- Email: [email protected]
Bulk analysis with heavy ion beams, calibration
Nuclear
66
Instruments
and Methods in Physics Research 81 (1984) 66-69
North-~oiiand,
BULK ANALYSlS G. BLONDIAUX C.N.R.S.
G.
Amsterdam
WITH HEAVY 1ON BEAMS, CAL~B~TI~~ and J.L. DEBRUN 3A, Rue de In
- Seruice du Cycbrron,
Fkrollerie
45045 O&nns CPdex, irrorxe
COSTA
C.N.R.S .- Centre de Reckerches Nucl&zires, Stra.qbourg, France A. KATSANOS and G. VOURVOPOULOS Nuclear center Demokritos, A them, Greece Received 10
June 1983
It is shown that for bulk analysis with heavy ion beams, one does not need to know the stopping power of the heavy ions. Instead, hydrogen or helium stopping powers at the same speed, can be used with an accuracy of l--2%. Also, it is shown that when using Coulomb excitation, the calculated cross-section curve {arbitrary units) is accurate enough to be used for the determination of the average energy when calibrating by the average stopping power method.
I. Introduction
power method to determine the average energy which is needed for quantitative results.
Heavy ions are of interest for the profiling of light elements, and also for the deter~natio~ of the bulk concentration of a number of impurities. In this latter case, one either takes advantage of the Coulomb barrier to determine light elements at trace level in heavy matrices using radioactivation [l], or uses Coulomb excitation to determine various medium weight and heavy elements in favourable matrices (using prompt gamma-ray spectromet~) [2]. In this work we will deal with bulk analysis only. The accuracy of the results depends on the method of calibration, on the knowledge of the cross-sections and of the stopping powers. The calibration method known as the “average stopping power” method is inherently accurate f3], and is insensitive to inaccuracies (even large) in the cross-sections. In addition, the cross-sections need only be known in a relative manner. The only sources of systematic errors then, are the stoping power data; in the average stopping power method, these data need only be known in a relative manner. In this work, we have examined the possibility of avoiding the use of heavy ion stopping power data which are scarce and often inaccurate. Instead, it is proposed to use H or He stopping power data, taken at the same speed 141. The advantage is that the data for H or He are abundant and sufficiently accurate. We have also examined the possibility of using calculated cross-section curves, in the case of Coulomb excitation; these curves are used in the average stopping 0168-583X/84/$03.00 @ Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
2. ~eth~
of study
The appro~mation S -S( v, Z,) .g(~‘, Z,), where S is the stopping power, u and Z, the speed and the atomic number of the incident ion, 2, the atomic number of the target, has often been proposed and has been tested with some success, using experimental data [4]. In this appro~mat~on, the ratio of the stopping powers for two given targets at a given ion speed, is independent of the incident ion. To test the degree of accuracy obtained using this approximation, we have used a me~od based on the average stopping power concept [3]. The normalized thick target yield, Y, when irradiating with charged particles is given by:
where n = concentration of the element of interest in the thick target; a{ E) = cross-section of the reaction of interest; .S( E, X) = stopping-power for the incident particle and for the matrix X, Ei = energy of the incident particles. Eq. (1) does not take into account the intensity and possible saturation and decay factors, since Y is a normalized yield.
G. Blondiaux et al. / Bulk analysis with heauy run beams In the average
stopping
power
method,
Y is given
67
4. Results and discussion
by: *=
S(EI, X)
4. I. Yield ratios
Et
/ 0
u(E)dE,
where E, is the “average energy” calculated either from the cross-section curve or from the thick target yield curve [3,5]. For a given ion, a given incident energy (which corresponds to a given E,), and two different targets (A and B) containing a common element that interacts with cross-section o(E), one obtains a yield ratio R.
(3) Using the approximation .S ==f( u, Z,) .g( u, Z,), ratio Y*/Y, should be independent of the incident since S(Krl: --= K&I,
B)
g(G.
Z,)
A)
gtGP
Z.4)
the ion,
and hence:
independent
of the incident
ion.
We have therefore used known targets (n,, nB known) and different ions to check whether the ratio Y,/Ya is constant, at a given average ion velocity. Ako, having measured Y,/ Y, experimentally, we could compare with values obtained by calculation, using known stopping power data, n,.., and plB.
