High resolution study of the K X-ray spectra of 3d transition
elements induced in collisions with fast heavy ions
M. Kavčič*, M. Budnar*, J.-Cl. Dousse**
* J. Stefan Institute, P.O. Box 3000, SI-1001 Ljubljana, Slovenia
** Physics Department, University of Fribourg, CH-1700 Fribourg, Switzerland
High-resolution measurements of the K x-ray spectra of metallic Ca, Ti, Cr, and Fe were performed with a
von Hamos Bragg crystal spectrometer. The target x-ray emission was induced by by 2-19 MeV/amu C, O
and Ne ions. The energies of the well resolved KαLN X-ray satellite lines were determined. Based on the
measured values the empirical formula for the KαLN satellite energy shift of the 3d transition elements is
given. For the Ca and Ti target bombarded with C ions also the KαhLN hypersatellite lines the KβLN satellite
lines and even the KβhLN hypersatellite lines have been measured and their energies determined. The possible
variation of the energy differences between neighboring satellite and hypersatellite lines with the projectile
energy and atomic number was probed. No significant dependence on the projectile characteristics was
observed. In contrast to that the absolute energies of the satellite and hypersatellite lines lines were found to
depend on the projectile velocity. This dependence was attributed to the M shell ionization of the target atoms
accompanied to the K and L-shell ionization produced in collisions.
the L-shell), KαhLN lines (2p→1s transition with one
spectator hole in the K-shell and N spectator holes in the
L-shell), KβLN lines (3p→1s transition with N spectator
holes in the L-shell) and KβhLN lines (3p→1s transition
with one spectator hole in the K-shell and N spectator
holes in the L-shell). The separation of different lines in
such complex X-ray spectra can only be acchieved by
using high-resolution crystal spectrometer.
Eventhough the level of multiple ionization is much
lower when using protons instead of heavy ions the same
description is valid also in this case. Therefore a complete
description of the K X-ray spectra emitted due to proton
bombardment during PIXE analysis requires knowledge of
these non diagram lines. Especially the Kα satellites can be
rather intensive (few % of the diagram line) limiting the
accuracy of the analysis.
The main goal of this work was to provide energies of
non diagram lines in the K x-ray spectra of some 3d
transition elements. Heavy ions were used in order to have
high ionization probabilities resulting in rich structure
containing higher order satellites and hypersatellites.
INTRODUCTION
In a collision of fast heavy ion with low-Z atom
several inner-shell holes can be created. Multiple innershell hole states may decay through X-ray transitions. Due
to differences in nuclear charge screening caused by
additional holes in the core levels x-ray lines which
correspond to the multiply ionized atoms are shifted to
higher energies compared to the photons emitted in
transitions of singly ionized atoms. The energy shift
increases with the principal quantum number of the
electron which is active in the transition, and decreases
with the principal quantum number of the spectator
vacancy. For this reason K X-rays with doubly ionized Kshell (K hypersatellites) are more shifted than the K x-rays
with spectator vacancy in the L-shell (KL satellites). Also
the energy shift relative to the diagram line is larger for the
Kβ satellites which correspond to 3p→1s transition than
for the Kα satellites (2p→1s transition). For 3d transition
elements the Kα and Kβ hypersatellites are shifted, with
respect to the parent diagram line, by 200-300 eV and 250400 eV, respectively.The energy shifts of the KL satellites
are approximatelly 10 times smaller. When the spectator
vacancy is lying in the M-shell (or even higher shell) the
energy shift is comparable to the natural linewidth of the
transition and therefore M satellites lines cannot be
resolved separatelly. The K X-ray emission spectrum of a
target bombarded by fast heavy ions will present therefore
a complex structure consisting of 4 different groups of
lines corresponding in the direction of increasing energy to
the KαLN lines (2p→1s transition with N spectator holes in
EXPERIMENT
The experiment was performed at the variable energy
cyclotron of the Paul Scherrer Institute (PSI) in Villigen,
Switzerland. Metallic foils of Ca (15.5 mg/cm2), Ti (1.36,
2.71, 5.42 mg/cm2), Cr (1.44, 2.88, 4.31, 5.03 mg/cm2) and
Fe (1.57, 3.15, 5.51 mg/cm2) were bombarded by 34 MeV
C2+, 72 MeV C3+ and 134 MeV MeV C4+ ions, 28 MeV
O2+, 64 MeV O3+ and 230 MeV O6+ ions and 43 MeV
CP680, Application of Accelerators in Research and Industry: 17th Int'l. Conference, edited by J. L. Duggan and I. L. Morgan
© 2003 American Institute of Physics 0-7354-0149-7/03/$20.00
11
Ne3+, 160 MeV Ne6+ and 380 MeV Ne8+ ions in order to
measure KαLN satellite lines . Measurements of Kα,βh and
KβLN lines were performed only for Ca and Ti bombarded
with C ions.
