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Theoretical estimation of PIXE detection limits
Nuclear Instruments and Methods in Physics Research 834 (1988) 209-216 North-Holland, Amsterdam
THJZORETICAL ESTIMATION
K. ISHII Cyclotronand
OF PIXE DETECTION
209
LIMITS
Radioisotope Center, Tohoku University, 980 Sendai, Japan
S. MORITA Research Center of Ion Beam Technology, Hosei University, Koganei, 184 Tokyo, Japan
Received 17 November 1987 and in revised form 11 April 1988
Taking into account the various kinds of backgrounds in PIXE, the detection limit has been theoretically derived. A contour representation of the detection limit for trace-element analyses in biological samples has been calculated, and it is shown that the best detection limit is obtained with about 3 MeV protons.
1. Introduction
The elemental analysis by particle-induced X-ray emission has been developed by Johansson et al. [l] and is called PIXE. Trace elements of the order of parts per million (ppm), or sometimes sub-ppm, concentrations can be detected by this method. Even an element of the order of parts per trillion (ppt) can be quantitatively analysed by PIXE when combined with preconcentration techniques [2]. In a PIXE spectrum, characteristic X-ray peaks always overlap continuum backgrounds. As a small characteristic X-ray peak cannot be distinguished from fluctuations in the backgrounds, the intensity of the background determines the detection limit and the detection limit is usually defined by Ns = 3fi, where Ns is the total number of counts of a characteristic X-ray peak and N, is the number of background counts included in the full width at half maximum (FWHM) of the characteristic X-ray peak. Johansson et al. [l] have measured these continuum X-ray spectra on a carbon foil as a function of incident proton energy, and they obtained a representation of the detection limit as a function of the proton energy and of the atomic number of the element to be detected [l]. This result shows that the most suitable proton energy for PIXE is l-3 MeV and this result has been widely used. However, the detection limit of PIXE depends generally on the main elements in the matrix and the most suitable condition of PIXE is considered to change depending on the sample to be analysed. If we could theoretically estimate the detection limit, we would be able to find the most suitable condition for each sample. Studies of the continuum X-ray background were first reported by Folkmann et al. [3] and by Ishii et al. [4], and the main component was found to be secondary-electron bremsstrahlung (SEB). It was impossible, however, to estimate theoretically the detection limit, as the production mechanism for the background had not been fully investigated. Recently, it was elucidated by I&ii et al. [S] that the atomic bremsstrahlung (AB) becomes predominant at lower projectile energy whereas the quasi-free electron bremsstrahlung (QFEB) becomes appreciable at higher projectile energy [6], in addition to SEB in the intermediate energy region. Not only the excitation function of the production cross sections of these bremsstrahlungs, but also the angular distributions have been studied [7]. Thus, it is now possible to calculate the production of the background over a wide range of the projectile energy 181. Here, the detection limit of PIXE will theoretically be discussed and will be evaluated for the case of analyses of biological samples. 0168-583X/88/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
210
K. Ishii, S. Morira
/
Theoretical estimation of PIXE
detection limits
2. Theoretical
As has been mentioned, the detection limit value of the detection limit is expressed by “z -= no
is usually
defined
by N, = 3{%.
3 {Q dS2 n,[da,(Z)/dfi]cr(Z)
From
this relation,
the
(1)
ah(Z)
where n, is the atomic concentration of the matrix element, nz is that of a trace element Z, Q is the number of projectiles, dS2 is the solid angle subtended by a detector, and du,(Z)/dG, cr(Z), ah(Z), [daa( Z)/d( Ao) d&8] are, respectively, the production cross section of K or L X-rays for the trace element, the detection efficiency, absorption of X-rays by windows and others, and the production cross section of the background. The energy resolution of the detector (FWHM) is denoted by A E,. The production cross section of characteristic X-rays has been well studied theoretically and experimentally, especially for proton and o-particle bombardment, and is expressed by
(2) Here, ‘a: is the K X-ray production cross section, wx is the fluorescence yield for the K-shell, UL is the K-shell ionization cross section, at, is the La X-ray production cross section, w3 is the fluorescence yield for the L,-shell, F, is the radiative transition width between L, and M,.,, F, is the width of the L,-shell, UL is the ionization cross section for the L,-shell, and fij is the Coster-Kronig transition probability. These cross sections and coefficients have been tabulated for values by Bambynek et al. [9] and theoretical values by w,‘, +, f,3? fi, . . . experimental Krause et al. [lo], r,, r, 0.. calculated values by Scofield [II], a;, u;. . . * calculated values by Chohen and Harrigan [12], which take account of effects of the (A) Coulomb deflection and energy loss of the projectile, the binding energy effect, the polarization effect, and the electronic relativistic effect (ECPSSR-PWBA).
