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Experimental bremsstrahlung yields for MeV proton bombardment of beryllium and carbon
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NIM B Beam Interactions with Materials & Atoms
Nuclear Instruments and Methods in Physics Research B 266 (2008) 1149–1153 www.elsevier.com/locate/nimb
Experimental bremsstrahlung yields for MeV proton bombardment of beryllium and carbon David D. Cohen *, Eduard Stelcer, Rainer Siegele, Mihail Ionescu, Michael Prior Institute for Environmental Research, Australian Nuclear Science and Technology Organisation, Private Mail Bag 1, Menai, NSW 2234, Australia Received 14 September 2007; received in revised form 22 October 2007 Available online 22 November 2007
Abstract Experimental bremsstrahlung yields for 2, 3 and 4 MeV protons on thin beryllium and carbon targets have been measured. The yields have been corrected for detector efficiency, self-absorption in the target and fitted to 9th order polynomials over the X-ray energy range 1–10 keV for easy comparison with theoretical calculations. Crown Copyright Ó 2007 Published by Elsevier B.V. All rights reserved. PACS: 34.50.Fa; 41.75.Ak; 78.70.En; 03.50.z Keywords: Bremsstrahlung; PIXE; X-rays; Backgrounds
1. Introduction Particle induced X-ray emission (PIXE) is a well established multi-elemental analysis technique that has been applied for many years in accelerator laboratories around the world [1–10]. There are several well established PIXE codes, such as PIXAN [3], GUPIX [4,5] and GeoPIXE [6] currently being used to determine characteristic X-ray peak areas and to convert these to well determined elemental concentrations within a matrix. Experimental fluorescence yields, characteristic a, b and c peak ratios, Koster-Cronig transition rates and X-ray production cross-sections for a broad range of K and L lines are generally well determined [7–11]. One of the weaker links in this fitting process is related to a better physics-based determination of the bremsstrahlung background particularly under low intensity characteristic X-ray lines. The determination of the bremsstrahlung background for PIXE spectra in the 1–20 keV X-ray energy region is usually performed empirically and not from first principles
*
Corresponding author. Tel.: +61 2 9717 3042; fax: +61 2 9717 3257. E-mail address: [email protected] (D.D. Cohen).
using bremsstrahlung production cross-sections [12–15]. It is recognised that there are at least three significant contributions to the bremsstrahlung background in PIXE spectra [14]. In the 1–2 keV X-ray region quasi-free electron bremsstrahlung (QFEB) dominates falling rapidly to zero above this energy, this is produced by target electrons moving in the projectile frame. In the 2–7 keV region secondary electron bremsstrahlung (SEB), tends to dominate, this is produced when the ion ejects an electron from the target atom which is then scattered by another target atom. In the higher 5–15 keV region the atomic bremsstrahlung (AB) dominates and is produced when the ion excites inner shell (K and L) target atoms to the continuum which then return to their original states. Each of these contributions depends on the target atomic number Z2 and mass M2, the ion atomic number Z1 and mass M1 as well as the ion energy E1. Recently, Ishii and associated co-workers have identified theoretical models for each of these bremsstrahlung components and their production cross-sections [13–15]. This makes it possible to predict total bremsstrahlung cross-sections for proton PIXE, as well as for heavier ion PIXE, for most commonly used target materials. Here we report on parts of a systematic study experimental bremsstrahlung yields for 1–10 keV X-rays for
0168-583X/$ - see front matter Crown Copyright Ó 2007 Published by Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2007.10.040
2–4 MeV proton bombardment of beryllium and carbon targets. These yields have been corrected for detection efficiency and target absorption effects to better test the theoretical predictions of bremsstrahlung background in PIXE spectra. Hopefully these data will lead to a full, more physically realistic, PIXE spectrum fitting model covering most elements in the periodic table for both the characteristic lines and the bremsstrahlung background. 2. Theoretical bremsstrahlung production Fig. 1 shows typical production cross-sections [b/ (keV sr)] for 3 MeV protons on pure carbon taken from the theoretical work of Murozono et al. [15]. The different regions of interest for the QFEB, SEB and AB contributions are clearly distinguishable in the figure. Above 10 keV AB dominates and below 1 keV QFEB dominates with SEB being the primary contributor in the intermediate X-ray regions between 2 and 10 keV. Between 1 and 10 keV the cross-sections span 7 orders of magnitude from 1 b/(keV sr) down to 107 b/(keV sr). This range in cross-section is several orders of magnitude larger than the yield range (counts/(lC keV sr)) experienced in most experimental bremsstrahlung situations for typical PIXE measurements, which, for 1–10 keV, can span yields from 104 down to 1 counts/(lC keV sr). Fig. 2 shows expected theoretical bremsstrahlung yields, derived from these cross-sections, when typical detector efficiency [16] and self-absorption corrections in the target are considered. Since the targets are relatively thin, the self-absorption correction was performed assuming that all the X-rays originated from a thin layer situated at the centre of the target. The figure shows the theoretical yields/(lC keV sr) for a 1 mg cm2 thick target of 3 MeV protons on carbon. The low energy fall off below 2 keV is predominantly due to the 75 lm beryllium window used to stop 3 MeV protons entering the detector. Between 1 and 10 keV the bremsstrahlung yields cover 5 orders of magnitude considerably raising the background and hence the minimum detectable limits for PIXE analyses.
