Rutherford Value Research Articles

Deviations from Rutherford elastic scattering cross sections for Cu and Zn with He ions

The onset of non Rutherford cross section for medium heavy elements like Cu (Z=29; A=63, 65) and Zn (Z=30; A=64, 66, 67, 68, 70) for He as a projectile is studied by means of elastic backscattering measurements made on pure Cu and Zn material samples with He ions at energy ranges from 3 to 10MeV. The scattering cross section relative to Rutherford value is extracted from the experimental values in an energy range from 7 to 10MeV with the help of available computer codes for the simulation of elastic backscattering spectra. The measured energy value for the onset of the deviation of the Rutherford value is in agreement with the calculations of Bozoian et al. (1990) [14].

Hydrogen analysis in diamond like carbon by elastic recoil detection

Among the available surface analytic instruments, elastic recoil detection (ERD) is known as a reliable method for hydrogen analysis. Since conventional fluence determination i.e. beam current integration is incredible at a large tilt angle, ion fluence is determined by the scattering spectrum that is simultaneously measured with recoil spectrum. However scattering cross sections deviate Rutherford values in the ERD energy of 1–3 MeV. Carbon scattering cross section is different from Rutherford value for higher beam energies over 1.8 MeV. As a result hydrogen content is exaggerated when fluence is determined by carbon matrix because of fluence underestimation due to lower value of scattering cross section than Rutherford’s. Therefore in order to quantify hydrogen in diamond like carbon (DLC) incident beam energy lower than 1.6 MeV should be used where carbon scattering cross sections are well agreed with Rutherford’s.

Complementary use of ion beam elastic backscattering and recoil detection analysis for the precise determination of the composition of thin films made of light elements

Rutherford backscattering spectrometry (RBS) is a well known powerful technique to obtain depth profiles of the constituent elements in a thin film deposited on a substrate made of lighter elements. In its standard use the probing beam is typically 2MeV He. Its capabilities to obtain precise composition profiles are severely diminished when the overlaying film is made of elements lighter than the substrate. In this situation the analysis of the energy of the recoiled element from the sample in the elastic scattering event, the ERDA technique may be advantageous. For the detection of light elements it is also possible to use beams at specific energies producing elastic resonances with these light elements to be analyzed, with a much higher scattering cross sections than the Rutherford values. This technique may be called non-RBS. In this work we report on the complementary use of ERDA with a 30MeV Cl beam and non-RBS with 1756keV H ions to characterize thin films made of boron, carbon and nitrogen (BCN) deposited on Si substrates.

Proton elastic scattering from aluminum for 120°, 150° and 165° in the energy interval from 2.4 to 5 MeV

The differential cross sections for elastic scattering of H ions from aluminum were measured at scattering angles of 120°, 150° and 165° in the energy range from 2.4 to 5MeV where no data relevant to backscattering analysis were previously reported. It was found that in the studied energy interval excitation functions show complex resonance structure with significant deviation from the Rutherford value. The benchmark experiment at 4.2 and 5.0MeV was performed in order to test how measured cross sections can interpret thick target yield from pure Al target.

Electron Compton scattering from methane and methane-d4

Quasi-elastic electron scattering at high-momentum transfer was measured for CH 4 and CD 4 in the gas phase. At high-momentum transfer, two scattering peaks are observed in each molecule. We interpret the splitting as due to independent Compton scattering from each nucleus, such that, at an impact energy of 2 keV and 100° scattering angle, the peaks for the C and H in CH 4 are split by 2.1 eV while those associated with the C and D in CD 4 are split by 1.1 eV. These splittings are in agreement with those predicted from Rutherford scattering of electrons from single atoms. The widths of the C, H, and D peaks are very different, and reflect the distribution of their momentum. The lineshapes of the H(D) peaks are in agreement with the momentum space vibrational wavefunction. Detailed peak area analysis reveals anomalously low intensities for the hydrogen and deuterium peaks relative to the carbon peak—the theoretical Rutherford C–H ratio is 9.0, compared with 9.8(2) (C–H) and 9.7(2) (C–D) measured in our experiments. Two possible explanations for this discrepancy, one due to deviations of the actual cross section from the Rutherford values, the other due to short lived quantum entanglement, are discussed. The Rutherford scattering interpretation is compared to that for vibrational Compton-like scattering predicted by Bonham and de Souza [R.A. Bonham, G.G.B. de Souza, J. Chem. Phys., 79 (1983) 134].

