Proton Stopping Cross Sections Research Articles

Impact-Parameter Dependence of the Electronic Energy Loss of Protons in Solids

We calculate the electronic energy loss of the low- and intermidiate-energy proton in collision with a solid atom as a function of the impact-parameter by using the linear-response dielectric theory, the semiclassical approximation and local electron density approximation. The correlation and exchange interaction of the electron gas in solids is taken into consideration by using a local-field-correction dielectric function. With the formalism we also calculate the electronic stopping cross section of protons in solids.

Bond stopping cross sections for protons incident on molecular targets within the OLPA/FSGO implementation of the kinetic theory

We report the predictions of the kinetic theory for proton stopping in molecular targets within the orbital local plasma approximation (OLPA) introduced by Meltzer, Sabin and Trickey [Phys. Rev. A 41 (1990) 220]. In order to present a self-contained treatment, all the quantities entering in the calculations are obtained through use of the floating spherical Gaussian orbital (FSGO) representation of localized molecular orbitals. The calculations are performed for representative molecular targets, generating S e values for cores, single, double, triple-bonds and lone pairs as a function of projectile velocity. Fair agreement is observed with available experimental data and with other theoretical estimates. The adequacy of the FSGO representation in the study of molecular stopping for protons within the spirit of the kinetic theory and the orbital implementation of the local plasma approximation is confirmed in this work.

Firsov approach to chemical bond effects on the low-energy electronic stopping power of heavy ions

A recently derived modified version of the Firsov model to account for the low-energy electronic stopping cross section of protons due to molecular targets is extended here for the case of heavy projectiles. The method is free of adjustable parameters and is applied to projectiles with 2 ≤ Z ≤ 18 incident on a wide class of hydrocarbon materials and other simpler molecules. A fair overall agreement is observed with available experimental data for He and Li projectiles. The use of characteristic molecular groups as well as the core and bond (CAB) formalism for stopping power studies of heavy ions in compound materials is strongly supported by the results of this work.

The stopping power of Ag and Au, with regard to higher-order Z1-effects

We have measured the absolute stopping cross section ϵ of Ag and Au with a precision of 3%, using backscattering geometry. The velocity of the projectiles (p, [d], He, Li, and C) ranges from about 1.5υ0 to 4υ0. These measurements are compared to calculations of ϵ including the Barkas and Bloch terms. We use a local density approximation employing the harmonic-oscillator calculations by Sigmund and Haagerup, by Mikkelsen and Sigmund, and the calculations by Bloch, introducing a simple shell correction. Within the energy range where our approximations apply, good agreement with the measured proton stopping cross section is found. Furthermore, we find from our calculations that the ratio of the stopping cross sections of Ag and Au does not depend on the type of projectile (in all orders of Z1), in agreement with our measurements.

Proton and helium stopping cross sections in H 2, He, N 2, O 2, Ne, Ar, Kr, Xe, CH 4 and CO 2

Proton and helium stopping cross sections were measured for the noble gases helium, neon, argon, krypton and xenon, the diatomic gases hydrogen, nitrogen and oxygen and for the molecules carbon dioxide and methane in the energy ranges 700 keV–2.1 MeV and 1.0–3.0 MeV, respectively. The statistical and systematical errors are between 1.0 and 1.5% each. Optimum parameters for the Andersen-Ziegler semi-empirical formula were deduced for all data sets by means of the least-squares method. From the stopping cross sections of protons and 4He-ions at same velocity higher order Z 1 corrections (Barkas-correction) for the noble gases He, Ne, Ar, Kr and Xe and the diatomic gases H 2, N 2 and O 2 were calculated, using theoretical values for the Bloch-correction approximated by Bichsel and Porter. The experimental Z 1 3-corrections were compared with the different theoretical predictions of Ashley, Ritchi and Brandt, Jackson and McCarthy and Lindhard and Esbensen.

