D. Semrad

Reference stopping cross sections for hydrogen and helium ions in selected elements

Abstract This article presents new fits to all the available published experimental data on electronic stopping for hydrogen projectiles (10 to 2500 keV/nucleon) on Au, Ag, Cu, Ni, and Al, and for helium projectiles (60 to 7500 keV) on Au and Ag. In all of these cases, we also have data measured in our own group. The data from 13 (Out of 123) publications are rejected a priori, mostly because the measurements are relative. We use a least-squares fit to a four-parameter function of the energy, and we reject discrepant data using two statistical criteria. Our fit results are shown graphically together with all the data points and with various fits by other authors. For hydrogen projectiles, we find that the stopping maximum has a lower value than given by Andersen and Ziegler, except in the case of Al, where almost all the fits agree well. For helium projectiles, the agreement of the various data sets and of the fits is generally better. For both types of projectiles, the fitted cross sections for Ag and Au do not cross in the energy region considered, which is not true of fits by other authors.

Determination of stopping power for ions by backscattering from thin targets

Abstract A new procedure is presented for extracting the stopping power from the widths of a number of backscattering spectra. It can be applied irrespectively of the magnitude of the kinematic factor. For this method we introduce a function dependent on four parameters, the shape of which is sufficiently adaptable not to cause a relevant bias. This is demonstrated by fitting this function to the proton stopping power tables of Janni: for all 92 elements we list the fit parameters together with the mean and the maximum deviation. By computer simulation it is shown that the projectile energies in the backscattering measurements have to cover a certain range — depending on the kinematic factor — to give the correct stopping cross section. Finally, we applied this procedure to the measurement of the stopping cross section of Al for He-ions.

The influence of different experimental methods on the measured energy dependence of stopping powers

The stopping cross section data measured by foil transmission often show an energy dependence different from that of RBS measurements. This cannot be due to problems connected with foil thickness-determination. Therefore, we investigate in this contribution, how the energy loss data in these types of measurements are influenced by the different projectile paths due to impact-parameter selection, plural and multiple scattering, by target properties such as bulk and surface impurities, texture and desity differences and by the use of different energy analyzers. Experiments have been performed which prove the reliability of our target preparation, stopping cross section measurements and data evaluation with respect to these influences.

Formulae and theories to predict proton stopping powers around the maximum

Abstract We test predictions of stopping powers available in the literature by our accurately measured copper data, for proton energies from 50 keV to 1 MeV. In particular, we compare the tabulations by Northcliffe and Schilling; Biersack et al.; Andersen and Ziegler; Janni; Ziegler and the theories by Lindhard and Winther; Sugiyama; Burenkov, Komarov and Temkin; Sigmund; Kuhrt, Wedell, Semrad and Bauer; McGuire. The models used in our calculations to describe the electron density in the solid are discussed.

Reference proton stopping cross sections for five elements around the maximum

Abstract Absolute values of the proton stopping cross sections of Al, Ni, Cu, Ag and Au are presented which have been carefully determined by different methods in two laboratories. An analytical function depending on four parameters is fitted to these data. As the chosen range from 30 to 700 keV covers the energies where the stopping powers reach their maxima, values for the position E m and the height s m of these maxima are deduced. These data are compared to available theories: on the one hand to theories which predict a smooth dependence of s m × E m on E m , and on the other hand to theories which show how these maxima arise from the contributions of the individual subshells of the target atom.

INFLUENCE OF THE CHEMICAL STATE ON THE STOPPING OF PROTONS AND HE-IONS IN SOME OXIDES

Abstract We present stopping cross section data of Al2O3 and SiO2 for hydrogen- and helium-ions in the energy range 2–1000 keV, measured in transmission and in backscattering geometry. To interpret the data, we discuss the high velocity and the low velocity limit of so-called chemical effects commonly defined as the difference in stopping of the compound and of a mixture of its constituents, as calculated by applying Braggs rule. At high velocities, the projectiles are point charges and only changes in the target electron states contribute to the chemical effect. In addition, at low velocities the charge states of the projectiles and the screening by the target valence electrons may differ in the compound and in the mixture, due to different electron densities.

