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Measurements of the elastic scattering cross sections for proton on T, 4He
Nuclear Instruments and Methods in Physics Research B 268 (2010) 3373–3376
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Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Measurements of the elastic scattering cross sections for proton on T, 4He T. Cai, J.Q. Li, Z.J. He, X.F. Wang, L.Q. Shi * Applied ion beam Physics Laboratory, Institute of Modern Physics, Fudan University, Shanghai 200433, People’s Republic of China
a r t i c l e
i n f o
Article history: Received 7 February 2010 Received in revised form 17 July 2010 Available online 4 August 2010 Keywords: Elastic scattering cross sections Proton Tritium Helium
a b s t r a c t The cross sections for the elastic scattering of protons from tritium at 151° and from helium at 155° angles in the laboratory frame, over the energy range of 1.2–3.4 MeV, have been measured in the present work, as a supplement to previous cross section measurements determined at different scattering angles recently. The currently measured cross section data are compared to data available in literature. The cross section enhancement was also investigated for both reactions. It was found that over the whole measured energy range, the elastic cross section for protons on tritium increases linearly with energy and is about 1000 times greater than the Rutherford cross section at 3.4 MeV. On the other hand, in the case of the elastic scattering of protons from helium, the cross section below 2.3 MeV increases almost linearly, and reaches a maximum of about 300 mb/str at the energy of 2.4 MeV for the scattering angle of 165°, and then, after this energy, it keeps oscillating around the maximum. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction Tritium and helium are of significant concern to a variety of fields, especially in the analysis of material distribution, diffusion, etc. For better understanding of tritium and helium’s behavior in materials, an accurate measurement of their respective concentration and depth profiles is mandatory. Ion beam analysis provides a suit of suitable and essentially non-destructive techniques, including proton backscattering (PBS) and elastic recoil detection (ERDA), [1–3] which are the most important analytical methods for tritium and helium concentration determination ranging from trace quantities to major constituents. Proton backscattering is generally considered to be a welldeveloped technique for the detection of light species in thick films or bulk materials due to a strong enhancement of two to three orders of magnitude in the elastic scattering cross section relative to the corresponding Rutherford value [3]. Since the main weakness of the technique lies on the fact that the low energy backscattered ion signal is often superimposed on the substrate and impurity spectra, its sensitivity depends on whether the tritium and helium signal can be separated from the background originated by the host materials. When the scattered protons are detected using the coincidence technique, the sensitivity can reach a value of 1 atom ppm [3]. In addition, by increasing the angle of incidence with respect to the normal of the target surface it is possible to increase both the depth resolution and the sensitivity but multiple scattering and straggling will limit the resolution for too small an angle. Generally, scattering angles between 150° and 175° are desirable
* Corresponding author. Tel.: +86 21 65642292; fax: +86 21 65642782. E-mail address: [email protected] (L.Q. Shi). 0168-583X/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2010.07.016
for separating various scattered and reaction particles. ERDA analysis is another method for concentration determination and depth profiling of light elements. Because of the implementation of a heavy-ion beam, it can present very high depth resolution and sensitivity (several atom ppm), while being rather unaffected by the substrate’s atomic number. However, it is usually limited to near surface region applications and can cause possible matrix irradiation damage [1]. In both cases, an accurate knowledge of the elastic scattering cross sections for the incident beam interaction with the tritium or helium is required. In our previous work, the cross sections for the interaction of p with T in the energy range of 1.6–3.6 MeV and at an angle of 165° [4] has been measured, since very little data of interest from literature [5,6] exist in the energy range 1–3 MeV, and at larger scattering angles, for application of the elastic backscattering technique. Moreover, the interaction of p with He in almost the same energy range and for the same scattering angle [7] has been studied by employing a high heliumcontent titanium (Ti) target, prepared by direct current (DC) magnetron sputtering [8]. In this work, the measurements of the differential cross sections for the same reactions and proton beam energy ranges are extended to different scattering angles, namely, 155° for the T(p, p) and 151° for the He(p, p) reaction. The obtained measured results are also analyzed and discussed. 2. Experimental techniques 2.1. Experimental apparatus The incident proton beam used in these cross section measurements, ranging between 1.2 and 3.7 MeV was provided by the NEC 9SDH-2 2 3 MV tandem accelerator of Fudan University. The
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T. Cai et al. / Nuclear Instruments and Methods in Physics Research B 268 (2010) 3373–3376