3. Experimental We have used the targets shown in table 1, and we measured the yields obtained by Coulomb excitation of the 159 keV level of 47Ti.3 **C and 160 beams were accelerated to energies between 7 and 21 MeV at the tandem accelerator of the Nuclear Research Center Demokritos (Athens). The yield ratios were measured at u, corresponding to 0.9X5 MeV/nucleon. Tabte 1 Targets a)
Composition (wt4;)
Ti TiNi
100 42.9 57.1 50.25 49.75 49.45 50.55
TiCu TiFe
Ni Ti cu Ti Fe Ti
e) Alloys prepared by the levitation technique by M. Bigot, CNRS, Vitry sur Seine.
Table 2 presents the experimental yield ratios obtained, and compares these with ratios calculated from semiemp~~cai or experimental stopping power data. In each case, we give the ratio R of the yield for a pure Ti target to the yield of a titanium-based alloy. ) is the experimental ratio measured in Rexp (12C or ‘@‘O this work; R elp (Forster) is the ratio calculated using the experimental data from the ref. 6 for heavy ions, and the parametrization of the effective charge; Rth (12C or 160) is the ratio obtained by calculation of heavy ion stopping powers, using the semiempirical stopping power for H from ref. [7] and the parametrizat~#n of the effective charge 181; is the ratio calculated using the semiR,, (a) empirical data for He, from ref. [4b]; is the ratio calculated using the semiR t,, (P) empirical data for H from ref. (71. The “C incident energy was 16 MeV, the average energy 11.8 MeV and u, = 0.984 MeV/amu. The ‘“0 incident energy was 21.325 MeV, the average energy 15.784 MeV, and v, = 0.986 MeV/amu. The associated errors represent our experimental uncertainty, or the uncertainty in the calculation assuming 2% error in the H 171 and in the He [4] stopping power data, and 5% error in the I60 stopping power data f6J. The agreement between the various ratios is generally good, the discrepancies being less than 1.5% except for Ti/TiCu (3% and 1.9%), as shown in table 3. 4.2. Cross-sections for Coulomb excitation Using the theory by Alder et al. 191, we have calculated the cross-sections for Coulomb excitation of “Ti, and also of “‘Ag, “09Ag, “‘Ag for 12C and I60 ions. The Table 2 Comparison of the experimental yield ratios, with calculated ratios for an ion velocity corresponding in each case to (I,,,zz 0.985 MeV/nucleon.
R lZC R ‘xp12c Th 160 R ‘=P R exp Forster R I60 REcr R,,P
Yield ratio for Ti/TiNi
Yield ratio for Ti/TiCu
Yield ratio for Ti/TiFe
1.68 kO.02 1.68 rto.12 1.655 f 0.015 1.645 rf:0.025 1.68 +0.12 1.66 io.05 1.68 f0.05
1.875 1.84 1.815 1.82 1.84 1.82 1.84
1.895 1.9 1.9 1.875 1.9 1.9 1.9
+_0.02 +0.13 +0.02 +0.03 kO.13 *to.05 50.05
+-0.02 kO.13 kO.02 * 0.04 io.13 10.05 &0.05
Table 3 Difference
between
experiment
and calculations
% difference
Targets
Ti/TiNi Ti/TiFe Ti/TiCu
(W)
between
R ew 12C and R Th Q
R =w ‘2C and R, “C
1.08 0.4 3
0.06 0.4 1.9
R ew I60 and
cross-sections were calculated assuming that all transitions were of the quadrupole (E2) type. The stopping powers for “C and I60 in Ti and Ag were calculated using the semi-empirical data for H [7] and the effective charge parametrization 181. Using the values obtained,
experimental
R e*P =0
RTl%a
R cxP ‘“0 and R,, j60
and R exp FORSTER
0.3 0.05 0.3
1.3 0.05 1.4
0.7 1.5 0.4
the yields Y [eq. (l)] were calculated as a function of the incident energy, For thick Ti and Ag targets. Experimental yields for thick Ti and Ag targets were determined as a function of energy in arbitrary units. After normalization it appears that the experimental and the calculated
pts
n s .sx
10 12 14 16 18 20 22 $0” 4
4
6
8
4
6
8 10 12 14 ?6 18 20 22
4
6
8 ,OT2~,618~22’
4
6
8 ~01214161820
6
8 301214
4
6
8 16 12 14 16 18 20 22
16182022
E(MeV) Fig. 1. Calculated
and experimental
thick target yield curves for Coulomb
excitation
22
Lab of 47Ti, lo7Ag, ‘09Agwith “C
and I60 ions.