The detection
efficiency
of a Si(Li) detector
~,(hw)=exp[-(~c~e~~+~l~~X~~+~lsl
is expressed
by
~~~~)I{~-exp[-~~~~~~I}~
(3)
Here, Aw is the photon energy, xar and pBe are thickness and absorption coefficient of the Be window of the detector, xAU and pAu are thickness and absorption coefficient of the Au layer on the Si(Li) crystal of the detector, and Axs,, xs, and clsi are, respectively, the thickness of the insensitive region of the Si(Li) crystal, the thickness and absorption coefficient of the Si crystal. Background continuum X-rays [13] are produced by (1) SEB [3,4,7], (2) QFEB [6], (3) AB [5,7] or radiative ionization (RI), and (4) nuclear bremsstrahlung (NB) [6]. In the case of heavy-ion bombardment, (5) radiative electron capture (REC) [14] and (6) molecular orbital X-rays [15] contribute to the continuum in addition to these bremsstrahlungs and the background increases. Moreover, a characteristic X-ray peak becomes broader because of multiple ionization. Thus, in general, heavy-ion projectiles are not used in PIXE. The production cross sections of these bremsstrahlung have been theoretically derived by Ishii et al. as expressed by (1) SEB: d,,“EB
dtid(Ao)
= xN,?1;;Zz( ,
$‘~~Z,~(C,
+ C, sin28),
(4)
K. Ishii. S. Morita / Theoretical estimation of PIXE detection limits
+-[8+(s-x)‘]
forI$-+scq for 1 - $ r s 2 0, fors+,
+9(y+8s2+8)[(1+s)(y-2+(x-1)(2x)*] +4(8y
-(l
-
3y2 - 27~s~ + 22s2 - 24s4 - 24)12(x
+ 1)
for /~JSs100.
+s)(2x~+2-2s+y)~) $2
+ ES4 4
+ ss6 16 + ;;y4 6
g2 =
4(u)
- 1)(x2+x
for 1 - $ r s 2 0, for+1.
= j d+” sin 6, de,
fi:,(~)-
Here, E=E,+ Vi, x2 xS2 + y, T= dm, y=E/T,, S=VJV,, Tr= I/~M,v,~; and Ni, V; and f;(u) are the number of electrons, the ionization energy and the velocity distribution for the i-shell electron, respectively; ZP, up are the atomic number and velocity of the projectile and Z, is the target-atomic number, r is the average io~tion potential of the target atom, and a0 is the Bohr radius [6]. (2) QFEB: &QFEB dQd(tto) h@c.,.
l-/32 GCBB(T,*
= l-@cos$,
1-8cosBAw = (1 _ 82),,Z
’
~%M?
8).
212
K. Ishii, S. Mon’ra / Theoretical estimation of PIXE detection limits
= fo,(l - (ttw + Q/T,), VImax ttw’ = hw f V;+ +mevz2, T,’ = 7;(1 - c?&J*, P;(u,) =J
dux/ du, f;:(vu uy’ uz).
The cross section aBrcmsin the above equation is expressed by 0
for ho’ > T,’
I [Xln( 5) + 5~s
and
8[(7 - T) sin28 + $(cos20 - $sin*e)(lOT+
T=
- 2/3’J7;COS
8(C0S2B
-
3 - 3T2)]
2 sin28) I
r,’ - Aid’ T,’
a
The factor g(&, 6) is the correction term for the Coulomb deflection and is given by
with
where Ry is the Rydberg constant 16,161. (3) AB:
where S,(q) and S,(q) are given by eqs. (12) and (16) of ref. [8]. (4) NB: daNB dS2 d( tto) where m,, is the mass of the projectile [13].
