Nuclear Instruments and Methods in Physics Research B 318 (2014) 11–14
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Nuclear Instruments and Methods in Physics Research B
journal homepage: www.elsevier.com/locate/nimb
Comparison of proton and helium induced M subshell X-ray production
cross sections with the ECUSAR theory
D.D. Cohen a,⇑, E. Stelcer a, J. Crawford a, A. Atanacio a, G. Doherty a, G. Lapicki b
a
b
Australian Nuclear Science and Technology Organisation, Locked Bag 2001, Kirrawee DC, NSW 2232, Australia
Department of Physics, East Carolina University, Greenville, NC 27858, USA
a r t i c l e
i n f o
Article history:
Received 18 February 2013
Received in revised form 29 April 2013
Accepted 27 May 2013
Available online 19 July 2013
a b s t r a c t
M subshell X-ray production cross sections have been measured for Ma12, Mb1, Mc, M2–N4 and M1–O23
transitions representing all five M subshells. These experimental cross sections have been compared with
the ECUSAR theory of Lapicki and four parameter fits are given to the experiment to theory ratios covering the proton and helium ion energy range from 0.5 to 3 MeV on thin W, Au, Pb, Th and U targets.
Ó 2013 Elsevier B.V. All rights reserved.
Keywords:
Protons
He ions
X-rays
PIXE
M-subshell
ECUSAR
1. Introduction
Particle induced X-ray emission (PIXE) has been used by many
laboratories for many years to characterise a broad range of samples. Current PIXE detection systems are readily capable of measuring X-rays between 1 and 20 keV and hence through the
characteristic X-rays from K and L shells cover most elements in
the periodic table for aluminium upwards. For common heavy elements with characteristic X-rays in the 1–5 keV region it has become more important to better understand and theoretically
predict the numerous M shell lines which often overlap with lighter element K and L shell lines. M shell ionisation cross sections
have been measured for more than a quarter of a century [1]. More
recently the focus has shifted to more accurate measurements of
the five M subshell X-ray production cross sections [2–8] to better
quantify these and to make comparisons with theory across all five
subshells.
The ECPSSR theory developed over the years by Brandt and
Lapicki [9] and applied specifically to the M shell [10], has more recently been extended to the ECUSAR theory [11]. Here the experimental and the ECUSAR X-ray production cross sections are
compared for dominant lines in each of the five M subshells for
slow proton and helium ion impact on selected high atomic
number targets from W to U. This covers the X-ray energy range
1.1–5.5 keV.
⇑ Corresponding author.
E-mail address: [email protected] (D.D. Cohen).
0168-583X/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.nimb.2013.05.094
Proton energies between 0.5 and 3 MeV and helium ion energies between 0.5 and 2 MeV were used to provide M subshell cross
sections for 0.3 < nMi < 3, where the reduced velocity nMi = 2v1/(hMiv2Mi),
was defined by Brandt and Lapicki [12] and distinguishes between
the slow (nMi < 1) and the fast (nMi > 1) collision regimes.
2. Experimental conditions
Five Mylar foils with thin metal coatings evaporated on their
front surfaces were used as targets. Table 1 gives the metal film
characteristics including typical detector efficiencies and self
absorption for the corresponding M line energies. Target thicknesses were calibrated to ±5% by standard Rutherford backscattering (RBS) techniques. Self-absorption corrections for these thin
targets were generally less than 6% and ion energy losses for the
lowest proton and helium ion energies (0.5 MeV) were less 5 and
19 keV, respectively.
Each target was bombarded with 10–20 nA of beam current for
between 20 and 60 lC of ion charge. This was sufficient to keep
counting statistical errors for each major M subshell peak below
10%. A modern VORTEX X-ray detector was used with a 25 lm
beryllium window and a 400 lm thick silicon chip.
3. Results
Fig. 1 shows a theoretical M shell PIXE spectrum without the
background for 3 MeV protons on U. It was generated in the
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D.D. Cohen et al. / Nuclear Instruments and Methods in Physics Research B 318 (2014) 11–14
Table 1
Thin target characteristics used for this study.