accelerator energy was calibrated using nuclear resonance reactions such as 27Al(p,)28Si at 992 keV, 13C(p,)14N at 1748 and 19 F(p,)16O at 872 keV. A set of collimating slits defined the beam to a size of 0.6 mm with a full angular divergence of 0.05° before hitting the target. The ion beam was incident on the target, tilted at 45° relative to the sample normal in order to increase the path length and thus the strength of tritium or He signal relative to the background. The Au/Si surface barrier detector was placed at the appropriate laboratory backscattering angle and it subtended a solid angle of 1.12 103 str by a defining slit of 3 4 mm. The angular resolution of this detector was thus 1°. The energy resolution of the detection system was typically 12 keV for proton. The beam was confined to 0.6 mm in diameter before bombarding the target and the beam currents were limited to less than 30 nA. The beam current was monitored with a Faraday cup located behind the target, and it was kept sufficiently low, thus the dead time of the ADC was negligible and the pulse pileup was minimized. Moreover, during the measurements, the Faraday cup was also used as a beam trap to prevent incident-beam particles passing through the film from being scattered from the chamber walls and eventually from hitting the detector. For the measurement, an energy step of 100 or 200 keV was chosen in the energy region between 1.4 and 3.7 MeV. The accumulated charge per energy was usually 25 lC. It was found that the Pd/TiTx and Ta/TiHex targets were all vary stable under the bombardment of the proton beam (with a current of 30 nA) and the average tritium losses were less than 0.2% during a 25 C run while no helium losses were observed.
2.2. Sample preparation The tritium-charged Pd/Ti/Al samples were prepared by a conventional hydrogenation method, but using an apparatus which enables tritium gas to be handled. A uniform Ti film of 4.5 1017 atoms/cm2 was first sputtered onto a 3 lm Al foil, and then a Pd overlayer of 2.8 1016 atoms/cm2 was deposited on the Ti film (here the thin Pd layer were adopted to prevent the interference of Pd with Ti peaks in spectra so as to extend the incident proton energy down to a lower value). Furthermore, the Pd film can prevent titanium from being oxidized and can also enhance tritium absorption capability. The reason that thin Al foil was chosen as the backing material was to obtain as low a background signal as possible in the spectrum region of the tritium one. The tritiation was carried out at an atmosphere of tritium– hydrogen mixture under a pressure of 103 Pa and at 150 °C for 0.5 h. The amount of tritium in the target was measured by implementing a 6 MeV 16O ion ERD analysis. This was done by simultaneously employing two detectors, one to detect the T and H recoils at a recoil angle of 30° and another to measure the backscattering yield of the incident 16O particles at a scattering angle of 165°. The peak area of the backscattering signal of Pd was used as ion dose calibration for the ERD measurement. It has to be noted that in order to apply the Rutherford formula for the scattering cross section, the O ion energy must be less than the non-Rutherford threshold energy. This threshold energy is determined by making the closest approach of the two atoms not less than 3–4 times the sum of their respective nuclear radii [9]. The closest approach of the two atoms is given by
D¼
For Ta/TiHex/Al samples, a new preparationing method called the magnetron sputtering, which has been reported in [7,8], was employed, and a uniform and surprisingly high concentration (1.87 1017 atoms/cm2 He atoms in 5.3 1017 atoms/cm2 Ti film) helium–titanium target was achieved. Ta here is used as an internal ion dose reference and it can likewise prevent titanium from oxidizing. A thin Al foil was also employed as backing material. Similarly to the tritium measurement, the helium amount was also determined by ERD, using a beam of 6.8 MeV 12C ions, and by simultaneously employing two detectors, one to detect He recoils at a recoil angle of 30° and another to measure the backscattering yield of the incident 12C particles at a scattering angle of 165°. Thus, the uncertainty associated with the determination of the absolute tritium and helium concentrations was less than 5%. 2.3. Cross section determination For both tritium and helium samples, the same relative method for calculating the cross section was used. For example, in the case of the Pd/TiTx/Al sample, the backscattering spectrum for protons incident on the sample is shown in Fig. 1. As shown, there are still some background signals below the peaks of tritium. They may originate from scattered ions from the target (or from the incident-beam particles escaping from the beam trap) and these ions can eventually hit the detector through multiple scattering. In the present energy range of 1.2–3.4 MeV, proton scattering from tantalum is purely Rutherford. So the Pd overlayer acts as an internal ion dose reference. By using the Pd/TiTx sample, the elastic scattering cross sections in the laboratory coordinates can be calculated from
rT ðEÞ ¼ rPd;Ruth ðE0 ÞAT ðNtÞPd =APd ðNtÞT ;
ð1Þ
where rPd;Ruth is the calculated proton Rutherford scattering cross section of Pd. E ¼ E0 DEPd 12 DETi , E0 is the incident proton ion energy, DEPd and DETi are the energy loss of ions in the Pd and Ti films, respectively. The signal peak area ratio APd/AT is determined from the measured spectra. The ratio (Nt)Pd/(Nt)T (N = atom density, t = layer thickness) is determined by using the areal density value for (Nt)T from the above ERD measurement and for (Nt)Pd by measuring 2 MeV helium RBS spectra of the sample. All Rutherford scattering cross sections used here have been corrected for the electron screening effect [10].