Barkas effect in electronic stopping power: Rigorous evaluation for the harmonic oscillator

The Coulomb interaction between a heavy fast charged particle and an electron bound by a harmonic force has been evaluated accurately up to the second-order term in the Born series. The resulting mean energy transfer is given as a function of impact parameter, projectile velocity, and the resonance frequency of the oscillator. Integration over the impact parameter yields the stopping cross section up to third order in the projectile charge ${e}_{1}$ without introduction of an adjustable cutoff radius. Unlike previous treatments, the validity of the evaluation of the stopping cross section within the given physical model is not restricted to the high-speed limit. Numerical results cover the velocity range 0.1\ensuremath{\le}2${\mathrm{mv}}^{2}$/\ensuremath{\Elzxh}\ensuremath{\omega}\ensuremath{\le}20. We find a significant ${e}_{1}^{3}$ (or Barkas) correction in the mean energy transfer at all impact parameters. The classical Barkas correction, as given for the harmonic oscillator in the high-speed limit by Ashley, Ritchie, and Brandt [Phys. Rev. B 5, 2393 (1972)], approaches the quantal result for large impact parameters, but the approach is slow in the velocity range covered, and large discrepancies are observed in the range of impact parameters that determine the stopping cross section. Stopping cross sections for protons on atomic hydrogen and helium have been estimated roughly by assigning a single resonance frequency to the target atom. The results cover a velocity range down to somewhat below the stopping maximum where the Barkas correction turns out to be large. This indicates that a properly executed Barkas correction plays an important role in the prediction of the height and the position of the stopping maximum.

Bragg rule additivity of bond stopping cross sections

The gas phase proton stopping cross sections and mean excitation energies for the C-H, C-C, CC, O-H, C-O, CO and N-H bonds are reported. They are obtained using the kinetic theory of stopping from theoretical mean excitation energies and localized bond Compton profiles. These bond cross section are designed for use in a bond type Bragg rule for prediction of the Z 1 2 (Bethe) contribution to molecular stopping.

Reference stopping cross sections for 30–600 keV protons in silicon

The stopping cross sections of protons were determined by using transmission and backscattering techniques at equivalent target foils. Over the whole energy range compared (30 to 370 keV) both methods delivered the same data within ± 1%. The uncertainty in the derived cross sections amounts to ± 2%.

Some regularities in proton stopping cross sections

The results of recent measurements of the stopping cross sections of protons and He ions are analyzed. The dependence of the maximum value of the stopping cross section, as well as of the energy at which the maximum is reached, on the atomic number of the target atoms is shown to be in correlation with the order of sequential filling of the electron shells of the stopping medium atoms. In the case of noble-gas atoms, a correlation is observed between the position of the maximum and the value of the orbital velocities of the electrons in the filled p-shells. The results obtained may be used to help in making an optimal selection among the methods for giving a semiempirical description of the stopping cross sections and to substantially improve the accuracy of such a description.

Investigation of the ratio of proton-stopping cross sections in Ag and Au.

Knowledge of the ratio of stopping cross sections may help in determining best values from measurements. The case of Ag and Au is discussed, where theoretical considerations show that this ratio always has a value smaller than 1. This is confirmed experimentally for proton energies larger than 70 keV, in contradiction to all published stopping-power tabulations.

Reference proton stopping cross sections for five elements around the maximum

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.

On the proton stopping power maximum in gases and vapours

The position and value of the maximum in the proton stopping cross section for atoms have been calculated, and a pronounced variation of these quantities with target atomic number is observed. The calculated values agree well with experiments for the noble and molecular gases, but show strong deviations from results of experiments performed on solid samples, especially metals. This deviation leads to the expectation of large solid-vapour differences in characteristics of the stopping maximum for metals and particularly for the alkali metals.

Proton stopping cross sections for carbon, aluminium and gold: New experimental data and critical analysis of the validity of empirical fit formulas

We report new experimental data for the stopping cross section S of protons in carbon, aluminium and gold at energies between 8 and 300 keV. The data are found to exhibit largely the same energy dependence as previously reported data. Using empirical fit functions we have analysed available experimental data in terms of the ratios S exp/ S fit from which we derive scaling factors b applicable to various sets of experimental data. These scaling factors, which typically range from 0.9 to 1.1, are attributed to deviations of the true foil thickness from the assumed one. Using b-corrections all sets of experimental data can be adjusted to fall on the same target specific stopping power curve (maximum deviation ± 3%). While the adjusted data are well described by the respective fit function (A1: Andersen and Ziegler) or tabulation (Au: Janni) the empirical data for carbon apparently deserve further improvements.

