for highly excited open-shell atomic states to better reflect realistic beam-based conditions. The improved model provided an enhancement of Mo93m depletion. The new probabilities for Mo93m isomer depletion are compared with two available experimental results and previous models. The excited-state configurations provide probabilities that are a factor of about 20 higher than those obtained from the ground-state-configuration approach without Compton profiles.
We investigated experimentally and theoretically x-ray properties of Mg, Al and Si to assess for new reliable x-ray useful quantities. We measured the KL⁰– diagram, and KL¹– and KL²– satellite lines in Mg, Al, and Si, ionized by photon excitation, using a high-resolution anti-parallel double-crystal x-ray spectrometer. Their energy values, full width at half maxima (FWHM), and relative intensities are obtained by the multiple fitting methods and compared with those reported by other excitation processes. It was found that the relative intensity of Mg and Si KL¹ and KL² satellite lines to the KL⁰ diagram lines depend on the method used to produce the K hole. The evidence of a new transition between Kα3 and Kα4 in Mg, Al, and S KL¹ satellite lines is suggested. These x-ray diagram and satellite lines were investigated theoretically and we found that Mg Kα1,2 diagram lines with hidden satellites are especially in very good agreement with the corresponding experimental ones. Moreover, we also determined the mass attenuation coefficients in a wide energy range covering the K-absorption edge, including a detailed evaluation of the associated uncertainties. From the absorption spectra of Mg and Al, the cross sections of the multi-electron transition processes were estimated and match the theoretical values.
The natural widths, lifetimes, and fluorescence yields for the double K-shell hole states have been calculated for atoms with 10 ≤ Z ≤ 30. The Grasp2018 package was adopted to carry out a systematic computation of the Khα1,2 and Khβ1,3 radiative transition rates and Fac was used to calculate the KK−KLL, KK−KLM, and KK−KMM non-radiative Auger transition rates. The dependence of the radiative and non-radiative rates on the existence of 3s, 3p, 3d, or 4s spectator holes is studied.
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Single-photon double K-shell ionization of low-Z neutral atoms in the range 12≤Z≤23 is investigated. The experimental method was based on measurements of the high-resolution K{alpha}{sup h} hypersatellite x-ray spectra following the radiative decay of the K-shell double-vacancy states excited by monochromatic synchrotron radiation. The photon energy dependence of the double K-shell ionization was measured over a wide range of photon energies from threshold up to and beyond the maximum of the double-to-single photoionization cross section ratios. From the high-resolution x-ray emission spectra the energies and linewidths of the hypersatellite transitions, as well as the K{alpha}{sub 1}{sup h}:K{alpha}{sub 2}{sup h} intensity ratios, were determined. The relative importance of the initial-state and final-state electron-electron interactions to the K-shell double photoionization is addressed. Physical mechanisms and scaling laws of the K-shell double photoionization are examined. A semiempirical universal scaling of the double-photoionization cross sections with the effective nuclear charge for neutral atoms in the range 2≤Z≤47 is established.
The K x-ray spectrum arising from doubly K-ionized gallium atoms has been studied by means of a coincidence experiment with two solid-state detectors. A new energy range in K x-ray spectra (hypersatellite range) is observed. Hypersatellite lines are shifted about 15 times more than the usual satellite lines. The K-satellite spectrum following KL-ionized states has also been studied.
Calculations of electron shake-off, based on the sudden approximation, have been made for several different processes. In particular, electron shake-off as the result of β decay has been computed for each of the shells in 15 different cases from an initial Z=2to92. An interpolation of the results has been made for the remaining elements. Calculations were made with nonrelativistic Hartree-Fock wave functions for the lighter elements, and relativistic Hartree-Fock-Slater wave functions for the heavier ones. A comparison is made with available experimental data, and satisfactory agreement is obtained. Other ionization processes amenable to the use of the sudden approximation are also discussed, viz. β+ decay, Auger processes, photo-ionization, internal conversion, electron capture, and inner-shell ionization by electron impact.
Atomic level widths obtained from experimental measurements are collected in Table I, along with the corresponding theoretical widths derived from the Evaluated Atomic Data Library (EADL) of Lawrence Livermore National Laboratory; these EADL values are based upon the Dirac–Hartree–Slater version of the independent-particle model. In a minority of cases, many-body theory predictions are also provided. A brief discussion of the manner in which the experimental widths were deduced from spectroscopic data is included. The bulk of the data are for elements in the solid state, but a few data for gases and simple compounds are included.For the K, L2, L3, and M5 levels, where Coster–Kronig contributions do not contribute or contribute only to a small extent to the overall widths, the EADL predictions appear satisfactory for elements in the solid state. For other levels, where Coster–Kronig and super-Coster–Kronig transitions have large probabilities within the independent-particle model, this model is not satisfactory. Table II provides a complete set of recommended elemental values based upon consideration of the available experimental data.