Z 1 Z 2 e2 M1 þ M2 1 ; 1þ sinðp=2 WÞ 2E M2
where Z1, M1 and Z1, M1 are the atomic number and mass of the projectile and target, respectively, E and W are the incident particle energy and recoil angle in the laboratory frame of reference.
Fig. 1. Backscattering spectrum for 2.2 MeV protons incident on the Pd/TiTx/Al sample.
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3. Results and discussion Results for the individual cross section measurements of the T(p, p)T and He(p, p)He elastic scattering reactions are shown in Figs. 2 and 3, and are presented in Tables 1 and 2, respectively. The adopted energy step was 200 keV in the energy region of 1.2–3.4 MeV for the T(p, p)T reaction and 100 keV between 1.4 and 3.7 MeV for the He(p, p)He one. Comparisons of the current data with some of those available in literature [6,11–14] are presented, including those from our previous works [4,7]. In Fig. 2, examining the energy range, the elastic cross section curve seems to have a broad peak with the maximum at about 1.4 MeV, while it subsequently decreases with energy, and the values from 2.4 to 3.5 MeV vary almost in a linear fashion. This behavior qualitatively agrees with our previous measured results for the T(p, p)T reaction at 165° and with Malcolm’s measurements shown in the figure as well. It shows a similar saturation, although the scattering angle is great different. In Fig. 3, the cross section data of the He(p, p)He reaction at scattering angles around 151°. These curves show a broad resonance in the neighborhood of 2.2 MeV, and the P2/3 ground state of the compound nucleus 5Li gives rise to resonance scattering [15]. The values determined in the present work at 151° are very close to the SigmaCalc data below 2.1 MeV. The same applies to the values of Barnard, but there is a relatively larger difference with a maximum up to 9.8% between our data and the SigmaCalc data in the energy range from 2.1 to 3.1 MeV. Over the whole studied energy region, current data agree with other available datasets from literature, especially with those of Freier and Miller.
Fig. 2. Measured T(p, p)T elastic scattering cross sections at laboratory angles of 155° and a comparison with the earlier data.
0
Scattering cross sectopm (kb/sr)
The accuracy of the proton scattering cross section measured here is limited by the uncertainties of all the parameters present in Eq. (1). The errors of AT and Apd result from statistical errors and background subtraction uncertainties in the T and Pd peak areas determination, and they are typically 2–3% in all cases less than 4%. The error in rPd;Ruth is less than 1% as related to uncertainties in the scattering angle (1%) and the proton beam energy (6 keV) in the measured energy region. Plus the measuring errors of areal densities (Nt)Pd, (Nt)T (under 5%), the total error associated with the cross sections is no larger than 7.3%. The same error level was achieved for the cross section measurement of protons from helium.
Present data, 151 0 Freier et.al, 153.74 0 Miller et. al. ,153.56 0 Barnard et.al, 153.56 0 Barnard et. al. , 147.02 0 Nurmela et. al. , 140 0 SignaCalc, 151
300
200
100
0
1
2
3 4 5 Proton energy (MeV)
6
Fig. 3. Measured He(p, p)He elastic scattering cross sections at laboratory angles of 151° and a comparison with the earlier data.