Target
Thickness (lg/cm2)
±5%
Detector efficiency for
Ma line
Self absorption for Ma
line
DE(keV) for 0.5 MeV
protons
DE(keV) for 0.5 MeV
helium
Range of energies for M lines
(keV)
WO3
Au
Pb
ThF4
UF4
48.1
46.6
49.6
45.8
45.3
0.231
0.420
0.522
0.728
0.763
0.939
0.977
0.977
0.977
0.977
3.30
4.01
4.44
3.18
2.96
14.3
15.8
18.8
14.3
14.1
1.1–2.9
1.4–3.6
1.6–3.9
2.1–5.2
2.2–5.5
Fig. 3. Fit of 11 Gaussians M line transitions (solid lines) and the CaKa line (dashed
line) to 0.6 MeV helium ion spectrum (with background) on a thin Au target.
Fig. 1. Theoretical M shell spectrum (no background) normalised to the Ma peak
with 22 Gaussian M line transitions for 3 MeV protons on thin U.
Table 2
Key M line transitions associated with individual M subshells and their possible
overlap transitions used for our targets W–U.
Sub-shell
Major line
Transition
Overlaps not fitted
M5
M4
M3
M2
M1
Ma12
Mb1
Mc
Mm1
M5–N67
M4–N6
M3–N5
M2–N4
M1–O23
M3–N1
M5–O3, M4–O23
M3–N4, M2–N1, M3–O1
M1–N23, M3–O1, M3–O67
M2–O1
Fig. 2. Typical background subtraction technique for 2 MeV protons on a thin Au
foil [13]. The dashed curves are original data, the solid curves are the efficiency
corrected data described in the text.
standard way [13] by generating 22 Gaussians at fixed known
energies, representing 22 M line transitions, with these Gaussians
having variable experimental X-ray detector resolutions (between
120 eV at 2 keV and 180 eV at 6 keV) and detector efficiencies the
same as the experimental efficiencies used in the present work.
The relative intensities were calculated using the ECUSAR subshell ionisation cross sections [11], the DHS fluorescence yields
and emission rates of Puri [14] and the Coster–Kronig rates of
Chauhan and Puri [15].
These 22 M lines varied in intensity over four orders of magnitude and a plot of this type was used to identify both individual
Gaussians to fit to the experimental data as well as any possible
key overlaps not fitted by separate Gaussians. There was no need
to use Gaussians with low energy tails as the response function
for our detector had low energy tail contributions to the total peak
area well below 1% for all lines considered here. Table 2 shows the
overlaps (not fitted separately) for the major lines used in the current work to represent each of the five M subshells. The main problematic line was the (M2–N1) shown in Fig. 1 which can for some
elements have (M1–N23) line interferences. We overcome this by
adding the theoretical ECUSAR (M2–N1) and (M1–N23) contributions together for comparison with the experiment for this line.
Appropriate background subtraction under the characteristic M
lines for experimental spectra was critical, especially for the low
intensity lines. Fig. 2 demonstrates the background subtraction
method used here and described in detail in Ref. [13]. Basically,
the experimental spectrum (dashed curve in Fig. 2) was divided
by the detector efficiency in the range 1.1–5.5 keV and a linear
background on a log-linear plot fitted and subtracted from it (solid
curve in Fig. 2). The background obtained in this way (dashed curve
under the data of Fig. 2) is compared with a standard linear background (solid line with *) in the same figure. This background
removedspectrum was then recorrected for detector efficiency
and the relevant M shell Gaussians fitted to obtain peak areas for
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D.D. Cohen et al. / Nuclear Instruments and Methods in Physics Research B 318 (2014) 11–14
Fig. 4. Ratios of experiment to ECUSAR X-ray production cross sections versus nM1–5 for (a) total M shell, (b) Ma12 line, (c) Mb12, M5–O3, M4–O23 lines, (d) Mc M2–N1 lines, (e)
M2–N4, M1–N23 lines and (f) M1–O23 line for both proton (p) and helium (He) ion bombardment of thin W, Au, Pb, Th and U targets.