Cross section [b/(keV.sr)]
1.E+01
3 MeVp on C
SEB
1.E+00 1.E-01 1.E-02
Total
1.E-03 1.E-04 1.E-05
AB
QFEB
1.E-06
Ylds [cnts/(keV.sr.µC.mgcm-2)]
D.D. Cohen et al. / Nucl. Instr. and Meth. in Phys. Res. B 266 (2008) 1149–1153
1E+06
3 MeVp on C
1E+05 1E+04
Total
1E+03 1E+02 1E+01 1E+00 0
1
2
3
4
5
6
7
8
9
10
E (keV) Fig. 2. The theoretical yields (counts/(keV sr lC mg cm2) for the total theoretical cross-sections shown in Fig. 1for a typical Si(Li) detector with 75 lm Be entrance window.
1.E+06
4MeVp on Be
Fe
Counts/ 400µ C
1150
1.E+05
Cr
1.E+04
Ni
1.E+03
aexp(-bEx) fit toγ-bkg
1.E+02 0
5
10
15
20
E (keV) Fig. 3. Experimental PIXE spectrum for 4 MeV protons on thin Be showing the gamma ray background well fitted by an exponential in the energy range 10–20 keV.
There are other significant background contributions to typical PIXE spectra; these include projectile nuclear bremsstrahlung (NA), Compton scattering in the detector of high energy gamma rays produced by nuclear reactions in the target and charging effects of some insulated targets. We will not discuss all of these here. For PIXE, Compton scattered gamma rays may contribute significantly in the 10–20 keV region as shown in Fig. 3 for 4 MeV protons on beryllium. This type of background can be well fitted by a two parameter (a, b) exponential function of the X-ray energy (Ex) in this region [a exp(bEx)], extended through to zero X-ray energy and then subtracted off the background leaving the pure bremsstrahlung background contributions in the 1–10 keV region similar to those shown in Fig. 2. Note it is an assumption that we have not fully tested yet that the exponential fit in the higher keV regions can be extended to lower energies (<10 keV) under the bremsstrahlung peak.
1.E-07 0
1
2
3
4
5
6
7
8
9
10
E (keV) Fig. 1. Bremsstrahlung cross-sections for QFEB, SEB and AB contributions for 3 MeV protons on carbon from Murozono et al. [15].
3. Results and discussion In order to accurately and precisely measure bremsstrahlung yields it is necessary to use thin solid targets of
D.D. Cohen et al. / Nucl. Instr. and Meth. in Phys. Res. B 266 (2008) 1149–1153
materials that do not have any characteristic X-rays in the energy range of interest. In our 1–10 keV X-ray range this effectively excludes all targets between Al and Zn. Furthermore these targets should be extremely pure containing no trace elements which also produce characteristic lines in our region of interest. PIXE is a very sensitive technique and this is very difficult to achieve. Beryllium and carbon are two elements that can meet these criteria if they can be obtained in a pure enough form. The thickness of these targets should be sufficient to contain the ion induced electrons (several lm) but not so thick so that self-absorption of the emergent X-rays at a few keV becomes a problem. For this work we used beryllium and carbon targets which were 1843 ± 56 and 1767 ± 54 lg cm2 thick, respectively. The Be target was 99.89% pure with Cr, Mn, Fe and Ni contaminants above 10 lg/g, and the carbon was 99.97% pure with S and Cl as contaminants above 10 lg/g. The total bremsstrahlung yields were obtained for 2, 3 and 4 MeV proton bombardment using the sum of 5 individual 40 lC runs on each target with between 10 and 30 nA of protons from a 6 mm diameter beam. The count rates into all spectra were deliberately kept low to keep dead times below 1% and reduce pileup effects which would change the shape of the bremsstrahlung backgrounds. The 1E+05
Counts/ 200µC
1E+04 4MeV 1E+03 1E+02 3MeV 2MeV
1E+01 1E+00 0
1
2
3
4
5
6
7
8
9 10 11 12 13 14
E (keV) Fig. 4. Experimental yields for 2, 3 and 4 MeV protons on Be 1843 lg cm2.