Table 1 Measured differential cross sections in the laboratory system for T(p, p)T at 155° from 1.2 to 3.5 MeV. Beam energy E (MeV)
dr/dX (mb/sr) (155°)
1.222 1.422 1.623 1.824 2.024 2.224 2.424 2.625 2.825 3.025 3.225 3.425
134.2 139.3 138.7 138.0 135.3 131.3 123.2 116.9 111.5 105.8 99.2 95.4
Table 2 Measured differential cross sections in the laboratory system for He(p, p)He at 151° from 1.4 to 3.7 MeV. Beam energy E (MeV)
dr/dX (mb/sr) (151°)
1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7
116.1 150.8 169.7 190.1 201.2 231.9 252.1 262.5 263.1 259.6 254.9 242.2 221.4 204.8 175.2 170.4 157.2 141.9 131.6 125.8 122.9 109.8 103.3 103.5
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value of about 300 at about 2.4 MeV at 165°, and then keeps oscillating around this maximum value as the incident proton energy increases. 4. Conclusion
Cross Section ratio of elas./Ruth.
Fig. 4. Measured cross sections enhancement for T(p, p)T elastic scattering at laboratory angles of 155° and 165°.
350
The differential cross sections for elastic scattering of protons from tritium in the energy range from 1.2 to 3.2 MeV at a backscattering angle of 155° in laboratory system and from helium between 1.4 and 3.7 MeV at 151° have been measured. The cross section enhancements of three orders of magnitude relative to the Rutherford case for the T(p, p)T reaction and of two orders of magnitude for the He(p, p)He reaction were recorded. For T(p, p)T, the determined values in the high energy region show that the cross section monotonically decreases with increasing energy, but in the low energy region a cross section curve maximum exists at around 2.1 MeV, which is consistent with the previous results from literature. Over the entire energy range the cross section enhancement increases almost linearly with energy. For the He(p, p)He reaction, the values determined in the present work at 151° are very close to the SigmaCalc data for incident proton beam energies of less then 2.1 MeV, while for the energies larger than 3.1 MeV, they agree rather well with available datasets such as Miller’s and Freier’s. The cross section enhancements below the 2.3 MeV increase almost linearly with energy and then keep oscillating around a maximum of about 300.
300
Acknowledgements 250 200
This work was supported by IAEA agency’s Co-ordinated Research Project under Contract No. 13268/R0 and in part by the National Natural Science Foundation of China under Grant No. 10975035. And the authors are grateful to the staff of the tandem accelerator of the Institute of Modern Physics at Fudan University.
0
165 0 151
150 100
References 50 0
1.0
1.5
2.0 2.5 3.0 Proton Energy (MeV)
3.5
4.0
Fig. 5. Measured cross sections enhancement for He(p, p)He elastic scattering at laboratory angles of 151° and 165°.
The cross section enhancements for the T(p, p)T and He(p, p)He elastic scattering reactions are shown in Figs. 4 and 5, respectively, in the form of ratio of the elastic scattering cross section to the Rutherford one. As far as the T(p, p) T reaction is concerned, the above mentioned ratio increases almost linearly with energy over the entire energy range, and a maximum enhancement of about three orders of magnitude is achieved at the energy of 3.4 MeV. However, in the case of the He(p, p)He reaction, the ratio increases almost linearly with energy below 2.3 MeV, reaches a maximum
[1] J.A. Sawicki, H.H. Plattner, I.V. Mitchell, J. Gallant. Nucl. Instr. Methods B15 (1986) 475. [2] J.F. Browning, J.C. Banks, W.R. Wampler, B.L. Doyle, Nucl. Instr. Methods B15 (2004) 317. [3] R.A. Langley, in: J.S. Walson, F.W. Wiffen (Eds.), Proc. Int. Conf. on Radiation effect and Tritium Technology for Fusion Reactors, vol IV, 1976, p. 158. [4] X.J. Xia, W. Ding, B. Zhang, X.G. Long, S.Z. Luo, S.M. Peng, R. Hutton, L.Q. Shi, Nucl. Instr. Methods Phys. Res. B 266 (2008) 705–708. [5] R.S. Claassen, R.J.S. Brown, G.D. Freier, W.R. Strattron, Phys. Rev. 82 (1951) 589. [6] Malcolm E. Ennis, Phys. Rev. 95 (1954) 772. [7] Y.F. Lu, L.Q. Shi, Z.J. He, L. Zhang, B. Zhang, R. Hutton, Nucl. Instr. Methods Phys. Res. B 267 (2009) 760–762. [8] L.Q. Shi, C.Z. Liu, S.L. Xu, Z.Y. Zhou, Thin Solid Films 479 (2005) 52. [9] J. Räisänen, E. Rauhala, J.M. Knox, J.F. Harmon, J. Appl. Phys. 75 (1994) 3273. [10] H.H. Andersen, F. Besenbacher, P. Loftager, W. Moller, Phys. Rev. A 21 (1980) 1891. [11] P.D. Miller, G.C. Phillips, Phys. Rev. 112 (1958) 2043. [12] G. Freier, E. Lampi, W. Sleator, J.H. Willams, Phys. Rev. 75 (1949) 1345. [13] A. Nurmela, E. Rauhala, J. Raisanen, J. Appl. Phys. 82 (1997) 1983. [14] A.C.L. Barnard, C.M. Jones, J.L. Weil, Nucl. Phys. 50 (1964) 604. [15] Miller, Philip D. The Elastic Scattering of Protons by Helium-4, and the Elastic Scattering of Helium-3 by Helium-4, Ph.D. Thesis, 1958.
