Helium elastic scattering from carbon for 30° to 150° in the energy region from 2 to 4.8 MeV

The differential cross-sections for elastic scattering of 4He ions by carbon atoms were measured at scattering angles of 30°, 45°, 60°, 135° and 150° in the energy range from 2 to 4.8 MeV. Up to now mostly data for angles larger than 150° were

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  Helium elastic scattering from carbon for 30   to 150   inthe energy region from 2 to 4.8 MeV I. Bogdanovi  cc Radovi  cc  a,* , M. Jak  ssi  cc  a , O. Benka  b , A.F. Gurbich  c a Rud  - er Bo   s s kovi   cc  Institute, P.O. Box 1016, 10000 Zagreb, Croatia b Institut f  € uu r Experimentalphysik, Johannes Kepler-Universit € aa t Linz, 4040 Linz, Austria c Institute of Physics and Power Engineering, 249020 Obninsk, Russia Abstract The differential cross-sections for elastic scattering of   4 He ions by carbon atoms were measured at scattering anglesof 30  , 45  , 60  , 135   and 150   in the energy range from 2 to 4.8 MeV. Up to now mostly data for angles larger than150   were published in the literature. A thick carbon target with a thin evaporated Cu layer on the surface was used forthe measurement. The number of impinging projectiles was obtained from the He ions scattered by the Cu layer as-suming Rutherford cross-sections. The carbon scattering cross-sections were then obtained from comparison of mea-sured He energy spectra with the simulated ones. Above 2 MeV all evaluated cross-sections become non-Rutherford.Deviations from Rutherford cross-sections are about 50% for 30   scattering angle and amount up to a factor 30 for 150  scattering angle. The measured experimental cross-sections were compared with the calculated theoretical cross-sectionsand already published data. Satisfactory agreement was obtained for all measured scattering angles and ener-gies.    2002 Elsevier Science B.V. All rights reserved. PACS:  25.45.De; 34.50.  s Keywords:  4 He elastic scattering from carbon ; Non-Rutherford cross-sections 1. Introduction Rutherford backscattering (RBS) is a wellknown and widely used analytical technique forproviding information such as elemental compo-sition, stoichiometry or thickness of the analyzingsample. Because of the  Z  2 dependence of RBScross-sections, this method cannot be effectivelyapplied for detecting low- Z   elements, especially inthe presence of a high- Z   substrate. In some cases(e.g. SiC films, Si wafers), detection of light ele-ments presented in the heavy matrix as impuritiesor major constituents can be of special concern.The fact that cross-sections for  4 He scatteringfrom N, C and O become non-Rutherford above2 MeV and are in some cases up to 100 times largerthan Rutherford can be used for analytical pur-poses. It has been already shown that the intenseresonance for  12 C or  16 O could be used as a pow-erful tool for profiling carbon and oxygen invarious substrates [1]. The non-Rutherford cross-sections for scattering of   4 He from C have beenreported by a number of researchers in the last few Nuclear Instruments and Methods in Physics Research B 190 (2002) 100–106www.elsevier.com/locate/nimb * Corresponding author. Tel.: +385-1-4561-161/4680-942;fax: +385-1-4680-239. E-mail address:  iva@rudjer.irb.hr (I. Bogdanovi cc  Radovi cc ).0168-583X/02/$ - see front matter    2002 Elsevier Science B.V. All rights reserved.PII: S0168-583X(01)01228-9  decades [1–10]. The available experimental infor-mation was compiled and the recommendeddifferential cross-sections were produced in theframeworks of a theoretical approach [11]. Thoughthe significant enhancement of the  4 He þ C cross-section is observed only at the very back scatteringangles, sometimes due to experimental arrange-ments or demands, smaller scattering angles be-come also interesting. As is already shown inprevious works, cross-sections for  4 He scatteringfrom C are changing rapidly with the scatteringangle. In our case due to the experimental ar-rangement particle detector was placed at 150  .Also in some ERDA setups [12], recoil H atomsand scattered  4 He projectiles are detected withinthe same solid-state detector. Elastic scattering of  4 He from C in the forward angles can also be usedfor normalization in the ERDA analysis. In thiscase scattering cross-sections for angles  < 60   hasto be known, which