1.E+05
Counts/ 200µC
1.E+04
1151
full 200 lC spectra are shown in Figs. 4 and 5 for beryllium and carbon targets, respectively. The solid curve under each spectrum is the bremsstrahlung fitted background used to produce the normalised yields calculated below. Each of the spectra contained a Si Ka fluorescence peak, small discontinuities associated with the SiK and AuM edges as well as the characteristic peaks associated with the trace contaminants. The SiK and AuM edge discontinuities have been discussed in detail elsewhere [16,17] and were used to quantify the detector silicon dead layer and the gold front contact layer thicknesses. The Si Ka fluorescence peak was produced by the bremsstrahlung radiation (above 1.838 keV) fluorescing the detector crystal itself. When the Compton scattered gamma ray component is removed the beryllium bremsstrahlung background peaks at lower X-ray energies than for the corresponding situations in carbon. This is due to the target atomic number (Z2) dependence of the cross-sections for these two targets [14]. Each 200 lC spectrum was divided by the detector efficiency [16] and corrected for self-absorption in the target channel by channel. The gamma ray back ground between 10 and 20 keV, if present, was fitted with a two parameter exponential function and stripped off. The resulting spectrum was then normalised to unit charge (lC), unit solid angle (sr) and unit target thickness (1 mg cm2), providing an efficiency and absorption corrected yield for each ion energy and target used. Typical experimental errors associated with each step of this process are given in Table 1. The natural log of this normalised yield (Yld) was fitted to a 9th order polynomial in the natural log of the X-ray energy Ex over the range 1–10 keV. That is, 2
9
lnðYldÞ ¼ a0 þ a1 ln Ex þ a2 ðln Ex Þ þ þ a9 ðln Ex Þ :
ð1Þ
The 10 coefficients for these polynomial fits are given in Table 2 for each ion energy and target. They are only applicable for 1 < Ex < 10 keV and should not be used outside this range. They have been quoted to 10 significant figures to avoid round off errors but generally reproduce the experimental bremsstrahlung cross-sections to ±6% or better at the 95% confidence interval over this range. Fig. 6 shows a comparison between the theoretical yield predictions from the cross-sections of Murozono et al. [15] and the current experimental polynomial fits for 3 MeV protons on beryllium and carbon.
1.E+03 4MeV 1.E+02
2MeV 3MeV
1.E+01
Table 1 Typical experimental errors associated with each step of the normalised yield calculations Typical experimental percentage errors (%) Type
1.E+00 0
1
2
3
4
5
6
7
8
9 10 11 12 13 14
E (keV) Fig. 5. Experimental yields for 2, 3 and 4 MeV protons on C 1767 lg cm2.
at 1 keV
Self-absorption ±10 Detector ±170 Counting <±1 Total ±170 sr ± 5%, lC ± 3%, qx ± 3%
at 5 keV
at 10 keV
<±1 ±2 ±2 ±7
<±1 <±1 ±20 ±20
1152
D.D. Cohen et al. / Nucl. Instr. and Meth. in Phys. Res. B 266 (2008) 1149–1153
Table 2 The 10 coefficients for the 9th order polynomial fits to the normalised bremsstrahlung yields for 2, 3 and 4 MeV protons on thin beryllium and carbon targets Beryllium
Counts with absorp/ (sr.keV.µC.mgcm-2)/100%Eff
a0 a1 a2 a3 a4 a5 a6 a7 a8 a9
Carbon
2 MeV
3 MeV
4 MeV
2 MeV
3 MeV
4 MeV
21.695235123 37.535477096 161.839939141 444.815912661 751.282273099 788.466632656 507.777557541 194.330412297 40.505488754 3.539516300
22.507479338 30.037382030 77.629671566 101.943670523 38.520636188 51.373203885 71.320050991 36.798673670 8.953738897 0.853677117
23.102958952 37.347459358 125.960309085 250.675196976 297.607971087 221.648694409 104.893674327 30.780362067 5.116854890 0.368109536
23.940800659 39.469435410 115.939402245 219.423803115 275.415124427 235.739146058 131.988545631 45.568495125 8.751651843 0.713709671
24.540257524 32.899546666 50.802870595 22.214297654 188.271382161 275.915302992 201.348869046 80.706727689 16.953834918 1.460876631
25.200270646 37.868856277 87.651819768 116.593775820 95.099571688 56.411436847 28.165460971 11.010676614 2.603931922 0.258763572
1E+09 1E+08 3MeV on C
1E+07 1E+06 3MeV on Be
1E+05 1E+04 1E+03 1E+02 0
1
2
3
4
5
6
7
8
9
10
E (keV) Fig. 6. Comparison of Murozono et al. [15] theoretical normalised yields (dashed curves) with current experimental yields (solid curves) for 3 MeV protons on Be and C.