K. Ishii, S. Morita / Theoretical estimation
of PIXE detection limits
213
In addition to these bremsstrahlungs, the following backgrounds must be taken into consideration: (7) gamma rays, which are produced by the Coulomb excitation of target nuclei, are scattered by electrons in the detectors, and produce the Compton background; (8) projectile particles, which are scattered by target nuclei and are incident on the detector, produce large pulses and pile up with characteristic X-ray pulses, giving rise to the Rutherford background; (9) the background due to tails of the response function of the detector; (10) the background due to cosmic rays and radiation from room walls; (11) the background due to electronic noise. The Compton background strongly depends on the matrix element of a sample and cannot be neglected for metallic elements, which usually have excited states of several hundred keV. On the other hand, the matrix elements of biological or environmental samples, in general, are light elements such as H, C, N, and 0, the nuclei of which have the first excited states at 2-6 MeV, so that in PIXE measurements of biological samples with incident protons below 6 MeV the Compton background is considered to be small. The Rutherford background can be eliminated simply by using a gated circuit or by inserting an absorber of Mylar foil between the target and the detector. However, the absorber for eli~nating the background decreases the sensitivity for light elements. Light elements can be measured without the absorber separately from heavier ones, as the Rutherford background is negligible in the light-element region of the X-ray spectrum in comparison with the bremsstrahlungs. It must be noted that the absorber becomes thicker for higher energy projectiles and the thicker absorber reduces the sensitivity for heavier elements. The background due to the tail of the response function is related to the electronic properties of the detector. An improvement in this respect has been reported for a Si(Li) detector: ECON (Philip Co.). The background due to cosmic rays or radiation from room walls can be reduced relatively by using a larger solid angle for the detector or by increasing the beam intensity. From the considerations mentioned above, it can be said that the substantial background in PIXE using proton or a-particle beams is the bremsstrahlungs of SEB, QFEB, AB and NB, and they determine the detection limit. Next, it must be mentioned that SEB, QFEB and AB are not isotropic in their angular distributions. Because of the relativistic effect, SEB and QFEB have forward peakings, which become significant with increase in the projectile energy [6,7], so that the sensitivity of PIXE is higher in the backward direction with respect to the incident beam [17]. On the basis of the above discussion, we can now estimate the detection limit for analysing biological samples from the tables of (A), and the formulae of eqs. (l-7).
3. Detection limit for PIXELanalysis of biological samples The matrix of biological samples consists of H, C, N and 0, and here we assume a matrix of the element oxygen to evaluate the detection limit for biological samples. The background bremsstr~lungs for an oxygen target were calculated from the theoretical formulae of eqs. (4)-(7) and are shown in figs. la, b, and c, respectively, for incident proton energies Ep of 0.6,3, and 5 MeV. Contributions from QFEB, SEB, AB and NB were calculated for the X-ray emission angle of 135 O. It can be seen that, at E,, = 0.6 MeV, SEB and QFEB do not contribute at all, and AB and NB are predominant, respectively, in the regions ttw = 1.4-6 keV and hw > 6 keV. At Ep = 3 MeV, SEB, AB and NB are predominant, respectively, in the regions of tiw = 1.4-6 keV (= T,), tiw = 6-12 keV, and Aw 2 12 keV. For the higher energy of Ep = 5 MeV, the cont~bution of QFEB appears in the low-energy X-ray region (Ao < 7;). By using the X-ray production cross sections tabulated in (A), background-production cross sections calculated from the formulae of eqs. (4)-(7), and eqs. (l)-(3), the detection limit for analysing trace elements in a sample of matrix element oxygen has been evaluated under the following conditions: Incident ions: protons of 0.6-5 MeV Integrated beam current: 1 PC Detection angle: 135” Solid angle of the detector: 4n/(50)*sr
K. Ishii, S. Morita / Theoretical estimation of PIXE detection limits
214
b
c QFEB b)
3 MeV a
c )
O-target
0 - targer 5 Mev
Proton
8 = 135’ Tn. i
0
I
0
Proton
8 = 135’
-target proton
5
Fig. 1. Production
Distance The results
3
15
IL
hw
Detector:
,@L
>
I
lo-‘-
Iv* I5
10
cross sections
hw
of NB, AB, SEB and QFEB for proton bombardment MeV (b), and 5 MeV (c).
of an oxygen
target
I keV1
at E, = 0.6 MeV (a), 3
2-mil Be window, 200 A thick Au electrode, Si(Li) crystal of 4 mm diameter and 4.4 mm length. Energy resolution of 160 eV for 6 keV X-rays. between target and detector: 50 mm. of this calculation are shown in fig. 2. The lefthand side of the dotted line in this figure is
El
I
I
I
I
I
I
I
I
I
IO
20
30
40
50
60
70
80
90
lo+
(0.1-0.5)x (0.5-
I
( I -
5 Ix lo+
lssssi
(0.5 -
I )xIo-5
EEEI
( I -
5 1 x lo-5
El
I
5
lluikeV)
>
1 x lo+
5 x IO’”
-1
Z Fig. 2. Contour representation of the detection limit for PIXE analysis of biological samples by proton bombardment. The detection angle of X-rays is taken as 135 “. The lefthand side of the dotted line is based on K X-ray detection and the righthand side on La X-ray detection.