are jet only published for highprojectile energies. The aim of the work was two-fold: to acquire new experimental data for the 4 He þ C cross-section and to check whether theevaluation [11] made for elastic backscattering of  4 He from carbon is also valid for forward scat-tering.The differential cross-sections for scattering of  4 He ions from carbon atoms were measured atthree forward (30  , 45  , 60  ) and two backwardangles (135  , 150  ) in the energy interval from 2to 4.8 MeV. The obtained experimental cross-sec-tions were compared with the calculated theoreti-cal cross-sections and with the already publishedexperimental data. 2. Experiment and data analysis Measurements were done using the 1.6 MV5SDH Pelletron tandem accelerator at the Johan-nes Kepler University in Linz. The energy cali-bration of the 90   magnet for defining theprojectile energy was made by use of two ex-tremely thin alpha sources:  148 Gd (3182.78 keV)and  239 Pu (5155.4 keV). The estimated accuracy of energy calibration is better than 1 keV. Thick highpurity graphite on which thin Cu film (77  10 15 atoms/cm 2 ) was evaporated was used for themeasurements. The thickness of a thin Cu film wasobtained from spectrum collected at 2 MeV for 30  scattering. Assuming that cross-sections for  4 Hescattering from C and Cu are Rutherford at2 MeV the best fit can be obtained for Cu thick-ness of 78  10 15 atoms/cm 2 . The angle betweenthe beam and the sample surface was 22 : 5   0 : 3  .The beam spot on the sample surface was 1.5 mmin diameter. The elastically scattered  4 He particleswere detected by a silicon surface barrier (SB)detector located 90 mm from the target. A circularaperture with a 4 mm 2 diameter was mounted infront of the detector defining an acceptance solidangle of 1.55 msr. The SB detector was mountedon the holder and it was possible to move thedetector without breaking the vacuum betweenscattering angles of 0   and 160  .Instead of using thin carbon target and point bypoint measurements we have decided to extract thecross-sections from a thick target yield. Using thismethod, only a few discrete measurements have tobe done to obtain the whole excitation curve. Wehave varied the energy of incident  4 He ions from2.5 to 4.8 MeV in steps of 0.5 MeV. At each en-ergy, cross-sections were determined for fivedifferent scattering angles (30  , 45  , 60  , 135   and150  ). The data were collected using typicalcharged particle spectroscopy system (solid-statedetector, charge sensitive preamplifier, spectro-scopy amplifier, analog-to-digital converter andmultichannel analyzer).The yield in each channel in the spectrum wasrelated to the detected energy of the scattered ionsthrough an energy calibration. Detected energieswere than correlated with the corresponding inci-dent ion energies. At particular depth in the target,incident energy was calculated by taking into ac-count ion energy loss on the way in and out fromthe target and change in energy due to the kine-matic factor. Finally, the yield at a given depth wascompared with the corresponding Rutherfordyield for the same depth. The number of incident 4 He projectiles was obtained from the projectilesscattered by the Cu atoms for which Rutherfordcross-sections were assumed for all energies andangles.Experimental spectra were compared withtheoretical ones using a computer program I. Bogdanovi   cc  Radovi   cc  et al. / Nucl. Instr. and Meth. in Phys. Res. B 190 (2002) 100–106   101  SIMNRA [13]. Resulting comparison betweenmeasured spectra and spectra calculated usingRutherford cross-section is shown on Fig. 1.Comparison is done for 60   spectra at two differ-ent  4 He energies, 2 and 4.5 MeV. The depth res-olution in SIMNRA is calculated taking intoaccount the electronic and nuclear energy lossstraggling, energy resolution of the detector andgeometrical straggling. Angular and lateral strag-gling due to the multiple scattering is not includedin SIMNRA calculations. Multiple scattering be-comes important for smaller ion energies and atlarger depths. Therefore, only the high-energy partof each spectrum (closer to the sample surface) wastaken for the cross-section evaluation. The pro-gram DEPTH [14] was used to take into accountmultiple scattering. The contribution of this effectwas found to be 2% in the worst case.Though simple the thick target method forcross-section