tor efficiency and target absorption and then fitted to 9th order polynomials. The coefficients of the fits reproduce these normalised yields to better than ±6% over the X-ray energy 1–10 keV and can be used to make direct comparisons with theoretical predictions for bremsstrahlung production. Comparisons with the theoretical crosssections of Murozono et al. [15] show (1) the current theoretical calculations generally under predict the experimental measurements by factors of between 1 and 3 around the bremsstrahlung peak; (2) there are small but significant differences for X-ray energies above 7 keV and theory may not accurately reproduce the experimental bremsstrahlung shape in this atomic bremsstrahlung (AB) region. More work is currently being performed to resolve some of these issues. Acknowledgements
The theoretical yields have been scaled up by 2.04 for beryllium and 2.67 for carbon to approximately match the experimental data in the 3–5 keV energy range. Generally the theoretical shape matched experiment in the mid X-ray energy range from 3 to 6 keV but the theory under predicted the experimental yields for energies above 6 keV. In the region between 8 and 10 keV counting statistics become smaller and their associated errors larger (see Table 1). This may account for some of the deviations of the carbon and beryllium experimental data above 6 keV not reproduced in the theoretical dashed line data of this figure. In the lower energy region around 1 keV and below the experimental data are unreliable as the detector efficiencies [16] are well below 0.01%, falling rapidly and have large uncertainties (see Table 1).
4. Summary Thin Be and C targets have been used to accurately and precisely measure bremsstrahlung yields induced by 2, 3 and 4 MeV protons. These yields have been normalise to unit charge (lC), unit solid angle (sr), corrected for detec-
We would like to acknowledge the help of the 2 MV STAR accelerator staff in several aspects of this work. This work was partly performed within the framework of IAEA CRP G.4.20.02 Unification of Nuclear Spectrometries. References [1] S.A.E. Johannson, J.L. Campbell, PIXE: A Novel Technique for Elemental Analysis, Wiley and Sons, New York, 1988. [2] D.D. Cohen, E. Clayton, Ion induced X-ray emission, in: J.R. Bird, J.S. Williams (Eds.), Ion Beams for Materials Analysis, Academic Press, Sydney, 1989, Chap 5. [3] E. Clayton, D.D. Cohen, P. Duerden, Nucl. Instr. and Meth. B 22 (1987) 64. [4] J.A. Maxwell, J.L. Campbell, W.J. Teesdale, Nucl. Instr. and Meth. B 43 (1989) 218. [5] J.A. Maxwell, W.J. Teesdale, J.L. Campbell, Nucl. Instr. and Meth. B 95 (1995) 407. [6] C.G. Ryan, D.R. Cousens, S.H. Sie, W.L. Griffin, Nucl. Instr. and Meth. B 49 (1990) 217. [7] D.D. Cohen, E. Clayton, Nucl. Instr. and Meth. B 22 (1987) 59. [8] D.D. Cohen, Nucl. Instr. and Meth. B 22 (1987) 55. [9] D.D. Cohen, M.F. Harrigan, Atom. Data Nucl. Data 33 (1985) 255. [10] D.D. Cohen, M.F. Harrigan, Atom. Data Nucl. Data 34 (1986) 393.
D.D. Cohen et al. / Nucl. Instr. and Meth. in Phys. Res. B 266 (2008) 1149–1153 [11] J.L. Campbell, Atom Data Nucl. Data 85 (2003) 291. [12] F. Folkmann, C. Gaarde, T. Huus, K. Kemp, Nucl. Instr. and Meth. 116 (1974) 487. [13] K. Ishii, S. Morita, Nucl. Instr. and Meth. B 22 (1987) 68. [14] K. Ishii, Radiat. Phys. Chem. 75 (2006) 1135.