Table 3
The coefficients of a four parameter fit of the form Ri = (a/nMi + b + cnMi + d/nMi2) for the ratio of experimental proton and helium ion data for the ECUSAR theory for each of the M
subshell lines and the total M X-ray production cross sections. R2 is the correlation coefficient of the least squares fit for each Ri.
Proton and helium fits
Mtotal
M5
M4
M3
M2
M1
a
b
1.96 ± 0.45
1.99 ± 0.57
2.45 ± 0.51
2.20 ± 0.76
1.08 ± 0.92
1.45 ± 2.4
c
2.30 ± 0.45
2.34 ± 0.59
2.86 ± 0.54
3.25 ± 0.82
0.625 ± 1.2
2.69 ± 3.3
R2
d
0.321 ± 0.12
0.333 ± 0.17
0.573 ± 0.16
0.475 ± 0.25
0.539 ± 0.42
1.91 ± 1.3
0.943 ± 0.13
0.945 ± 0.16
1.01 ± 0.14
0.744 ± 0.20
0.124 ± 0.21
0.125 ± 0.49
0.948
0.924
0.940
0.561
0.375
0.489
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D.D. Cohen et al. / Nuclear Instruments and Methods in Physics Research B 318 (2014) 11–14
the major M subshell lines. Clearly this technique tends to produce
tighter background cuts and better reflects the true nature of the
secondary electron background in the region under the M lines.
Fig. 3 shows a typical background and an 11 Gaussian fit to a
spectrum for 0.6 MeV He ions on Au. Note the CaKa peak
(3.69 keV) which was due to low level contamination in the Mylar
backing for our targets.
Experimental X-ray production cross sections for the Ma, Mb,
Mc, M2–N4 and M1–O23 lines, (together with their overlaps) representing all five M subshells are compared with the corresponding
ECUSAR theoretical cross sections [11] in Fig. 4(a–f). The DHS fluorescence yields and emission rates of Puri [14] and the Coster–Kronig rates of Chauhan and Puri [15] were used to convert the
theoretical ionisation cross sections to X-ray production cross sections for each of the fitted X-ray lines.
The ratios of the experimental values to the ECUSAR theoretical
values (Ri) for both proton (open symbols in Fig. 4) and helium ion
(solid symbols in Fig. 4) bombardment were then fitted to a single
four parameter function of the form y = (a/n + b + c n + d/n2) whose
coefficients are presented for each subshell in Table 3 and plotted
as a solid line in each of the figures.
The larger errors on the fitting parameters particularly for the
M1 subshell stem from the difficulties in extracting the smaller
peak areas associated with the M1 lines (see for example the Au
spectra shown in Fig. 3).
4. Summary
The X-ray production cross sections for key transitions in each
of the five M subshells have been measured for low energy proton
and helium ion bombardment on selected thin heavy targets. In the
fast collision regime defined by (nMi > 1) the average experiment to
ECUSAR theory ratios for the individual subshells were;
Rtot = (0.92 ± 0.09),
R5 = (0.92 ± 0.10),
R4 = (0.78 ± 0.17),
R3 = (1.35 ± 0.22), R2 = (0.89 ± 0.17) and R1 = (1.20 ± 0.60). In a com-
pensating way, the M1 ratio increases with increasing nMi while the
M4 ratio decreases. Conceivably the transitions from the O subshells to M1 and M4 in the overlapping peaks that were not fitted
could have been undercounted in the extraction of the M1 vs. M4
cross sections from the other transitions.
In the slow collision regime (nMi < 1), ratios increase rapidly with
decreasing ions velocities, with the experimental values for Mtotal
being 3 times higher than the ECUSAR predictions at the lowest
velocity. Similar trends are exhibited for M-subshells where the fitted ratios lie between 2 and 4 at the lowest velocity.
Tabulated X-ray production cross sections may be obtained by
contacting the corresponding author (DDC) at [email protected].
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