G. Blondiaux et al. / Bulk analysis with heavy ion beams
yields are in good agreement, as shown in fig. 1. Since for qualitative results and/or for the determination of E,, one needs only relative values for the yields or for the cross-sections (shape of the curves only), the calculated curves are quite satisfactory.
[2] [3]
5. Conclusions [4]
It has been shown experimentally and by calculation in a number of cases that when heavy ions are used for bulk analysis, the associated stopping power data are not needed. Instead one can use reliable H or He data taken at the same speed. This result can quite probably be extended to other ions and energies, and this will increase the simplicity and the accuracy of heavy ion bulk
analysis.
calculated
Also,
when
cross-section
calculation of the average mental time.
using
Coulomb
excitation,
curves can be used for the energy, which saves experi-
References [I] (a) J.R. McGinley, R. Zeisler and (1978) 559.
G.J. Stock, E.A. Schweikert, L. Zikovsky, J. of Radioanal.
J.B. Cross, Chem. 43
[5] [6] [7] [8] [9]
69
(b) C. Friedli, B.D. Lass and E.A. Schweikert, J. of Radioanal. Chem. 54 91979) 281. (c) B.D. Lass, C. Friedli and E.A. Schweikert, J. of Radioanal. Chem. 57 91980) 481. B. Borderie, J.N. Barrandon, B. Delaunay and M. Basutcu, Nucl. Instr. and Meth. 163 (1979) 441. K. Ishii, M. Valladon and J.L. Debrun, Nucl. Instr. and Meth. 150 (1978) 212. (a) J.F. Ziegler, Appl. Phys. Lett. 31 (1977) 544. (b) J.F. Ziegler, in Helium: Stopping powers and ranges in all elements (Pergamon, 1977). K. Ishii, M. Valladon, C.S. Sastri and J.L. Debrun, Nucl. Instr. and Meth. 153 (1978) 503. J.S. Forster et al., Nucl. Instr. and meth. 136 (1976) 349. H.H. Andersen and J.F. Ziegler, H. stopping powers, and ranges in all elements (Pergamon, 1977). D. Ward et al., AECL Report no 5313 (1976). (a) K. Alder et al., Rev. Mod. Phys. 28 (1956) 432. (b) K. Alder and A. Winther, Perspectives in Physics, (Academic Press, New York, 1966).
66
Instruments
and Methods in Physics Research 81 (1984) 66-69
North-~oiiand,
BULK ANALYSlS G. BLONDIAUX C.N.R.S.
G.
Amsterdam
WITH HEAVY 1ON BEAMS, CAL~B~TI~~ and J.L. DEBRUN 3A, Rue de In
- Seruice du Cycbrron,
Fkrollerie
45045 O&nns CPdex, irrorxe
COSTA
C.N.R.S .- Centre de Reckerches Nucl&zires, Stra.qbourg, France A. KATSANOS and G. VOURVOPOULOS Nuclear center Demokritos, A them, Greece Received 10
June 1983
It is shown that for bulk analysis with heavy ion beams, one does not need to know the stopping power of the heavy ions. Instead, hydrogen or helium stopping powers at the same speed, can be used with an accuracy of l--2%. Also, it is shown that when using Coulomb excitation, the calculated cross-section curve {arbitrary units) is accurate enough to be used for the determination of the average energy when calibrating by the average stopping power method.
I. Introduction
power method to determine the average energy which is needed for quantitative results.
Heavy ions are of interest for the profiling of light elements, and also for the deter~natio~ of the bulk concentration of a number of impurities. In this latter case, one either takes advantage of the Coulomb barrier to determine light elements at trace level in heavy matrices using radioactivation [l], or uses Coulomb excitation to determine various medium weight and heavy elements in favourable matrices (using prompt gamma-ray spectromet~) [2]. In this work we will deal with bulk analysis only. The accuracy of the results depends on the method of calibration, on the knowledge of the cross-sections and of the stopping powers. The calibration method known as the “average stopping power” method is inherently accurate f3], and is insensitive to inaccuracies (even large) in the cross-sections. In addition, the cross-sections need only be known in a relative manner. The only sources of systematic errors then, are the stoping power data; in the average stopping power method, these data need only be known in a relative manner. In this work, we have examined the possibility of avoiding the use of heavy ion stopping power data which are scarce and often inaccurate. Instead, it is proposed to use H or He stopping power data, taken at the same speed 141. The advantage is that the data for H or He are abundant and sufficiently accurate. We have also examined the possibility of using calculated cross-section curves, in the case of Coulomb excitation; these curves are used in the average stopping 0168-583X/84/$03.00 @ Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
2. ~eth~
of study
The appro~mation S -S( v, Z,) .g(~‘, Z,), where S is the stopping power, u and Z, the speed and the atomic number of the incident ion, 2, the atomic number of the target, has often been proposed and has been tested with some success, using experimental data [4]. In this appro~mat~on, the ratio of the stopping powers for two given targets at a given ion speed, is independent of the incident ion. To test the degree of accuracy obtained using this approximation, we have used a me~od based on the average stopping power concept [3]. The normalized thick target yield, Y, when irradiating with charged particles is given by:
where n = concentration of the element of interest in the thick target; a{ E) = cross-section of the reaction of interest; .S( E, X) = stopping-power for the incident particle and for the matrix X, Ei = energy of the incident particles. Eq. (1) does not take into account the intensity and possible saturation and decay factors, since Y is a normalized yield.