Detailed multiconfiguration Dirac-Fock calculations through the proposed alternative special average-level version with the inclusion of the transverse (Breit) interaction, self-energy, and vacuum polarization corrections have been carried out on molybdenum, palladium, and holmium to elucidate the structure of the KalphaL0Mr lines in their x-ray spectra and to explain reliably the influence of additional holes in the M shell on the shapes and positions of KalphaL0 bands. The structure of KalphaL0Mr lines has been shown to be very complex. Because the distances between the neighboring KalphaL0Mr lines are very small, the effects of multiple M-shell ionization are manifested in the spectra as an asymmetric broadening and net shift of Kalpha1L0 and Kalpha2L0 bands. The results obtained in the present work corroborate some of my previous conclusions [Polasik, Phys. Rev. A 39, 616 (1989)]: that removing a 3rho electron is more effective than a 3s or 3d electron in producing a KalphaL0 energy shift and that the shift effects remarkably increase with atomic number and are strongly nonadditive. The results of this work can be used to construct different shapes of theoretical KalphaL0 bands for molybdenum, palladium, and holmium, satisfactorily reproducing the shapes and positions of various experimental KalphaL0 bands generated by different inducing projectiles.
Very extensive multiconfiguration-Dirac-Fock calculations in the modified special average-level version with the inclusion of the transverse (Breit) interaction and quantum electrodynamics corrections have been carried out on molybdenum, palladium, and lanthanum to elucidate the structure of the Kβ1,3L0Mr lines in their x-ray spectra and to explain reliably the influence of additional holes in the M shell on the shapes and positions of Kβ1,3L0 bands. For each type of line, two theoretical spectra have been synthesized, one being a sum of the Lorentzian natural line shapes and the other one being a convolution of the sum of the Lorentzian natural line shapes with the Gaussian instrumental response. It has been shown that the structures of the appropriate groups of Kβ1,3L0Mr lines of molybdenum, palladium, and lanthanum are similar, while the relevant bands being the sum of the Lorentzian natural line shapes are much smoother for lanthanum (large natural line width) than for molybdenum and palladium. For atoms having sufficiently large atomic mumbers (such as lanthanum), the convolution of a sum of the Lorentzian line shapes with the Gaussian instrumental response can be well represented as two Voigt functions in all cases (large distances between the Kβ1L0Mr and Kβ3L0Mr lines).
Hollow atoms in which the K shell is empty while the outer shells are populated allow studying a variety of important and unusual properties of atoms. The diagram x-ray emission lines of such atoms, the Khα1,2 hypersatellites (HSs), were measured for the 3d transition metals, Z=23–30, with a high energy resolution using photoexcitation by monochromatized synchrotron radiation. Good agreement with ab initio relativistic multiconfigurational Dirac-Fock calculations was found. The measured HS intensity variation with the excitation energy yields accurate values for the excitation thresholds, excludes contributions from shake-up processes, and indicates domination near threshold of a nonshake process. The Z variation of the HS shifts from the diagram line Kα1,2, the Khα1−Khα2 splitting, and the Khα1/Khα2 intensity ratio, derived from the measurements, are also discussed with a particular emphasis on the QED corrections and Breit interaction.
Kβ-to-Kα x-ray intensity ratios have been measured for all the 3d transition metals from titanium to copper, and the valence electronic structures of these metals have been determined by comparing the measured Kβ-to-Kα x-ray intensity ratios with the results of our multiconfiguration Dirac-Fock calculation. Our experimentally determined valence electronic structures for all the metals except V, Cr, and Mn are found to agree reasonably well with the results of augmented plane-wave (APW) band structure calculations. Our results for the valence electronic structure of V and Mn are found to be closer to the free atom values whereas the valence electronic structure of Cr is found to lie in between the valence electronic structure predicted by Compton profile studies and the one given by APW band structure calculations. The electron occupancies of 3d and (4s,4p) states of V, Mn, and Cu are similar to free atom occupancies whereas for the other metals we find rearrangement of electrons between 3d and (4s,4p) states of the metal with the transfer of electrons from 3d to (4s,4p) states for Cr and from (4s,4p) to 3d states in the case of Ti, Fe, Co, and Ni.
We have investigated double K-shell vacancy production in x-ray photoionization of silver. Measurements were carried out with photon energies (50–90 keV) varying from below threshold to beyond the expected maximum of the double K-shell ionization cross section. The limit of asymptotically high energies was deduced from measurements of double K-shell ionization following K-electron capture by 109Cd nuclei. The photon energy dependence of the ratio of double to single K vacancies produced is compared to similar measurements in helium and models thereof. The dependence of that ratio on atomic number is assessed by combining these data with previous experimental and theoretical estimates. The results show a clear growth in the relative importance of the dynamical electron-electron scattering contribution in heavy atoms.