Deviations from Rutherford backscattering cross section for backscattering of 6Li ions from fluorine between 2.5 and 7 MeV

The differential elastic backscattering cross section has been determined for backscattering of 6Li ions from fluorine at energies between 2.5 and 7 MeV. The scattering angle was 150° in the laboratory system. It was found that the ratio between the measured cross section and the Rutherford value is constant up to an energy of 4.5 MeV. Significant deviations from the Rutherford value have been found for energies above 5 MeV. Experimental results of the cross section were corrected for the screening effect. Deviations from the Rutherford cross sections are compared with predictions of the theoretical model developed by Bozoian.

Measurement of elastic recoil cross sections of light nuclei by 35Cl using inverse scattering

The elastic recoil cross sections of 6Li, 12C, 16O and 19F by 35Cl below the incident energy of 10 MeV have been measured by the inverse scattering method. About 10 17 Cl/cm 2 BaCl 2 vacuum-deposited on 1 μm DLC (Diamond Like Carbon) was used as a target. During the irradiation the target showed good stability. The Cl isotope effect has an influence on the recoil cross section of less than 0.5%. In the useful energy region for quantitative analysis by elastic recoil detection, the measured recoil cross sections agree with the Rutherford's values within a few percent.

Distribution in angle of the Bloch correction in electronic stopping

The position in angular space of the Bloch correction to the perturbative electronic stopping power formula of Bethe is investigated. It is demonstrated that this nonperturbative correction which originates in close collisions between the penetrating ion and target electrons appears at small scattering angles and that its position depends on the (adiabatic) cutoff at large distances. In the limit of infinite range the correction moves to infinitely small angles but remains finite and both the exact and the perturbative cross sections approach the Rutherford value at all finite angles. The picture is consistent with the lack of a Bloch-type correction in the energy-loss straggling. {copyright} {ital 1997} {ital The American Physical Society}

Quantitative calibration of intense (α, α) elastic scattering resonances for 12C at 5.50–5.80 MeV and for 16O at 7.30–7.65 MeV

Extremely strong (α, α) elastic scattering resonances — more than 100 times the Rutherford value — occur in 16O at 7.35–7.65 keV and in 12C at 5.50–5.80 MeV, thus allowing the normal RBS technique to be extended to low-Z components, such as oxygen and carbon. Both resonances have been calibrated over the appropriate 300 keV energy regime with an overall accuracy of ±4%. Some recent examples of their use in profiling oxygen and carbon in various substrates are given.

Cross sections for 170° backscattering of 4He from oxygen in the energy range of 2.0–9.0 MeV

We report the 170° backscattering cross sections of 4He from O in the energy range of 2.0–9.0 MeV. Our measurements show that the alpha-oxygen scattering remains Rutherfordlike up to E α = 2.35 MeV, and there exist two energy regions, 5.55–5.85 MeV and 8.50–8.80 MeV, where the cross sections present an enhanced and smooth variation. The measured cross sections in these two regions exhibit enhancement factors of 9.7 and 34, respectively, compared to the Rutherford values. In the 8.50–8.80 MeV region, the cross sections at scattering angles of 160°, 165°, 170° and 175° were measured and found to be strongly angle-dependent. The strongest resonance was seen at 7.60 MeV, where the cross section is 200 times its Rutherford value. We report the use of this resonance to measure the O areal density on a Cu surface, with a sensitivity of 1 × 10 15 oxygen atoms cm 2 . We have also studied the scattering angle dependence of the threshold energy at which the cross section begins to depart from its Rutherford value. Our experimental results are not in agreement with the prediction from the analytical formula developed by Bozoian et al. [Nucl. Instr. and Meth. B 51 (1990) 311].