The target X-ray emission was measured with a highresolution von Hamos Bragg crystal spectrometer
presented in detail in [1]. Emitted photons were reflected
in the first order by the (200) reflecting planes of a LiF
crystal. The curvature radius of the 5 cm wide and 10 cm
high crystal lamina was 25.4 cm and the reflecting area 1.3
x 10 cm2. Reflected photons were detected by a 27.65 mm
long and 6.9 mm high front-illuminated CCD (Charge
Coupled Device) detector. The detector which consisted of
1024 x 256 pixels, each having a size of 27 x 27 µm2, was
thermoelectrically cooled to –60oC. The whole
spectrometer was enclosed in a 180 x 62 x 24.5 cm3
stainless steel chamber evacuated by a turbomolecular
pump down to 10-7 mbar.
The measurements of the photoinduced Kα X-ray
spectra were performed using the bremsstrahlung of a
Coolidge X-ray tube equipped with a Cr anode and a 0.5
mm thick non-porous Be window for the target irradiation.
The tube was operated typically at 20 kV x 10 mA. The
photoinduced spectra were used for the energy calibration
of the heavy ion induced spectra and for the determination
of the instrumental resolution which was found to vary
from 1.3 eV at 3.7 keV (Ca Kα transition) up to 3.5 eV at
6.4 keV (Fe Kα transition).
In relation (2), Eref and θref stand for the energy and Bragg
angle of the X-ray line taken as reference. For each target,
the photoinduced Kα1 diagram line was chosen as
reference. The energies of the reference lines were taken
from [2]. By comparing the values obtained for the
coefficient k from four photoinduced calibration spectra
we were able to estimate the accuracy of our energy
calibrations. Uncertainties comprised between about 0.1
eV (Fe) and 0.2 eV (Ca) were found which are included in
the total errors quoted in Tables 1-5.
Yield
[counts]
X-ray Energy [keV]
FIGURE 1. KαLN satellite spectrum of Ti ionized by 64 MeV O
ions, decomposed by the fitting method as explained in the text.
Slight asymmetry on the low energy tail of the KαL1 lines comes
from transitions (1S0 → 1P1 and 1P1 → 1S0), which represent less
than 10% of the total KαL1 line intensity, and are shifted by 10
eV to the lower energies. The above mentioned asymmetry
observed in the KαL1 line of Ca was assigned to these two lowenergy components. Actually, similar asymmetries were also seen
in the KαL1 lines of Ti, Cr and Fe. They were accounted for by
adding an additional peak slightly below the Voigtian describing
the main part of the KαL1 line.
DATA ANALYSIS
A) Energy calibration
The X rays diffracted by the crystal hit the CCD
detector and form a two dimensional intensity pattern on
the detector plane. Each measurement consisted in
collecting several hundreds of two-dimensional images.
For each image, good event pixels were sorted by setting
an energy window corresponding to the X rays of interest.