determination has some drawbacks.It is evident that the use of a stopping power in thesynthesis of the backscattering spectra introducesan additional uncertainty. In addition, the datameasured in the vicinity of the narrow resonancesare smoothed due to the finite energy resolution of the method.The error in the cross-section ratio is estimatedto be less than 8% for all energies and scatteringangles, considering the statistical error of thecounting rates and the error of detector angularsettings. The error in the stopping power should beadded to this estimation. Above the stoppingpower maximum, i.e. above 1 MeV, the stoppingpower data for stopping of   4 He in C are wellknown [15]. From the data for stopping of He in C[15] can be concluded that absolute errors are less Fig. 1. Comparison between measured (  ––  ) and calculated using Rutherford cross-sections (- - -) spectra at 60   for two different  4 Heenergies: (a) 2 MeV and (b) 4.5 MeV.102  I. Bogdanovi   cc  Radovi   cc  et al. / Nucl. Instr. and Meth. in Phys. Res. B 190 (2002) 100–106   than 10% and relative errors are for 4.8 MeV lessthan 5% and for the smaller energies smaller res-pectively. 3. Results and discussion Ratios of measured cross-sections to Ruther-ford cross-sections are shown in Fig. 2(a)–(c) forforward scattering angles. Fig. 3(a) and (b) showthe same cross-section ratios but for two back-ward angles, 135   and 150  . For comparison, theother available experimental data, as well as the-oretical calculations [11] are given in the samefigures. There are only few measurements at anglesstudied in our work or close to them. Marvin andSingh [2] published in 1972 16 excitation functionsfor c.m. angles between 30.6   and 158.8   but onlyfor energies above 4 MeV. Cross-sections for29.7  , 44  , 136   and 148.9   were compared with Fig. 2. Ratios of   4 He–C cross-sections to Rutherford cross-sections for three different forward scattering angles: (a) 30  , (b) 45   and(c) 60  . ( ): present measurements, (  ––  ): theory, ( ): Marvin and Singh [2]. I. Bogdanovi   cc  Radovi   cc  et al. / Nucl. Instr. and Meth. in Phys. Res. B 190 (2002) 100–106   103  our results at Figs. 2 and 3. It can be seen that forall angles except 150   agreement between the twosets of data is very good. For 150  , in the high-energy part, our data are about 20% higher thandata from Marvin and Singh. Another three da-tabases exist for angles close to 135  . Data fromMiller Jones et al. [7] for 136   are in excellentagreement with our data up to 4.2 MeV and thenthey become higher than our data up to 20%. Datafrom Bittner and Moffat [8] for 134   are lower forabout 20% then ours. Hill [9] published data forenergies from 2.5 to 4 MeV and 133  . His data areless than 10% lower than present measurementsand in excellent agreement with theoretical calcu-lations.In the theoretical calculations, which are de-scribed in details in [11] the interaction betweenthe impinging ion and the target nucleus wastreated as scattering from a real potential well. Thecompound nucleus level contributions were takeninto account by addition of Breit–Wigner reso-nance terms to the amplitudes obtained by re-solving Schr € oodinger equations for partial waves.The model parameters were adjusted using theexisting experimental excitation functions andangular distributions taken from different sources.Thus the evaluated cross-sections have been pro-duced. The main idea of the evaluation is to in-corporate all available experimental informationin the framework of the theoretical model, which isbased on the appropriate physics. Because of thelow statistical weight of a single data set and sinceonly minor discrepancy between measured andcalculated cross-sections was found no attemptwas made in the present work to revise the rec-ommended cross-sections [11].As can be seen from Figs. 2 and 3, agreementbetween present measurements and theory is very Fig. 3. Ratios of   4 He–C cross-sections to Rutherford cross-sections for two different backscattering angles: (a) 135   and (b) 150  . ( ):present measurement, (  ––  ): theory, ( ): Marvin and Singh [2], ( ): Miller Jones et al. [7], ( ): Bittner and Moffat [8], ( ): Hill [9].104  I. Bogdanovi   cc  Radovi   cc  et al. / Nucl. Instr. and Meth. in Phys. Res. B 190 (2002) 100–106 
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