The studies of non-Rutherford backscattering cross sections of 4 He from 16 O

In this article, we report the 170° backscattering cross sections of 4He from 16O in the energy range of 2.0-9.0 MeV. Our measurements show that the alpha-oxygen scattering remains Rutherford scattering up to Eα=2.35 MeV, and there exist two energy regions, namely 5.55-5.85 MeV and 8.50-8.80 MeV, where the cross sections are enhanced and show a smooth variation. The measured laboratory cross sections are 9.50-9.97 and 35.0-33.0 times greater than the Rutherford values, respectively. In the 8.50-8.80 MeV region, the cross sections at scattering angles of 160°, 165°, 170° and 175° were measured and found to be strongly angle-dependent. A most strong resonance occurred at 7.60 MeV, where the cross section is 200 times of its Rutherford value. This resonance has been used to measure the 16O concentration on a Cu surface, with a sensitivity of 1×1015 oxygen atoms/cm2. Besides, we have studied the backscattering angle dependence of the threshold energy, i. e., the energy at which the elastic cross section begins to deviate from its Rutherford value. The experimental result seems not in agreement with the prediction made from the analytical formula developed by Bozoian et al.

Comments on the classical approach to non-Rutherford cross section calculations

Non-Rutherford cross sections are needed in high energy backscattering spectroscopy. Bozoian et al. have developed a classical model and derived an analytical expression to calculate the projectile energy E nr at which the scattering cross section begins to deviate from its Rutherford value. We make comments on the model and conclude, through discussions and experiments, that (1) it is useful in estimating the energy value but gives incorrect dependences of E nr on the departure factor F and the scattering angle χ, and (2) these inadequacies originate from the classical approach, which is an over-simplified and phenomenal description of nature.

Cross section for 160° elastic scattering of 1.4–2.4 MeV protons from nitrogen and titanium

Differential elastic scattering cross sections for 1·4–2·4 MeV protons from natural nitrogen and titanium were measured at laboratory scattering angle 160°. The present cross section data are tabulated for later use in backscattering analyses. Our results for nitrogen are in qualitative agreement with previous data taken at slightly different scattering angles. The cross sections of titanium agree with theoretical Rutherford values within experimental errors. Examples of recent analytical applications of proton backscattering are given.

Measured deviations from Rutherford backscattering cross sections using Li-ion beams

Bozoian et al. have developed an analytical theory which predicts the incident ion energy at which elastic-scattering cross sections begin to deviate from their Rutherford values as the result of nuclear perturbations. The predictions are in good agreement with experimental data for proton and helium-ion beams, and should be applicable to heavier projectiles. The theory has also been extended to account for isotopic variation of the incident beam. As a further test of the theory, we have performed a series of backscattering measurements using both 6Li and 7Li ion beams. Lithium-ion backscattering is of importance to thin-film analysis because it offers improved depth sensitivity and kinematic mass resolution as compared to helium. Elastic-backscattering cross sections for O, F, Al, and Ti were measured relative to those ofhigh- Z reference elements over an energy range of 2.5–9.25 MeV, and the energies at which they began to deviate from their Rutherford values were determined. The experimental results are compared to predictions from the analytical theory, and from optical-model calculations.

Thresholds of non-Rutherford nuclear cross sections for ion beam analysis

A theoretical model of classical scattering in the presence of combined Coulomb and weakly perturbing nuclear fields predicts the incident ion energies at which elastic backscattering cross sections begin to deviate from their Rutherford values [M. Bozoian et al., Nucl. Instr. and Meth. B51 (1990) 311]. The model, parameterized with two nuclear constants, is in good agreement with experimental data for proton and helium-ion beams. This classical model was revised by including the nature of the Z = 1 and 2 projectiles. In this paper the revised model is applied to Z = 3 projectiles. Although little backscattering data exists, there is consistency among the optical model calculations of departures from Rutherford backscattering for the lithium-target systems considered. The revised model is in good agreement with these calculations. New experimental results for 6Li and 7Li ion beams compared with the revised model are presented at this conference [K.M. Hubbard et al., Bull. Am. Phys. Soc. 35 (1990) 1785].