G. Blondiaux et al. / Bulk analysis with heauy run beams In the average
stopping
power
method,
Y is given
67
4. Results and discussion
by: *=
S(EI, X)
4. I. Yield ratios
Et
/ 0
u(E)dE,
where E, is the “average energy” calculated either from the cross-section curve or from the thick target yield curve [3,5]. For a given ion, a given incident energy (which corresponds to a given E,), and two different targets (A and B) containing a common element that interacts with cross-section o(E), one obtains a yield ratio R.
(3) Using the approximation .S ==f( u, Z,) .g( u, Z,), ratio Y*/Y, should be independent of the incident since S(Krl: --= K&I,
B)
g(G.
Z,)
A)
gtGP
Z.4)
the ion,
and hence:
independent
of the incident
ion.
We have therefore used known targets (n,, nB known) and different ions to check whether the ratio Y,/Ya is constant, at a given average ion velocity. Ako, having measured Y,/ Y, experimentally, we could compare with values obtained by calculation, using known stopping power data, n,.., and plB.
3. Experimental We have used the targets shown in table 1, and we measured the yields obtained by Coulomb excitation of the 159 keV level of 47Ti.3 **C and 160 beams were accelerated to energies between 7 and 21 MeV at the tandem accelerator of the Nuclear Research Center Demokritos (Athens). The yield ratios were measured at u, corresponding to 0.9X5 MeV/nucleon. Tabte 1 Targets a)
Composition (wt4;)
Ti TiNi
100 42.9 57.1 50.25 49.75 49.45 50.55
TiCu TiFe
Ni Ti cu Ti Fe Ti
e) Alloys prepared by the levitation technique by M. Bigot, CNRS, Vitry sur Seine.
Table 2 presents the experimental yield ratios obtained, and compares these with ratios calculated from semiemp~~cai or experimental stopping power data. In each case, we give the ratio R of the yield for a pure Ti target to the yield of a titanium-based alloy. ) is the experimental ratio measured in Rexp (12C or ‘@‘O this work; R elp (Forster) is the ratio calculated using the experimental data from the ref. 6 for heavy ions, and the parametrization of the effective charge; Rth (12C or 160) is the ratio obtained by calculation of heavy ion stopping powers, using the semiempirical stopping power for H from ref. [7] and the parametrizat~#n of the effective charge 181; is the ratio calculated using the semiR,, (a) empirical data for He, from ref. [4b]; is the ratio calculated using the semiR t,, (P) empirical data for H from ref. (71. The “C incident energy was 16 MeV, the average energy 11.8 MeV and u, = 0.984 MeV/amu. The ‘“0 incident energy was 21.325 MeV, the average energy 15.784 MeV, and v, = 0.986 MeV/amu. The associated errors represent our experimental uncertainty, or the uncertainty in the calculation assuming 2% error in the H 171 and in the He [4] stopping power data, and 5% error in the I60 stopping power data f6J. The agreement between the various ratios is generally good, the discrepancies being less than 1.5% except for Ti/TiCu (3% and 1.9%), as shown in table 3. 4.2. Cross-sections for Coulomb excitation Using the theory by Alder et al. 191, we have calculated the cross-sections for Coulomb excitation of “Ti, and also of “‘Ag, “09Ag, “‘Ag for 12C and I60 ions. The Table 2 Comparison of the experimental yield ratios, with calculated ratios for an ion velocity corresponding in each case to (I,,,zz 0.985 MeV/nucleon.