K. Ishii, S. Morita
/ Theorerical estimation of PIXE
detection limits
215
estimated for K X-ray detection and the righthand side is for L X-ray detection. It is seen from this figure that, at low bombarding energy, the detection limit is high - the sensitivity is low - and we can obtain the highest sensitivity at E, i 3 MeV for almost all elements. This figure shows high sensitivity for protons background due to the higher than 5 MeV. As has been mentioned before, however, the Compton Coulomb excitation would not be negligible for this higher proton energy and this region is not considered to be practical. Though the sensitivity itself is highest in the region E, = 3-6 MeV [6,18], the absorber for eliminating the Rutherford background must be thick for E, = 6 MeV and the sensitivity then decreases because of its X-ray absorption. For 3 MeV protons, the thickness of the Mylar absorber needed to stop the scattered proton is - 0.1 mm, and its absorption for X-rays of elements heavier than Ca is quite small. Therefore, taking account of the Rutherford background, the Compton background, and the behavior of detection limit shown in fig. 3, it is concluded that proton beams of about 3 MeV would be the best projectiles for PIXE. The behavior of the detection limit in the low projectile-energy region, shown in fig. 2, is considerably different from that of Johansson et al. [l]. That result shows a high sensitivity of 0.1-0.5 x 10e6 for the elements of Z = 20-25 even in the energy region lower than 3 MeV, whereas, in the present result, the sensitivity gets worse at lower energies. Both results are in agreement in supporting the use of 3 MeV protons to obtain high sensitivity.
4. Summary The origins of the background in PIXE have been discussed. Taking into consideration the unavoidable sources of background and the removable ones, it is pointed out that light ions, such as protons, are preferable to heavy ions for PIXE. The contribution from SEB, QFEB, AB and NB in an oxygen target was calculated for 0.6, 3.0, and 5.0 MeV protons. Using the inner-shell ionization cross section calculated from the ESCCR-PWBA theory, the detection limit of PIXE for analysing trace elements in a biological sample has been evaluated, and the results show high sensitivity for proton energy higher than 3 MeV. However, because of the Compton and the Rutherford backgrounds, about 3 MeV protons are considered to be the most suitable projectile for PIXE.
This work was supported by the Special Project Research Ministry of Education, Science and Culture.
on Ion Beam Interaction
with Solids from the
References [l] [2] [3] [4] [5] [6] [7] [8] [9] [lo] [ll] [12] [13]
S.A.E. Johansson and T.B. Johansson, Nucl. Instr. and Meth. 137 (1976) 472. E.M. Johansson and S.A.E. Johansson, Nucl. Instr. and Meth. B3 (1984) 154. F. Folkmann, C. Gaarde, T. Huns, and K. Kemp, Nucl. Instr. and Meth. 116 (1974) 487. K. Ishii, S. Morita, and H. Tawara, Phys. Rev. Al3 (1976) 131. K. Ishii and S. Morita, Phys. Rev. A30 (1984) 2278. A. Yamadera, K. Ishii, K. Sera, and S. Morita, Phys. Rev. A23 (1981) 24; T.C. Chu, K. Ishii, A. Yamadera, M. Sebata, and S. Morita, Phys. Rev. A24 (1981) 1720. K. Ishii, M. Kamiya, K. Sera, and S. Morita, Phys. Rev. Al5 (1977) 2126; K. Gzawa, J.H. Chang, Y. Yamamoto, S. Morita, and K. Ishii, Phys. Rev. A33 (1986) 3018. K. Ishii and S. Morita, Phys. Rev. A30 (1984) 2278. W. Bambyncck, B. Crasemann, R.W. Fink, H.U. Freund, H. Mark. C.D. Swift, R.E. Price, and P. Vengopala Rao, Rev. Mod. Phys. 44 (1972) 716. M.O. Krause, J. Phys. Chem. Ref. Data 8 (1979) 315. J.H. Scofield, Phys. Rev. 179 (1969) 9. D.D. Cohen and M. Harrigan, At. Data Nucl. Data Tables 33 (1985) 255. K. Ishii and S. Morita, Nucl. Instr. and Meth. B3 (1984) 57.