Deviations from Rutherford-scattering cross sections

Recent experiments have demonstrated the utility of high-energy backscattering for thin-film analysis, often exploiting elastic-scattering resonances to increase sensitivity to low- Z elements. However, higher- Z elements may also exhibit deviations from Rutherford scattering, and it is desirable to examine the problem theoretically so that such deviations can be predicted and corrected for. We have used the optical-model computer code SCAT86 to calculate the projectile energy E nr at which the scattering cross section begins to deviate from its Rutherford value. The results agree well with data for both alpha particle and proton projectiles, but the interaction potentials are complicated, and the program does not provide an analytical predictive formula. We have therefore developed a simple classical model which treats the interaction as a sum of Coulomb and Yukawa-like potentials. For small deviations from Coulomb scattering, the problem can be solved analytically, providing a simple expression for E nr which agrees well with both experimental data and SCAT86. The classical approach is valid for all but small-angle forward scattering and can easily be extended to heavier projectiles such as Li.

Determination of nitrogen content in thick TiN layers by proton backscattering

Non-Rutherford proton backscattering has been employed for the determination of the nitrogen content in TiN layers of a thickness of several micrometres deposited on a steel backing. The required proton scattering cross section has been measured using standards comprising thin TiN films on a light substrate. The scattering cross section of 2 MeV protons of nitrogen for θ lab = 160° was found to be 5.7 times the Rutherford value. Nitrogen detection limits in thick TiN samples are discussed.

Backscattering of 7Li-ions from oxygen below 6.25 MeV

Differential scattering cross sections for 7Li-ion scattering from oxygen between 2.75 and 6.25 MeV at a laboratory detection angle 170° have been determined. Rutherford scattering was observed below 3 MeV. Above 3.50 MeV the cross sections were found to vary from 1.07 to 0.18 of the Rutherford value. No sharp resonances were detected, 7Li-induced charged particle thick target reaction yields from carbon were investigated. From the point of view of Li-ion backscattering analysis, these reaction yields will cause significant interference above 5 MeV whenever major amounts of carbon are present in the sample under study.

Measurement of 4He-p recoil cross sections

The recoil cross sections of protons induced by 4He + particles were experimentally determined in an energy range of 1.3–2.1 MeV at recoil angles of 20° and 30 ° . The angular dependence of the recoil cross section at 2.0 MeV was also measured. By using the principle of detailed balance, a calculation of 4He-p recoil cross sections were calculated from p- 4He phase shift data. Good agreement between the experimental data and theoretical values was found. The results show that recoil cross sections at low energies are non-Rutherford and are larger than the Rutherford value by approximately a factor of 2 at 2.0 MeV.

Elastic and inelastic scattering of 79.5 MeV 11B and 87.5 MeV 10B ions

The elastic scattering of 79.5 MeV 11B ions has been studied for seven targets ranging in mass from 24Mg to 197Au and of 87.5 MeV 10B ions for three of these targets ( 24, 25Mg, 60Ni). Angular distributions were measured from ~10° c.m. in steps of 0.5°, to angles beyond 40° c.m. where the elastic cross sections are ≲ 10 −3 of the Rutherford values (except for 197Au). Inelastic data for exciting the lowest 2 + states of 24,26Mg and 60Ni were also obtained. Important odd- A-even- A differences are observed in the 11B elastic angular distributions for the Mg and Al targets; for 10B scattering these are obscured by projectile quadrupole moment effects on the elastic scattering. The elastic data were analyzed using the optical model with potentials of both Woods-Saxon and double-folding form. The data for both 10B and 11B are consistent with the potential obtained in the folding model with the M3Y interaction without renormalization. The inelastic data were analyzed by the distorted-waves method.