This permitted us to reject background events and higherorder reflections. The filtered images were then added and
their sum projected on the horizontal detector axis that
coincides with the dispersion axis. The so-obtained
position spectra were transformed in energy spectra, using
the following relation:
E pixel = k
1 + tg 2θ pixel
tgθ pixel
,
B) Fitting procedure
As the L-shell spectator vacancies can be located in
different subshells and many couplings between the total
angular momenta of the open subshells are possible in the
initial and final states, each satellite and hypersatellite line
consists of numerous components that vary in energy and
intensity. However, the energy differences between the
components, being usually smaller than the natural widths
of the latter, which are in addition broadened by the
spectrometer
response,
Kα,βLN
satellites
and
hypersatellites can only be observed as broad lines even if
the experimental resolution is high. Therefore, the satellite
or hypersatellite spectra consist of several juxtaposed
broad lines. As the latter were found to be in most cases
almost symmetric, they could be fitted with single Voigt
profiles. The only exceptions were the Kα,βL0 lines, which
showed asymmetric structures on their high energy sides,
(1)
where Epixel is the energy corresponding to a particular
pixel on the dispersion axis of the position spectrum, θpixel
the Bragg angle associated to that pixel which can be
calculated from the detector position. K is a calibration
coefficient defined by:
k = E ref
tgθ ref
(2)
1 + tg 2θ ref
12
and therefore could not be fitted with a single Voigt
profile. This asymmetry was attributed to additional M
shell ionization that was produced simultaneously in the
collisions. As mentioned before, M satellites are indeed
much less shifted in energy than L satellites and cannot
therefore be separated from the parent diagram lines. These
unresolved M satellite structures are also present in the
higher order satellites but their asymmetric contributions
are smeared out by strong line broadening resulting from
the L shell ionization. Because of these asymmetries the
Kα,βL0 lines had to be fitted in a different way. For the
Kα,L0 line we have used two Voigt profiles obtained from
the fit of the photoinduced Kα X-ray spectra with wellresolved Kα1 and Kα2 diagram lines. The widths of these
two Voigtians were then kept fixed in the fits of the heavy
ion induced KαL0 lines. The unresolved M satellite
structures of the latter were accounted for by adding in the
fit an asymmetric profile to each Voigtian. The asymmetric
KβL0 line was fitted with one Voigt representing the Kβ1,3
line plus additional contributions on the high energy tail
describing the M satellite structures. With this model the
measured spectra could be fitted satisfactorily and reliable
values could also be obtained for the energies of the
satellite and hypersatellite lines. The fitting procedure was
performed using the EWA dedicated program package [3].
An example of a fitted KαLN spectrum is presented in
Fig.1.
Our values differ from the ones calculated with the above
equation by few eV. From our values we can propose
similar empirical equation valid for 3d transition elements
[
[
+ 3.053 N 2 − 20.016 N + 10.010
Energy shifts of the KαLN satellites of 3d transition
elements predicted by our equation are valid within 1-2eV.
∆E This work - ∆ E Torok, Papp [eV]
5
20
22
24
26
N=3
68.8±0.3
77.7±0.3
87.9±0.3
95.5±0.5
N=4
94.6±0.7
106.0±0.7
116.1±1.0
130.0±1.1
2
1
2
3
4
FIGURE 2. Difference between the energy shift of the KαLN
satellite predicted by our Eq. (4) and the Eq. (3) proposed in [4].
Energy shifts of the KαhLN hypersatellites KβLN
satellites and for the case of Ti bombarded with 134 MeV
C ions even the Kβh hypersatellites are tabulated in Tables
2, 3, 4. Similar as for the case of KαLN satellites the values
are averaged over different measured collisions since no
dependence on the projectile energy or the projectile
atomic number has been observed. Since we have
measured hypersatellites and KβL satellites only for Ca
and Ti we cannot give similar equation for the energy shift
as for the KαL satellites, but nevertheless we can see from
Tables 2,3 that the energy shift between the neighboring
KαhLN hypersatellite or KβLN satellite lines increase appr.
linearly with the increasing number of L shell holes.
N=5
121.3±1.5
138.4±1.3
/
/
In the recent compilation [4] the energy shift of the n-th
order L satellite is given by the following empirical
formula
∆E( KαLN ) = N × 1.530[Z + 0.5( N − 1 ) − 6.828]
Fe
N
TABLE 1. Energy shifts (in eV) of the KαLN satellites relative to
the Kα diagram line. The tabulated values were derived from a
least-squares-fit to a constant value of the energy shifts measured
with different projectile energies and different projectile species.
N=2
44.8±0.2
50.6±0.3
58.2±0.3
61.6±0.5
3
1
Since we have observed no significant dependence of
the energy shift ∆E(KαLN) on the projectile energy nor the
projectile atomic number we have determined the energy
shift of the KαLNsatellite by averaging the shifts over
different measured collisions. The values are tabulated in
Table 1.
N=1
21.9±0.2
24.5±0.3
28.5±0.3
29.4±0.5
Ca
4
0
RESULTS AND DISCUSSION
Z
]
]
∆E( KαLN ) = − 0.119 N 2 + 2.038 N − 0.474 Z . (4)
TABLE 2. Energy shifts (in eV) of the KαhLN hypersatellites
relative to the Kα diagram line.