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Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Measurements of the elastic scattering cross sections for proton on T, 4He T. Cai, J.Q. Li, Z.J. He, X.F. Wang, L.Q. Shi * Applied ion beam Physics Laboratory, Institute of Modern Physics, Fudan University, Shanghai 200433, People’s Republic of China
a r t i c l e
i n f o
Article history: Received 7 February 2010 Received in revised form 17 July 2010 Available online 4 August 2010 Keywords: Elastic scattering cross sections Proton Tritium Helium
a b s t r a c t The cross sections for the elastic scattering of protons from tritium at 151° and from helium at 155° angles in the laboratory frame, over the energy range of 1.2–3.4 MeV, have been measured in the present work, as a supplement to previous cross section measurements determined at different scattering angles recently. The currently measured cross section data are compared to data available in literature. The cross section enhancement was also investigated for both reactions. It was found that over the whole measured energy range, the elastic cross section for protons on tritium increases linearly with energy and is about 1000 times greater than the Rutherford cross section at 3.4 MeV. On the other hand, in the case of the elastic scattering of protons from helium, the cross section below 2.3 MeV increases almost linearly, and reaches a maximum of about 300 mb/str at the energy of 2.4 MeV for the scattering angle of 165°, and then, after this energy, it keeps oscillating around the maximum. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction Tritium and helium are of significant concern to a variety of fields, especially in the analysis of material distribution, diffusion, etc. For better understanding of tritium and helium’s behavior in materials, an accurate measurement of their respective concentration and depth profiles is mandatory. Ion beam analysis provides a suit of suitable and essentially non-destructive techniques, including proton backscattering (PBS) and elastic recoil detection (ERDA), [1–3] which are the most important analytical methods for tritium and helium concentration determination ranging from trace quantities to major constituents. Proton backscattering is generally considered to be a welldeveloped technique for the detection of light species in thick films or bulk materials due to a strong enhancement of two to three orders of magnitude in the elastic scattering cross section relative to the corresponding Rutherford value [3]. Since the main weakness of the technique lies on the fact that the low energy backscattered ion signal is often superimposed on the substrate and impurity spectra, its sensitivity depends on whether the tritium and helium signal can be separated from the background originated by the host materials. When the scattered protons are detected using the coincidence technique, the sensitivity can reach a value of 1 atom ppm [3]. In addition, by increasing the angle of incidence with respect to the normal of the target surface it is possible to increase both the depth resolution and the sensitivity but multiple scattering and straggling will limit the resolution for too small an angle. Generally, scattering angles between 150° and 175° are desirable
* Corresponding author. Tel.: +86 21 65642292; fax: +86 21 65642782. E-mail address: [email protected] (L.Q. Shi). 0168-583X/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2010.07.016
for separating various scattered and reaction particles. ERDA analysis is another method for concentration determination and depth profiling of light elements. Because of the implementation of a heavy-ion beam, it can present very high depth resolution and sensitivity (several atom ppm), while being rather unaffected by the substrate’s atomic number. However, it is usually limited to near surface region applications and can cause possible matrix irradiation damage [1]. In both cases, an accurate knowledge of the elastic scattering cross sections for the incident beam interaction with the tritium or helium is required. In our previous work, the cross sections for the interaction of p with T in the energy range of 1.6–3.6 MeV and at an angle of 165° [4] has been measured, since very little data of interest from literature [5,6] exist in the energy range 1–3 MeV, and at larger scattering angles, for application of the elastic backscattering technique. Moreover, the interaction of p with He in almost the same energy range and for the same scattering angle [7] has been studied by employing a high heliumcontent titanium (Ti) target, prepared by direct current (DC) magnetron sputtering [8]. In this work, the measurements of the differential cross sections for the same reactions and proton beam energy ranges are extended to different scattering angles, namely, 155° for the T(p, p) and 151° for the He(p, p) reaction. The obtained measured results are also analyzed and discussed. 