216
K. Ishir, S. Morua / Theorerical esfimarlon of PIXE derection lrmus
[14] H.W. Schnopper. J.P. Dlvaille, K. Kalata, A.R. Sohval, M. Abdulwahab, K.W. Jones, and H.E. Wegner. 61. [lS] F.W. Saris. W.F. van der Weg. H. Tawara, and R. Laubert. Phys. Rev. Lett 28 (1972) 717. [16] K. Ishii. K. Sera. H. Arai, S. Morita. and K. Tokuda. Phys. Rev. A27 (1983) 2225. [17] T.C. Chu, K. Ishii, A. Yamadera, M. Sebata, and S. Morita. Nucl. Instr. and Meth. 190 (1981) 395. (181 A. Yamadera K. I&ii. K. Sera, S. Morita, and T.C. Chu, Nucl. Instr. and Meth. 181 (1981) 15.
Phys. Lett. 47A (1974)
THJZORETICAL ESTIMATION
K. ISHII Cyclotronand
OF PIXE DETECTION
209
LIMITS
Radioisotope Center, Tohoku University, 980 Sendai, Japan
S. MORITA Research Center of Ion Beam Technology, Hosei University, Koganei, 184 Tokyo, Japan
Received 17 November 1987 and in revised form 11 April 1988
Taking into account the various kinds of backgrounds in PIXE, the detection limit has been theoretically derived. A contour representation of the detection limit for trace-element analyses in biological samples has been calculated, and it is shown that the best detection limit is obtained with about 3 MeV protons.
1. Introduction
The elemental analysis by particle-induced X-ray emission has been developed by Johansson et al. [l] and is called PIXE. Trace elements of the order of parts per million (ppm), or sometimes sub-ppm, concentrations can be detected by this method. Even an element of the order of parts per trillion (ppt) can be quantitatively analysed by PIXE when combined with preconcentration techniques [2]. In a PIXE spectrum, characteristic X-ray peaks always overlap continuum backgrounds. As a small characteristic X-ray peak cannot be distinguished from fluctuations in the backgrounds, the intensity of the background determines the detection limit and the detection limit is usually defined by Ns = 3fi, where Ns is the total number of counts of a characteristic X-ray peak and N, is the number of background counts included in the full width at half maximum (FWHM) of the characteristic X-ray peak. Johansson et al. [l] have measured these continuum X-ray spectra on a carbon foil as a function of incident proton energy, and they obtained a representation of the detection limit as a function of the proton energy and of the atomic number of the element to be detected [l]. This result shows that the most suitable proton energy for PIXE is l-3 MeV and this result has been widely used. However, the detection limit of PIXE depends generally on the main elements in the matrix and the most suitable condition of PIXE is considered to change depending on the sample to be analysed. If we could theoretically estimate the detection limit, we would be able to find the most suitable condition for each sample. Studies of the continuum X-ray background were first reported by Folkmann et al. [3] and by Ishii et al. [4], and the main component was found to be secondary-electron bremsstrahlung (SEB). It was impossible, however, to estimate theoretically the detection limit, as the production mechanism for the background had not been fully investigated. Recently, it was elucidated by I&ii et al. [S] that the atomic bremsstrahlung (AB) becomes predominant at lower projectile energy whereas the quasi-free electron bremsstrahlung (QFEB) becomes appreciable at higher projectile energy [6], in addition to SEB in the intermediate energy region. Not only the excitation function of the production cross sections of these bremsstrahlungs, but also the angular distributions have been studied [7]. Thus, it is now possible to calculate the production of the background over a wide range of the projectile energy 181. Here, the detection limit of PIXE will theoretically be discussed and will be evaluated for the case of analyses of biological samples. 0168-583X/88/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
210
K. Ishii, S. Morira
/
Theoretical estimation of PIXE
detection limits
2. Theoretical
As has been mentioned, the detection limit value of the detection limit is expressed by “z -= no
is usually
defined
by N, = 3{%.
3 {Q dS2 n,[da,(Z)/dfi]cr(Z)
From
this relation,
the
(1)
ah(Z)
where n, is the atomic concentration of the matrix element, nz is that of a trace element Z, Q is the number of projectiles, dS2 is the solid angle subtended by a detector, and du,(Z)/dG, cr(Z), ah(Z), [daa( Z)/d( Ao) d&8] are, respectively, the production cross section of K or L X-rays for the trace element, the detection efficiency, absorption of X-rays by windows and others, and the production cross section of the background. The energy resolution of the detector (FWHM) is denoted by A E,. The production cross section of characteristic X-rays has been well studied theoretically and experimentally, especially for proton and o-particle bombardment, and is expressed by
(2) Here, ‘a: is the K X-ray production cross section, wx is the fluorescence yield for the K-shell, UL is the K-shell ionization cross section, at, is the La X-ray production cross section, w3 is the fluorescence yield for the L,-shell, F, is the radiative transition width between L, and M,.,, F, is the width of the L,-shell, UL is the ionization cross section for the L,-shell, and fij is the Coster-Kronig transition probability. These cross sections and coefficients have been tabulated for values by Bambynek et al. [9] and theoretical values by w,‘, +, f,3? fi, . . . experimental Krause et al. [lo], r,, r, 0.. calculated values by Scofield [II], a;, u;. . . * calculated values by Chohen and Harrigan [12], which take account of effects of the (A) Coulomb deflection and energy loss of the projectile, the binding energy effect, the polarization effect, and the electronic relativistic effect (ECPSSR-PWBA).