Energy loss of hydrogen and helium ions in hydrogen and helium gas: looking for exceptions from velocity proportionality

Abstract At projectile velocities ν 1 below the Bohr velocity the electronic stopping cross section e of hydrogen (H 2 , D 2 ) and helium gas for hydrogen isotopes (H, D) and of helium gas for helium projectiles has been measured by a time-of-flight technique. We find the hydrogen stopping in He to show a significant departure from the ν 1 -proportionality commonly assumed (e α ν 1 3.3 at 4 keV per nucleon) [R. Golser and D. Semrad, Phys. Rev. Lett. 66 (1991) 1831]. Electronic stopping of H, D onto H 2 , D 2 (e α ν 1 0.9 at 4 keV per nucleon) and He onto He (e α ν 1 0.8 at 4 keV per nucleon,if nuclear stopping is not subtracted) may be considered velocity proportional. We attribute this behavior to the probability of charge changing processes, which is small if projectile and target ground state levels are strongly different. The helium to hydrogen stopping ratio of helium gas has the strange value 5.8 at 4 keV per nucleon; possible implications to the concept of “effective charge” are discussed.

Investigation of hydrogen stopping in noble metals around the stopping power maximum

Abstract The stopping cross sections of copper, silver and gold for protons and deuterons were measured in the energy range from 50 keV/amu to 500 keV/amu. All measurements were performed on supported films evaporated onto polished backings employing both transmission and backscattering type techniques. By use of different hydrogen isotopes — assuming velocity scaling — and of different target thicknesses we showed that plural and multiple scattering do not influence our results within the experimental uncertainties of ± 3%. As a cross check the stopping ratios were also measured by evaluation of the heights of the backscattering spectra and were found to be consistent with the absolute values. Our results are compared to the theory of Lindhard-Winther using different solid state charge distributions and to the binary encounter theory of Kuhrt and Wedell. Best agreement is achieved for those calculations which take the correct density of the valence electrons into account. Furthermore, our results are compared to the fitted data by Andersen and Ziegler (1977), by Janni (1982) and by Ziegler (to be published). In general, better agreement with the more recent fit-data was found.

How to predict physical and chemical state effects in electronic stopping

Abstract In the field of material modification and ion beam analysis, one often wants to know accurately the electronic stopping power of a compound, which defines the depth scale. Obviously, experimental data are not available for all materials of interest. Therefore theoretical models are required to yield this information. In this contribution we present approaches of how to obtain reasonably accurate estimates of the magnitude of chemical (and physical) state effects at high velocities, i.e. in the Bethe regime. First, we discuss how the I value (mean ionization potential) of a material in a certain physical state can be constructed from the I values of its constituents in their common state of aggregation, by including appropriate sub-shell I values (theoretical or experimental ones). Second, we discuss an approach to obtain the I value of a compound beyond Braggs rule, by an empirical correction making use of the heat of formation of the compound.

Energy calibration at several hundred keV by time-of-flight and by comparing protons with H2+ ions

Abstract Energy calibration techniques for a 700 keV Van de Graaff accelerator down to 80 keV have been studied. For this purpose a method has been developed, by which the time-of-flight of that part of the beam hitting the target can be measured directly and which is therefore easily installed in an existing beam transport system. The given flight path of 5.6 m was found to be sufficient. These results were compared to a calibration procedure for the switching magnet, where we employ protons and H 2 + ions of either equal energy or equal velocity. It is discussed how far this will be influences by the Coulomb explosion of the H 2 + ion when hitting the target; also considered is this influence when H 2 + ions inducing the (p, γ) resonance in Al at 992 keV are used for calibration purposes. In the energy range from 80 keV to 700 keV a precision in determining the energy by time-of-flight of 0.5% for protons and 0.3% for He ions and by the magnet calibration procedure including comparison of p and H 2 + of 0.2% was found.