2. Experimental techniques 2.1. Experimental apparatus The incident proton beam used in these cross section measurements, ranging between 1.2 and 3.7 MeV was provided by the NEC 9SDH-2 2 3 MV tandem accelerator of Fudan University. The
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T. Cai et al. / Nuclear Instruments and Methods in Physics Research B 268 (2010) 3373–3376
accelerator energy was calibrated using nuclear resonance reactions such as 27Al(p,)28Si at 992 keV, 13C(p,)14N at 1748 and 19 F(p,)16O at 872 keV. A set of collimating slits defined the beam to a size of 0.6 mm with a full angular divergence of 0.05° before hitting the target. The ion beam was incident on the target, tilted at 45° relative to the sample normal in order to increase the path length and thus the strength of tritium or He signal relative to the background. The Au/Si surface barrier detector was placed at the appropriate laboratory backscattering angle and it subtended a solid angle of 1.12 103 str by a defining slit of 3 4 mm. The angular resolution of this detector was thus 1°. The energy resolution of the detection system was typically 12 keV for proton. The beam was confined to 0.6 mm in diameter before bombarding the target and the beam currents were limited to less than 30 nA. The beam current was monitored with a Faraday cup located behind the target, and it was kept sufficiently low, thus the dead time of the ADC was negligible and the pulse pileup was minimized. Moreover, during the measurements, the Faraday cup was also used as a beam trap to prevent incident-beam particles passing through the film from being scattered from the chamber walls and eventually from hitting the detector. For the measurement, an energy step of 100 or 200 keV was chosen in the energy region between 1.4 and 3.7 MeV. The accumulated charge per energy was usually 25 lC. It was found that the Pd/TiTx and Ta/TiHex targets were all vary stable under the bombardment of the proton beam (with a current of 30 nA) and the average tritium losses were less than 0.2% during a 25 C run while no helium losses were observed.
2.2. Sample preparation The tritium-charged Pd/Ti/Al samples were prepared by a conventional hydrogenation method, but using an apparatus which enables tritium gas to be handled. A uniform Ti film of 4.5 1017 atoms/cm2 was first sputtered onto a 3 lm Al foil, and then a Pd overlayer of 2.8 1016 atoms/cm2 was deposited on the Ti film (here the thin Pd layer were adopted to prevent the interference of Pd with Ti peaks in spectra so as to extend the incident proton energy down to a lower value). Furthermore, the Pd film can prevent titanium from being oxidized and can also enhance tritium absorption capability. The reason that thin Al foil was chosen as the backing material was to obtain as low a background signal as possible in the spectrum region of the tritium one. The tritiation was carried out at an atmosphere of tritium– hydrogen mixture under a pressure of 103 Pa and at 150 °C for 0.5 h. The amount of tritium in the target was measured by implementing a 6 MeV 16O ion ERD analysis. This was done by simultaneously employing two detectors, one to detect the T and H recoils at a recoil angle of 30° and another to measure the backscattering yield of the incident 16O particles at a scattering angle of 165°. The peak area of the backscattering signal of Pd was used as ion dose calibration for the ERD measurement. It has to be noted that in order to apply the Rutherford formula for the scattering cross section, the O ion energy must be less than the non-Rutherford threshold energy. This threshold energy is determined by making the closest approach of the two atoms not less than 3–4 times the sum of their respective nuclear radii [9]. The closest approach of the two atoms is given by
D¼