The detection
efficiency
of a Si(Li) detector
~,(hw)=exp[-(~c~e~~+~l~~X~~+~lsl
is expressed
by
~~~~)I{~-exp[-~~~~~~I}~
(3)
Here, Aw is the photon energy, xar and pBe are thickness and absorption coefficient of the Be window of the detector, xAU and pAu are thickness and absorption coefficient of the Au layer on the Si(Li) crystal of the detector, and Axs,, xs, and clsi are, respectively, the thickness of the insensitive region of the Si(Li) crystal, the thickness and absorption coefficient of the Si crystal. Background continuum X-rays [13] are produced by (1) SEB [3,4,7], (2) QFEB [6], (3) AB [5,7] or radiative ionization (RI), and (4) nuclear bremsstrahlung (NB) [6]. In the case of heavy-ion bombardment, (5) radiative electron capture (REC) [14] and (6) molecular orbital X-rays [15] contribute to the continuum in addition to these bremsstrahlungs and the background increases. Moreover, a characteristic X-ray peak becomes broader because of multiple ionization. Thus, in general, heavy-ion projectiles are not used in PIXE. The production cross sections of these bremsstrahlung have been theoretically derived by Ishii et al. as expressed by (1) SEB: d,,“EB
dtid(Ao)
= xN,?1;;Zz( ,
$‘~~Z,~(C,
+ C, sin28),
(4)
K. Ishii. S. Morita / Theoretical estimation of PIXE detection limits
+-[8+(s-x)‘]
forI$-+scq for 1 - $ r s 2 0, fors+,
+9(y+8s2+8)[(1+s)(y-2+(x-1)(2x)*] +4(8y
-(l
-
3y2 - 27~s~ + 22s2 - 24s4 - 24)12(x
+ 1)
for /~JSs100.
+s)(2x~+2-2s+y)~) $2
+ ES4 4
+ ss6 16 + ;;y4 6
g2 =
4(u)
- 1)(x2+x
for 1 - $ r s 2 0, for+1.
= j d+” sin 6, de,
fi:,(~)-
Here, E=E,+ Vi, x2 xS2 + y, T= dm, y=E/T,, S=VJV,, Tr= I/~M,v,~; and Ni, V; and f;(u) are the number of electrons, the ionization energy and the velocity distribution for the i-shell electron, respectively; ZP, up are the atomic number and velocity of the projectile and Z, is the target-atomic number, r is the average io~tion potential of the target atom, and a0 is the Bohr radius [6]. (2) QFEB: &QFEB dQd(tto) h@c.,.
l-/32 GCBB(T,*
= l-@cos$,
1-8cosBAw = (1 _ 82),,Z
’
~%M?
8).
212
K. Ishii, S. Mon’ra / Theoretical estimation of PIXE detection limits
= fo,(l - (ttw + Q/T,), VImax ttw’ = hw f V;+ +mevz2, T,’ = 7;(1 - c?&J*, P;(u,) =J
dux/ du, f;:(vu uy’ uz).
The cross section aBrcmsin the above equation is expressed by 0
for ho’ > T,’
I [Xln( 5) + 5~s
and
8[(7 - T) sin28 + $(cos20 - $sin*e)(lOT+
T=
- 2/3’J7;COS
8(C0S2B
-
3 - 3T2)]
2 sin28) I
r,’ - Aid’ T,’
a
The factor g(&, 6) is the correction term for the Coulomb deflection and is given by
with
where Ry is the Rydberg constant 16,161. (3) AB:
where S,(q) and S,(q) are given by eqs. (12) and (16) of ref. [8]. (4) NB: daNB dS2 d( tto) where m,, is the mass of the projectile [13].