Z
20
22
N=0
195.0±0.6
216.4±0.2
N=1
218.0±0.2
241.7±0.3
N=2
242.5±0.5
268.4±0.5
TABLE 3. Energy shifts (in eV) of the KβLN rsatellites relative
to the Kβ diagram line.
Z
(3)
20
22
13
N=1
52.0±0.2
57.7±0.2
N=2
104.1±0.6
117.8±0.9
N=3
160.2±0.3
179.3±0.6
TABLE 4. Energy shift (in eV) of the KβhLN hypersatellites
relative to the Kβ diagram line for Ti bombarded with 134 MeV
C ions.
Z
20
N=0
282.3±4.8
measured by means of a high-resolution von Hamos Bragg
crystal spectrometer. The KαLN, the KαhLN, the KβLN,
and the KβhLN could be resolved and their energies
determined. It was confirmed that the energy spacing
between neighboring L satellites and hypersatellites does
not depend on the projectile atomic number nor its
velocity. Furthermore, the spacing was found to increase,
almost linearly, with the number of spectator holes in the L
shell. New empirical equation for the energy shift of the nth order KαL satellite of the 3d transition element is given.
It has been also demonstrated that the absolute energies of
the Kα satellite and hypersatellite lines depend on the
projectile energy. This dependence was attributed to the M
shell ionization induced simultaneously in the target atoms
as a result of the collisions.
N=1
344.7±6.8
Theoretical prediction for the energy shifts of the Kα,βhL0
hypersatellite lines have been calculated by Chen [5] using
the Dirac-Hartree-Slater wave functions. Comparison of
our measured values with Chen theoretical predictions is
presented in Table 5. Excellent agreement with the
theoretical values was found.
TABLE 5. Energy shifts (in eV) of the hypersatellites relative to
the diagram line. Values in the parentheses are theoretical values
from [5].
20
22
E(Kαh)-E(Kα2)
197.4±0.6 [197.5]
220.3±0.2 [221.1]
E(Kβh)-E(Kβ1,3)
/
282.3±4.8 [282.7]
As it was already mentioned the energy shift of the
satellite and hypersatellite lines relative to the diagram
ones does not depend on projectile energy or atomic
number. On the other hand the absolute energies
significantly depend on the energy of the projectile. The
reason is the degree of M shell ionization which
accompanies the KL shell ionization. As we already
mentioned the contribution of the M-shell satellites is
presented in the satellite and hypersatellite lines although it
is somehow hidden in rather complex multiplet structure of
these lines. Therefore what we usually observe in the
spectra is just a broad line but the precise analysis shows
the influence of the M-shell satellites. On Fig. 3 we can see
the dependence of the KαL0 and KαhL0 lines for Ti on the
energy of the projectile for the case of C ions. In order to
explain the dropping dependence we have calculated the
average M shell ionization probabilities for the collisions
presented on Fig. 3. The direct ionization probabilities
were calculated according to the first order SCA model of
Trautmann and Rösel [6], which employs classical
hyperbolic trajectories and uses hydrogen-like Dirac
electron wave functions. The calculated average M shell
ionization probabilities for Ti were 0.071, 0.032 and 0.017
for the 34 MeV, 72 MeV, and 134 MeV C ions
respectively. These values support the idea that the
absolute energies of the satellite and hypersatellite lines
depend on the degree of the M shell ionization. Since this
depend also on the atomic number of the projectile we can
expect similar dependence of the energies on the atomic
number of the projectiles also. Indeed such dependence
has been already reported in the literature [8].
h
0
Kα L
0
KαL
4730
4729
X-ray Energy [keV]
Z
4731
4728
4727
4514
4513
4512
4511
4510
20
40
60
80
E
proj ect ile
100
120
140
[MeV]
FIGURE 3. Absolute energies of the KαL0 and KαhL0 satellite
lines of Ti induced in collisions with C ions. The dropping
dependence on the projectile energy was attributed to the
additional M shell ionization.
This work was supported by the Slovenian Ministry of
Science and Technology through the research program
“Low energy physics” (PO-0521-0106-02) and by the
Swiss National Science Foundation.
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14
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