For Ta/TiHex/Al samples, a new preparationing method called the magnetron sputtering, which has been reported in [7,8], was employed, and a uniform and surprisingly high concentration (1.87 1017 atoms/cm2 He atoms in 5.3 1017 atoms/cm2 Ti film) helium–titanium target was achieved. Ta here is used as an internal ion dose reference and it can likewise prevent titanium from oxidizing. A thin Al foil was also employed as backing material. Similarly to the tritium measurement, the helium amount was also determined by ERD, using a beam of 6.8 MeV 12C ions, and by simultaneously employing two detectors, one to detect He recoils at a recoil angle of 30° and another to measure the backscattering yield of the incident 12C particles at a scattering angle of 165°. Thus, the uncertainty associated with the determination of the absolute tritium and helium concentrations was less than 5%. 2.3. Cross section determination For both tritium and helium samples, the same relative method for calculating the cross section was used. For example, in the case of the Pd/TiTx/Al sample, the backscattering spectrum for protons incident on the sample is shown in Fig. 1. As shown, there are still some background signals below the peaks of tritium. They may originate from scattered ions from the target (or from the incident-beam particles escaping from the beam trap) and these ions can eventually hit the detector through multiple scattering. In the present energy range of 1.2–3.4 MeV, proton scattering from tantalum is purely Rutherford. So the Pd overlayer acts as an internal ion dose reference. By using the Pd/TiTx sample, the elastic scattering cross sections in the laboratory coordinates can be calculated from
rT ðEÞ ¼ rPd;Ruth ðE0 ÞAT ðNtÞPd =APd ðNtÞT ;
ð1Þ
where rPd;Ruth is the calculated proton Rutherford scattering cross section of Pd. E ¼ E0 DEPd 12 DETi , E0 is the incident proton ion energy, DEPd and DETi are the energy loss of ions in the Pd and Ti films, respectively. The signal peak area ratio APd/AT is determined from the measured spectra. The ratio (Nt)Pd/(Nt)T (N = atom density, t = layer thickness) is determined by using the areal density value for (Nt)T from the above ERD measurement and for (Nt)Pd by measuring 2 MeV helium RBS spectra of the sample. All Rutherford scattering cross sections used here have been corrected for the electron screening effect [10].
Z 1 Z 2 e2 M1 þ M2 1 ; 1þ sinðp=2 WÞ 2E M2
where Z1, M1 and Z1, M1 are the atomic number and mass of the projectile and target, respectively, E and W are the incident particle energy and recoil angle in the laboratory frame of reference.
Fig. 1. Backscattering spectrum for 2.2 MeV protons incident on the Pd/TiTx/Al sample.
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3. Results and discussion Results for the individual cross section measurements of the T(p, p)T and He(p, p)He elastic scattering reactions are shown in Figs. 2 and 3, and are presented in Tables 1 and 2, respectively. The adopted energy step was 200 keV in the energy region of 1.2–3.4 MeV for the T(p, p)T reaction and 100 keV between 1.4 and 3.7 MeV for the He(p, p)He one. Comparisons of the current data with some of those available in literature [6,11–14] are presented, including those from our previous works [4,7]. In Fig. 2, examining the energy range, the elastic cross section curve seems to have a broad peak with the maximum at about 1.4 MeV, while it subsequently decreases with energy, and the values from 2.4 to 3.5 MeV vary almost in a linear fashion. This behavior qualitatively agrees with our previous measured results for the T(p, p)T reaction at 165° and with Malcolm’s measurements shown in the figure as well. It shows a similar saturation, although the scattering angle is great different. In Fig. 3, the cross section data of the He(p, p)He reaction at scattering angles around 151°. These curves show a broad resonance in the neighborhood of 2.2 MeV, and the P2/3 ground state of the compound nucleus 5Li gives rise to resonance scattering [15]. The values determined in the present work at 151° are very close to the SigmaCalc data below 2.1 MeV. The same applies to the values of Barnard, but there is a relatively larger difference with a maximum up to 9.8% between our data and the SigmaCalc data in the energy range from 2.1 to 3.1 MeV. Over the whole studied energy region, current data agree with other available datasets from literature, especially with those of Freier and Miller.
Fig. 2. Measured T(p, p)T elastic scattering cross sections at laboratory angles of 155° and a comparison with the earlier data.