R lZC R ‘xp12c Th 160 R ‘=P R exp Forster R I60 REcr R,,P
Yield ratio for Ti/TiNi
Yield ratio for Ti/TiCu
Yield ratio for Ti/TiFe
1.68 kO.02 1.68 rto.12 1.655 f 0.015 1.645 rf:0.025 1.68 +0.12 1.66 io.05 1.68 f0.05
1.875 1.84 1.815 1.82 1.84 1.82 1.84
1.895 1.9 1.9 1.875 1.9 1.9 1.9
+_0.02 +0.13 +0.02 +0.03 kO.13 *to.05 50.05
+-0.02 kO.13 kO.02 * 0.04 io.13 10.05 &0.05
Table 3 Difference
between
experiment
and calculations
% difference
Targets
Ti/TiNi Ti/TiFe Ti/TiCu
(W)
between
R ew 12C and R Th Q
R =w ‘2C and R, “C
1.08 0.4 3
0.06 0.4 1.9
R ew I60 and
cross-sections were calculated assuming that all transitions were of the quadrupole (E2) type. The stopping powers for “C and I60 in Ti and Ag were calculated using the semi-empirical data for H [7] and the effective charge parametrization 181. Using the values obtained,
experimental
R e*P =0
RTl%a
R cxP ‘“0 and R,, j60
and R exp FORSTER
0.3 0.05 0.3
1.3 0.05 1.4
0.7 1.5 0.4
the yields Y [eq. (l)] were calculated as a function of the incident energy, For thick Ti and Ag targets. Experimental yields for thick Ti and Ag targets were determined as a function of energy in arbitrary units. After normalization it appears that the experimental and the calculated
pts
n s .sx
10 12 14 16 18 20 22 $0” 4
4
6
8
4
6
8 10 12 14 ?6 18 20 22
4
6
8 ,OT2~,618~22’
4
6
8 ~01214161820
6
8 301214
4
6
8 16 12 14 16 18 20 22
16182022
E(MeV) Fig. 1. Calculated
and experimental
thick target yield curves for Coulomb
excitation
22
Lab of 47Ti, lo7Ag, ‘09Agwith “C
and I60 ions.
G. Blondiaux et al. / Bulk analysis with heavy ion beams
yields are in good agreement, as shown in fig. 1. Since for qualitative results and/or for the determination of E,, one needs only relative values for the yields or for the cross-sections (shape of the curves only), the calculated curves are quite satisfactory.
[2] [3]
5. Conclusions [4]
It has been shown experimentally and by calculation in a number of cases that when heavy ions are used for bulk analysis, the associated stopping power data are not needed. Instead one can use reliable H or He data taken at the same speed. This result can quite probably be extended to other ions and energies, and this will increase the simplicity and the accuracy of heavy ion bulk
analysis.
calculated
Also,
when
cross-section
calculation of the average mental time.
using
Coulomb
excitation,
curves can be used for the energy, which saves experi-
References [I] (a) J.R. McGinley, R. Zeisler and (1978) 559.
G.J. Stock, E.A. Schweikert, L. Zikovsky, J. of Radioanal.
J.B. Cross, Chem. 43
[5] [6] [7] [8] [9]
69
(b) C. Friedli, B.D. Lass and E.A. Schweikert, J. of Radioanal. Chem. 54 91979) 281. (c) B.D. Lass, C. Friedli and E.A. Schweikert, J. of Radioanal. Chem. 57 91980) 481. B. Borderie, J.N. Barrandon, B. Delaunay and M. Basutcu, Nucl. Instr. and Meth. 163 (1979) 441. K. Ishii, M. Valladon and J.L. Debrun, Nucl. Instr. and Meth. 150 (1978) 212. (a) J.F. Ziegler, Appl. Phys. Lett. 31 (1977) 544. (b) J.F. Ziegler, in Helium: Stopping powers and ranges in all elements (Pergamon, 1977). K. Ishii, M. Valladon, C.S. Sastri and J.L. Debrun, Nucl. Instr. and Meth. 153 (1978) 503. J.S. Forster et al., Nucl. Instr. and meth. 136 (1976) 349. H.H. Andersen and J.F. Ziegler, H. stopping powers, and ranges in all elements (Pergamon, 1977). D. Ward et al., AECL Report no 5313 (1976). (a) K. Alder et al., Rev. Mod. Phys. 28 (1956) 432. (b) K. Alder and A. Winther, Perspectives in Physics, (Academic Press, New York, 1966).