1153
[15] K. Murozono, K. Ishii, H. Yamazaki, S. Matsuyama, S. Iwasaki, Nucl. Instr. and Meth. B 150 (1999) 76. [16] D.D. Cohen, Nucl. Instr. and Meth. 178 (1980) 481. [17] D.D. Cohen, E. Stelcer, R. Siegele, M. Ionescu, M. Prior, X-ray Spectrom., accepted for publication.
NIM B Beam Interactions with Materials & Atoms
Nuclear Instruments and Methods in Physics Research B 266 (2008) 1149–1153 www.elsevier.com/locate/nimb
Experimental bremsstrahlung yields for MeV proton bombardment of beryllium and carbon David D. Cohen *, Eduard Stelcer, Rainer Siegele, Mihail Ionescu, Michael Prior Institute for Environmental Research, Australian Nuclear Science and Technology Organisation, Private Mail Bag 1, Menai, NSW 2234, Australia Received 14 September 2007; received in revised form 22 October 2007 Available online 22 November 2007
Abstract Experimental bremsstrahlung yields for 2, 3 and 4 MeV protons on thin beryllium and carbon targets have been measured. The yields have been corrected for detector efficiency, self-absorption in the target and fitted to 9th order polynomials over the X-ray energy range 1–10 keV for easy comparison with theoretical calculations. Crown Copyright Ó 2007 Published by Elsevier B.V. All rights reserved. PACS: 34.50.Fa; 41.75.Ak; 78.70.En; 03.50.z Keywords: Bremsstrahlung; PIXE; X-rays; Backgrounds
1. Introduction Particle induced X-ray emission (PIXE) is a well established multi-elemental analysis technique that has been applied for many years in accelerator laboratories around the world [1–10]. There are several well established PIXE codes, such as PIXAN [3], GUPIX [4,5] and GeoPIXE [6] currently being used to determine characteristic X-ray peak areas and to convert these to well determined elemental concentrations within a matrix. Experimental fluorescence yields, characteristic a, b and c peak ratios, Koster-Cronig transition rates and X-ray production cross-sections for a broad range of K and L lines are generally well determined [7–11]. One of the weaker links in this fitting process is related to a better physics-based determination of the bremsstrahlung background particularly under low intensity characteristic X-ray lines. The determination of the bremsstrahlung background for PIXE spectra in the 1–20 keV X-ray energy region is usually performed empirically and not from first principles
*
Corresponding author. Tel.: +61 2 9717 3042; fax: +61 2 9717 3257. E-mail address: [email protected] (D.D. Cohen).
using bremsstrahlung production cross-sections [12–15]. It is recognised that there are at least three significant contributions to the bremsstrahlung background in PIXE spectra [14]. In the 1–2 keV X-ray region quasi-free electron bremsstrahlung (QFEB) dominates falling rapidly to zero above this energy, this is produced by target electrons moving in the projectile frame. In the 2–7 keV region secondary electron bremsstrahlung (SEB), tends to dominate, this is produced when the ion ejects an electron from the target atom which is then scattered by another target atom. In the higher 5–15 keV region the atomic bremsstrahlung (AB) dominates and is produced when the ion excites inner shell (K and L) target atoms to the continuum which then return to their original states. Each of these contributions depends on the target atomic number Z2 and mass M2, the ion atomic number Z1 and mass M1 as well as the ion energy E1. Recently, Ishii and associated co-workers have identified theoretical models for each of these bremsstrahlung components and their production cross-sections [13–15]. This makes it possible to predict total bremsstrahlung cross-sections for proton PIXE, as well as for heavier ion PIXE, for most commonly used target materials. Here we report on parts of a systematic study experimental bremsstrahlung yields for 1–10 keV X-rays for
0168-583X/$ - see front matter Crown Copyright Ó 2007 Published by Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2007.10.040