Proton stopping cross sections of liquid water

The proton stopping cross section of liquid water for the energy range from 40 keV to 10 MeV is calculated by applying the modified local-plasma model and employing a simple model of liquid water. The calculated stopping cross section of liquid water is about 5.6% to 14% lower than the calculated vapor-state results for the range of 80 to 500 keV and is about 8.5% to 13.4% lower than measured vapor-state results. The present results agree well with the measurements for ice crystals. The mechanism of this physical-state effect is also presented.

Proton energy loss in solids

The backscattering method is used to measure the 0.1–6.0 MeV proton stopping cross sections. The results obtained are compared with the data published elsewhere and with the Andersen-Ziegler semiempirical curves.

Effects of electronic structure on ion stopping cross-section in solids

A model for the proton stopping cross section in solids is suggested, which treats stopping in collisions with electrons of different electronic structure subsystems as independent processes. A number of effects due to the influence of the electronic structure on energy losses of protons moving randomly are described. Good agreement between theoretical results and experimental data is obtained. A “fine structure” for the maximum of the stopping cross section energy dependence is predicted. The reasons for the difference in stopping cross sections between protons moving randomly in diamond and graphite are discussed. [Russian Text Ignored]

Measurement of the stopping cross section for protons in copper by backscattering using various methods for foil-thickness determination

Copper films evaporated on pyrolitic carbon are used to determine the stopping cross section of copper for protons in the energy range from 60 to 500 keV by evaluating the energy width of Rutherford backscattering (RBS)-spectra. For this purpose we need both the number of atoms per unit area of the copper-foils and the spectrum widths. The number of atoms per unit area is determined for all copper films by a quartz-thickness monitor during evaporation, by weighing on a microbalance and by RBS, where a reference target of known thickness has been used to obtain absolute values without the input of stopping cross section data. The results of the quartz monitor and of RBS always agree within 2%, they agree with the results obtained by weighing within a mean relative error of less than 6% for each target. From the width of the RBS-spectra the stopping cross section is extracted by an iteration procedure which starts with Warters' approximation [1] and afterwards corrects for the small systematic errors arising there. The resulting stopping cross section data lead to a maximum at 125 keV. They are in excellent agreement with the data of Luomajärvi [2] and in fair agreement with the data of Mertens and Krist [3], In comparison with the Andersen and Ziegler curve, our data are lower in the whole energy range.

Stopping cross sections of 80- to 500-KeV protons in phosphorus compounds

Abstract The cross sections for the stopping of 80-500 keV protons in InP, GaP, and ZnSiP2 have been determined from the backscattering spectra. Using the additivity rule for stopping powers, we have found, from the cross sections obtained, the proton stopping cross sections in phosphorus. Possible corrections to the additivity rule are discussed. A method for their estimation is proposed.

Proton-stopping cross sections and mean excitation energies for gaseousCl2andBr2

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Electronic stopping cross sections for 30–300 keV protons in materials with 23 ⩽ Z2 ⩽ 30

The simplified stopping function has been successfully applied by Ziegler [3] to evaluate electronic stopping cross sections for helium ions in all materials. In a preceding work [4] we found that helium stopping cross sections extrapolated from hydrogen data by means of the simplified stopping function are of poor accuracy, if the corresponding proton stopping cross section is near its maximum as a function of ion velocity. This effect might be attributed to the fact that those maxima occur at different velocities for different ions. Therefore the goal of our experiments was to exactly measure the proton velocity at maximum stopping cross section in different materials. Using a magnetic spectrometer the energy losses for protons near the maximum stopping cross section ( E ≈ 100 keV) were measured in thin foils of C, Al, Si, V, Cr, Fe, Co, Ni, Cu, Zn, Ge, Ag and Au. The energy at maximum stopping could be located within a few keV. The position of the maximum only varied slightly for the elements with 23 ⩽ Z 2 ⩽ 30, whereas for C and Au the energy at the maximum was shifted noticeably. Tables are given for the stopping cross sections.