K. Ishii, S. Morita / Theoretical estimation
of PIXE detection limits
213
In addition to these bremsstrahlungs, the following backgrounds must be taken into consideration: (7) gamma rays, which are produced by the Coulomb excitation of target nuclei, are scattered by electrons in the detectors, and produce the Compton background; (8) projectile particles, which are scattered by target nuclei and are incident on the detector, produce large pulses and pile up with characteristic X-ray pulses, giving rise to the Rutherford background; (9) the background due to tails of the response function of the detector; (10) the background due to cosmic rays and radiation from room walls; (11) the background due to electronic noise. The Compton background strongly depends on the matrix element of a sample and cannot be neglected for metallic elements, which usually have excited states of several hundred keV. On the other hand, the matrix elements of biological or environmental samples, in general, are light elements such as H, C, N, and 0, the nuclei of which have the first excited states at 2-6 MeV, so that in PIXE measurements of biological samples with incident protons below 6 MeV the Compton background is considered to be small. The Rutherford background can be eliminated simply by using a gated circuit or by inserting an absorber of Mylar foil between the target and the detector. However, the absorber for eli~nating the background decreases the sensitivity for light elements. Light elements can be measured without the absorber separately from heavier ones, as the Rutherford background is negligible in the light-element region of the X-ray spectrum in comparison with the bremsstrahlungs. It must be noted that the absorber becomes thicker for higher energy projectiles and the thicker absorber reduces the sensitivity for heavier elements. The background due to the tail of the response function is related to the electronic properties of the detector. An improvement in this respect has been reported for a Si(Li) detector: ECON (Philip Co.). The background due to cosmic rays or radiation from room walls can be reduced relatively by using a larger solid angle for the detector or by increasing the beam intensity. From the considerations mentioned above, it can be said that the substantial background in PIXE using proton or a-particle beams is the bremsstrahlungs of SEB, QFEB, AB and NB, and they determine the detection limit. Next, it must be mentioned that SEB, QFEB and AB are not isotropic in their angular distributions. Because of the relativistic effect, SEB and QFEB have forward peakings, which become significant with increase in the projectile energy [6,7], so that the sensitivity of PIXE is higher in the backward direction with respect to the incident beam [17]. On the basis of the above discussion, we can now estimate the detection limit for analysing biological samples from the tables of (A), and the formulae of eqs. (l-7).
3. Detection limit for PIXELanalysis of biological samples The matrix of biological samples consists of H, C, N and 0, and here we assume a matrix of the element oxygen to evaluate the detection limit for biological samples. The background bremsstr~lungs for an oxygen target were calculated from the theoretical formulae of eqs. (4)-(7) and are shown in figs. la, b, and c, respectively, for incident proton energies Ep of 0.6,3, and 5 MeV. Contributions from QFEB, SEB, AB and NB were calculated for the X-ray emission angle of 135 O. It can be seen that, at E,, = 0.6 MeV, SEB and QFEB do not contribute at all, and AB and NB are predominant, respectively, in the regions ttw = 1.4-6 keV and hw > 6 keV. At Ep = 3 MeV, SEB, AB and NB are predominant, respectively, in the regions of tiw = 1.4-6 keV (= T,), tiw = 6-12 keV, and Aw 2 12 keV. For the higher energy of Ep = 5 MeV, the cont~bution of QFEB appears in the low-energy X-ray region (Ao < 7;). By using the X-ray production cross sections tabulated in (A), background-production cross sections calculated from the formulae of eqs. (4)-(7), and eqs. (l)-(3), the detection limit for analysing trace elements in a sample of matrix element oxygen has been evaluated under the following conditions: Incident ions: protons of 0.6-5 MeV Integrated beam current: 1 PC Detection angle: 135” Solid angle of the detector: 4n/(50)*sr
K. Ishii, S. Morita / Theoretical estimation of PIXE detection limits
214
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2-mil Be window, 200 A thick Au electrode, Si(Li) crystal of 4 mm diameter and 4.4 mm length. Energy resolution of 160 eV for 6 keV X-rays. between target and detector: 50 mm. of this calculation are shown in fig. 2. The lefthand side of the dotted line in this figure is
El
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30
40
50
60
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K. Ishii, S. Morita
/ Theorerical estimation of PIXE
detection limits
215
estimated for K X-ray detection and the righthand side is for L X-ray detection. It is seen from this figure that, at low bombarding energy, the detection limit is high - the sensitivity is low - and we can obtain the highest sensitivity at E, i 3 MeV for almost all elements. This figure shows high sensitivity for protons background due to the higher than 5 MeV. As has been mentioned before, however, the Compton Coulomb excitation would not be negligible for this higher proton energy and this region is not considered to be practical. Though the sensitivity itself is highest in the region E, = 3-6 MeV [6,18], the absorber for eliminating the Rutherford background must be thick for E, = 6 MeV and the sensitivity then decreases because of its X-ray absorption. For 3 MeV protons, the thickness of the Mylar absorber needed to stop the scattered proton is - 0.1 mm, and its absorption for X-rays of elements heavier than Ca is quite small. Therefore, taking account of the Rutherford background, the Compton background, and the behavior of detection limit shown in fig. 3, it is concluded that proton beams of about 3 MeV would be the best projectiles for PIXE. The behavior of the detection limit in the low projectile-energy region, shown in fig. 2, is considerably different from that of Johansson et al. [l]. That result shows a high sensitivity of 0.1-0.5 x 10e6 for the elements of Z = 20-25 even in the energy region lower than 3 MeV, whereas, in the present result, the sensitivity gets worse at lower energies. Both results are in agreement in supporting the use of 3 MeV protons to obtain high sensitivity.