2–4 MeV proton bombardment of beryllium and carbon targets. These yields have been corrected for detection efficiency and target absorption effects to better test the theoretical predictions of bremsstrahlung background in PIXE spectra. Hopefully these data will lead to a full, more physically realistic, PIXE spectrum fitting model covering most elements in the periodic table for both the characteristic lines and the bremsstrahlung background. 2. Theoretical bremsstrahlung production Fig. 1 shows typical production cross-sections [b/ (keV sr)] for 3 MeV protons on pure carbon taken from the theoretical work of Murozono et al. [15]. The different regions of interest for the QFEB, SEB and AB contributions are clearly distinguishable in the figure. Above 10 keV AB dominates and below 1 keV QFEB dominates with SEB being the primary contributor in the intermediate X-ray regions between 2 and 10 keV. Between 1 and 10 keV the cross-sections span 7 orders of magnitude from 1 b/(keV sr) down to 107 b/(keV sr). This range in cross-section is several orders of magnitude larger than the yield range (counts/(lC keV sr)) experienced in most experimental bremsstrahlung situations for typical PIXE measurements, which, for 1–10 keV, can span yields from 104 down to 1 counts/(lC keV sr). Fig. 2 shows expected theoretical bremsstrahlung yields, derived from these cross-sections, when typical detector efficiency [16] and self-absorption corrections in the target are considered. Since the targets are relatively thin, the self-absorption correction was performed assuming that all the X-rays originated from a thin layer situated at the centre of the target. The figure shows the theoretical yields/(lC keV sr) for a 1 mg cm2 thick target of 3 MeV protons on carbon. The low energy fall off below 2 keV is predominantly due to the 75 lm beryllium window used to stop 3 MeV protons entering the detector. Between 1 and 10 keV the bremsstrahlung yields cover 5 orders of magnitude considerably raising the background and hence the minimum detectable limits for PIXE analyses.
Cross section [b/(keV.sr)]
1.E+01
3 MeVp on C
SEB
1.E+00 1.E-01 1.E-02
Total
1.E-03 1.E-04 1.E-05
AB
QFEB
1.E-06
Ylds [cnts/(keV.sr.µC.mgcm-2)]
D.D. Cohen et al. / Nucl. Instr. and Meth. in Phys. Res. B 266 (2008) 1149–1153
1E+06
3 MeVp on C
1E+05 1E+04
Total
1E+03 1E+02 1E+01 1E+00 0
1
2
3
4
5
6
7
8
9
10
E (keV) Fig. 2. The theoretical yields (counts/(keV sr lC mg cm2) for the total theoretical cross-sections shown in Fig. 1for a typical Si(Li) detector with 75 lm Be entrance window.
1.E+06
4MeVp on Be
Fe
Counts/ 400µ C
1150
1.E+05
Cr
1.E+04
Ni
1.E+03
aexp(-bEx) fit toγ-bkg
1.E+02 0
5
10
15
20
E (keV) Fig. 3. Experimental PIXE spectrum for 4 MeV protons on thin Be showing the gamma ray background well fitted by an exponential in the energy range 10–20 keV.
There are other significant background contributions to typical PIXE spectra; these include projectile nuclear bremsstrahlung (NA), Compton scattering in the detector of high energy gamma rays produced by nuclear reactions in the target and charging effects of some insulated targets. We will not discuss all of these here. For PIXE, Compton scattered gamma rays may contribute significantly in the 10–20 keV region as shown in Fig. 3 for 4 MeV protons on beryllium. This type of background can be well fitted by a two parameter (a, b) exponential function of the X-ray energy (Ex) in this region [a exp(bEx)], extended through to zero X-ray energy and then subtracted off the background leaving the pure bremsstrahlung background contributions in the 1–10 keV region similar to those shown in Fig. 2. Note it is an assumption that we have not fully tested yet that the exponential fit in the higher keV regions can be extended to lower energies (<10 keV) under the bremsstrahlung peak.
1.E-07 0
1
2
3
4
5
6
7
8
9
10
E (keV) Fig. 1. Bremsstrahlung cross-sections for QFEB, SEB and AB contributions for 3 MeV protons on carbon from Murozono et al. [15].