0
Scattering cross sectopm (kb/sr)
The accuracy of the proton scattering cross section measured here is limited by the uncertainties of all the parameters present in Eq. (1). The errors of AT and Apd result from statistical errors and background subtraction uncertainties in the T and Pd peak areas determination, and they are typically 2–3% in all cases less than 4%. The error in rPd;Ruth is less than 1% as related to uncertainties in the scattering angle (1%) and the proton beam energy (6 keV) in the measured energy region. Plus the measuring errors of areal densities (Nt)Pd, (Nt)T (under 5%), the total error associated with the cross sections is no larger than 7.3%. The same error level was achieved for the cross section measurement of protons from helium.
Present data, 151 0 Freier et.al, 153.74 0 Miller et. al. ,153.56 0 Barnard et.al, 153.56 0 Barnard et. al. , 147.02 0 Nurmela et. al. , 140 0 SignaCalc, 151
300
200
100
0
1
2
3 4 5 Proton energy (MeV)
6
Fig. 3. Measured He(p, p)He elastic scattering cross sections at laboratory angles of 151° and a comparison with the earlier data.
Table 1 Measured differential cross sections in the laboratory system for T(p, p)T at 155° from 1.2 to 3.5 MeV. Beam energy E (MeV)
dr/dX (mb/sr) (155°)
1.222 1.422 1.623 1.824 2.024 2.224 2.424 2.625 2.825 3.025 3.225 3.425
134.2 139.3 138.7 138.0 135.3 131.3 123.2 116.9 111.5 105.8 99.2 95.4
Table 2 Measured differential cross sections in the laboratory system for He(p, p)He at 151° from 1.4 to 3.7 MeV. Beam energy E (MeV)
dr/dX (mb/sr) (151°)
1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7
116.1 150.8 169.7 190.1 201.2 231.9 252.1 262.5 263.1 259.6 254.9 242.2 221.4 204.8 175.2 170.4 157.2 141.9 131.6 125.8 122.9 109.8 103.3 103.5
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value of about 300 at about 2.4 MeV at 165°, and then keeps oscillating around this maximum value as the incident proton energy increases. 4. Conclusion
Cross Section ratio of elas./Ruth.
Fig. 4. Measured cross sections enhancement for T(p, p)T elastic scattering at laboratory angles of 155° and 165°.
350
The differential cross sections for elastic scattering of protons from tritium in the energy range from 1.2 to 3.2 MeV at a backscattering angle of 155° in laboratory system and from helium between 1.4 and 3.7 MeV at 151° have been measured. The cross section enhancements of three orders of magnitude relative to the Rutherford case for the T(p, p)T reaction and of two orders of magnitude for the He(p, p)He reaction were recorded. For T(p, p)T, the determined values in the high energy region show that the cross section monotonically decreases with increasing energy, but in the low energy region a cross section curve maximum exists at around 2.1 MeV, which is consistent with the previous results from literature. Over the entire energy range the cross section enhancement increases almost linearly with energy. For the He(p, p)He reaction, the values determined in the present work at 151° are very close to the SigmaCalc data for incident proton beam energies of less then 2.1 MeV, while for the energies larger than 3.1 MeV, they agree rather well with available datasets such as Miller’s and Freier’s. The cross section enhancements below the 2.3 MeV increase almost linearly with energy and then keep oscillating around a maximum of about 300.
300
Acknowledgements 250 200
This work was supported by IAEA agency’s Co-ordinated Research Project under Contract No. 13268/R0 and in part by the National Natural Science Foundation of China under Grant No. 10975035. And the authors are grateful to the staff of the tandem accelerator of the Institute of Modern Physics at Fudan University.
0
165 0 151
150 100
References 50 0
1.0
1.5
2.0 2.5 3.0 Proton Energy (MeV)
3.5
4.0
Fig. 5. Measured cross sections enhancement for He(p, p)He elastic scattering at laboratory angles of 151° and 165°.
The cross section enhancements for the T(p, p)T and He(p, p)He elastic scattering reactions are shown in Figs. 4 and 5, respectively, in the form of ratio of the elastic scattering cross section to the Rutherford one. As far as the T(p, p) T reaction is concerned, the above mentioned ratio increases almost linearly with energy over the entire energy range, and a maximum enhancement of about three orders of magnitude is achieved at the energy of 3.4 MeV. However, in the case of the He(p, p)He reaction, the ratio increases almost linearly with energy below 2.3 MeV, reaches a maximum
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