4. Summary The origins of the background in PIXE have been discussed. Taking into consideration the unavoidable sources of background and the removable ones, it is pointed out that light ions, such as protons, are preferable to heavy ions for PIXE. The contribution from SEB, QFEB, AB and NB in an oxygen target was calculated for 0.6, 3.0, and 5.0 MeV protons. Using the inner-shell ionization cross section calculated from the ESCCR-PWBA theory, the detection limit of PIXE for analysing trace elements in a biological sample has been evaluated, and the results show high sensitivity for proton energy higher than 3 MeV. However, because of the Compton and the Rutherford backgrounds, about 3 MeV protons are considered to be the most suitable projectile for PIXE.
This work was supported by the Special Project Research Ministry of Education, Science and Culture.
on Ion Beam Interaction
with Solids from the
References [l] [2] [3] [4] [5] [6] [7] [8] [9] [lo] [ll] [12] [13]
S.A.E. Johansson and T.B. Johansson, Nucl. Instr. and Meth. 137 (1976) 472. E.M. Johansson and S.A.E. Johansson, Nucl. Instr. and Meth. B3 (1984) 154. F. Folkmann, C. Gaarde, T. Huns, and K. Kemp, Nucl. Instr. and Meth. 116 (1974) 487. K. Ishii, S. Morita, and H. Tawara, Phys. Rev. Al3 (1976) 131. K. Ishii and S. Morita, Phys. Rev. A30 (1984) 2278. A. Yamadera, K. Ishii, K. Sera, and S. Morita, Phys. Rev. A23 (1981) 24; T.C. Chu, K. Ishii, A. Yamadera, M. Sebata, and S. Morita, Phys. Rev. A24 (1981) 1720. K. Ishii, M. Kamiya, K. Sera, and S. Morita, Phys. Rev. Al5 (1977) 2126; K. Gzawa, J.H. Chang, Y. Yamamoto, S. Morita, and K. Ishii, Phys. Rev. A33 (1986) 3018. K. Ishii and S. Morita, Phys. Rev. A30 (1984) 2278. W. Bambyncck, B. Crasemann, R.W. Fink, H.U. Freund, H. Mark. C.D. Swift, R.E. Price, and P. Vengopala Rao, Rev. Mod. Phys. 44 (1972) 716. M.O. Krause, J. Phys. Chem. Ref. Data 8 (1979) 315. J.H. Scofield, Phys. Rev. 179 (1969) 9. D.D. Cohen and M. Harrigan, At. Data Nucl. Data Tables 33 (1985) 255. K. Ishii and S. Morita, Nucl. Instr. and Meth. B3 (1984) 57.
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[14] H.W. Schnopper. J.P. Dlvaille, K. Kalata, A.R. Sohval, M. Abdulwahab, K.W. Jones, and H.E. Wegner. 61. [lS] F.W. Saris. W.F. van der Weg. H. Tawara, and R. Laubert. Phys. Rev. Lett 28 (1972) 717. [16] K. Ishii. K. Sera. H. Arai, S. Morita. and K. Tokuda. Phys. Rev. A27 (1983) 2225. [17] T.C. Chu, K. Ishii, A. Yamadera, M. Sebata, and S. Morita. Nucl. Instr. and Meth. 190 (1981) 395. (181 A. Yamadera K. I&ii. K. Sera, S. Morita, and T.C. Chu, Nucl. Instr. and Meth. 181 (1981) 15.
Phys. Lett. 47A (1974)