3. Results and discussion In order to accurately and precisely measure bremsstrahlung yields it is necessary to use thin solid targets of
D.D. Cohen et al. / Nucl. Instr. and Meth. in Phys. Res. B 266 (2008) 1149–1153
materials that do not have any characteristic X-rays in the energy range of interest. In our 1–10 keV X-ray range this effectively excludes all targets between Al and Zn. Furthermore these targets should be extremely pure containing no trace elements which also produce characteristic lines in our region of interest. PIXE is a very sensitive technique and this is very difficult to achieve. Beryllium and carbon are two elements that can meet these criteria if they can be obtained in a pure enough form. The thickness of these targets should be sufficient to contain the ion induced electrons (several lm) but not so thick so that self-absorption of the emergent X-rays at a few keV becomes a problem. For this work we used beryllium and carbon targets which were 1843 ± 56 and 1767 ± 54 lg cm2 thick, respectively. The Be target was 99.89% pure with Cr, Mn, Fe and Ni contaminants above 10 lg/g, and the carbon was 99.97% pure with S and Cl as contaminants above 10 lg/g. The total bremsstrahlung yields were obtained for 2, 3 and 4 MeV proton bombardment using the sum of 5 individual 40 lC runs on each target with between 10 and 30 nA of protons from a 6 mm diameter beam. The count rates into all spectra were deliberately kept low to keep dead times below 1% and reduce pileup effects which would change the shape of the bremsstrahlung backgrounds. The 1E+05
Counts/ 200µC
1E+04 4MeV 1E+03 1E+02 3MeV 2MeV
1E+01 1E+00 0
1
2
3
4
5
6
7
8
9 10 11 12 13 14
E (keV) Fig. 4. Experimental yields for 2, 3 and 4 MeV protons on Be 1843 lg cm2.
1.E+05
Counts/ 200µC
1.E+04
1151
full 200 lC spectra are shown in Figs. 4 and 5 for beryllium and carbon targets, respectively. The solid curve under each spectrum is the bremsstrahlung fitted background used to produce the normalised yields calculated below. Each of the spectra contained a Si Ka fluorescence peak, small discontinuities associated with the SiK and AuM edges as well as the characteristic peaks associated with the trace contaminants. The SiK and AuM edge discontinuities have been discussed in detail elsewhere [16,17] and were used to quantify the detector silicon dead layer and the gold front contact layer thicknesses. The Si Ka fluorescence peak was produced by the bremsstrahlung radiation (above 1.838 keV) fluorescing the detector crystal itself. When the Compton scattered gamma ray component is removed the beryllium bremsstrahlung background peaks at lower X-ray energies than for the corresponding situations in carbon. This is due to the target atomic number (Z2) dependence of the cross-sections for these two targets [14]. Each 200 lC spectrum was divided by the detector efficiency [16] and corrected for self-absorption in the target channel by channel. The gamma ray back ground between 10 and 20 keV, if present, was fitted with a two parameter exponential function and stripped off. The resulting spectrum was then normalised to unit charge (lC), unit solid angle (sr) and unit target thickness (1 mg cm2), providing an efficiency and absorption corrected yield for each ion energy and target used. Typical experimental errors associated with each step of this process are given in Table 1. The natural log of this normalised yield (Yld) was fitted to a 9th order polynomial in the natural log of the X-ray energy Ex over the range 1–10 keV. That is, 2
9
lnðYldÞ ¼ a0 þ a1 ln Ex þ a2 ðln Ex Þ þ þ a9 ðln Ex Þ :
ð1Þ
The 10 coefficients for these polynomial fits are given in Table 2 for each ion energy and target. They are only applicable for 1 < Ex < 10 keV and should not be used outside this range. They have been quoted to 10 significant figures to avoid round off errors but generally reproduce the experimental bremsstrahlung cross-sections to ±6% or better at the 95% confidence interval over this range. Fig. 6 shows a comparison between the theoretical yield predictions from the cross-sections of Murozono et al. [15] and the current experimental polynomial fits for 3 MeV protons on beryllium and carbon.
1.E+03 4MeV 1.E+02
2MeV 3MeV
1.E+01
Table 1 Typical experimental errors associated with each step of the normalised yield calculations Typical experimental percentage errors (%) Type
1.E+00 0
1
2
3
4
5
6
7
8
9 10 11 12 13 14
E (keV) Fig. 5. Experimental yields for 2, 3 and 4 MeV protons on C 1767 lg cm2.
at 1 keV
Self-absorption ±10 Detector ±170 Counting <±1 Total ±170 sr ± 5%, lC ± 3%, qx ± 3%
at 5 keV
at 10 keV
<±1 ±2 ±2 ±7
<±1 <±1 ±20 ±20
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D.D. Cohen et al. / Nucl. Instr. and Meth. in Phys. Res. B 266 (2008) 1149–1153
Table 2 The 10 coefficients for the 9th order polynomial fits to the normalised bremsstrahlung yields for 2, 3 and 4 MeV protons on thin beryllium and carbon targets Beryllium
Counts with absorp/ (sr.keV.µC.mgcm-2)/100%Eff
a0 a1 a2 a3 a4 a5 a6 a7 a8 a9
Carbon
2 MeV
3 MeV
4 MeV
2 MeV
3 MeV
4 MeV
21.695235123 37.535477096 161.839939141 444.815912661 751.282273099 788.466632656 507.777557541 194.330412297 40.505488754 3.539516300
22.507479338 30.037382030 77.629671566 101.943670523 38.520636188 51.373203885 71.320050991 36.798673670 8.953738897 0.853677117
23.102958952 37.347459358 125.960309085 250.675196976 297.607971087 221.648694409 104.893674327 30.780362067 5.116854890 0.368109536
23.940800659 39.469435410 115.939402245 219.423803115 275.415124427 235.739146058 131.988545631 45.568495125 8.751651843 0.713709671
24.540257524 32.899546666 50.802870595 22.214297654 188.271382161 275.915302992 201.348869046 80.706727689 16.953834918 1.460876631
25.200270646 37.868856277 87.651819768 116.593775820 95.099571688 56.411436847 28.165460971 11.010676614 2.603931922 0.258763572
1E+09 1E+08 3MeV on C
1E+07 1E+06 3MeV on Be
1E+05 1E+04 1E+03 1E+02 0
1
2
3
4
5
6
7
8
9
10
E (keV) Fig. 6. Comparison of Murozono et al. [15] theoretical normalised yields (dashed curves) with current experimental yields (solid curves) for 3 MeV protons on Be and C.
tor efficiency and target absorption and then fitted to 9th order polynomials. The coefficients of the fits reproduce these normalised yields to better than ±6% over the X-ray energy 1–10 keV and can be used to make direct comparisons with theoretical predictions for bremsstrahlung production. Comparisons with the theoretical crosssections of Murozono et al. [15] show (1) the current theoretical calculations generally under predict the experimental measurements by factors of between 1 and 3 around the bremsstrahlung peak; (2) there are small but significant differences for X-ray energies above 7 keV and theory may not accurately reproduce the experimental bremsstrahlung shape in this atomic bremsstrahlung (AB) region. More work is currently being performed to resolve some of these issues. Acknowledgements
The theoretical yields have been scaled up by 2.04 for beryllium and 2.67 for carbon to approximately match the experimental data in the 3–5 keV energy range. Generally the theoretical shape matched experiment in the mid X-ray energy range from 3 to 6 keV but the theory under predicted the experimental yields for energies above 6 keV. In the region between 8 and 10 keV counting statistics become smaller and their associated errors larger (see Table 1). This may account for some of the deviations of the carbon and beryllium experimental data above 6 keV not reproduced in the theoretical dashed line data of this figure. In the lower energy region around 1 keV and below the experimental data are unreliable as the detector efficiencies [16] are well below 0.01%, falling rapidly and have large uncertainties (see Table 1).
4. Summary Thin Be and C targets have been used to accurately and precisely measure bremsstrahlung yields induced by 2, 3 and 4 MeV protons. These yields have been normalise to unit charge (lC), unit solid angle (sr), corrected for detec-
We would like to acknowledge the help of the 2 MV STAR accelerator staff in several aspects of this work. This work was partly performed within the framework of IAEA CRP G.4.20.02 Unification of Nuclear Spectrometries. References [1] S.A.E. Johannson, J.L. Campbell, PIXE: A Novel Technique for Elemental Analysis, Wiley and Sons, New York, 1988. [2] D.D. Cohen, E. Clayton, Ion induced X-ray emission, in: J.R. Bird, J.S. Williams (Eds.), Ion Beams for Materials Analysis, Academic Press, Sydney, 1989, Chap 5. [3] E. Clayton, D.D. Cohen, P. Duerden, Nucl. Instr. and Meth. B 22 (1987) 64. [4] J.A. Maxwell, J.L. Campbell, W.J. Teesdale, Nucl. Instr. and Meth. B 43 (1989) 218. [5] J.A. Maxwell, W.J. Teesdale, J.L. Campbell, Nucl. Instr. and Meth. B 95 (1995) 407. [6] C.G. Ryan, D.R. Cousens, S.H. Sie, W.L. Griffin, Nucl. Instr. and Meth. B 49 (1990) 217. [7] D.D. Cohen, E. Clayton, Nucl. Instr. and Meth. B 22 (1987) 59. [8] D.D. Cohen, Nucl. Instr. and Meth. B 22 (1987) 55. [9] D.D. Cohen, M.F. Harrigan, Atom. Data Nucl. Data 33 (1985) 255. [10] D.D. Cohen, M.F. Harrigan, Atom. Data Nucl. Data 34 (1986) 393.
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