Current status of kinematically complete studies of basic fragmentation processes in atomic systems

Recent developments on kinematically complete experiments on basic atomic fragmentation processes are reviewed. Comparisons between theoretical and experimental fully differential cross sections for single ionization of light atoms by charged particle impact are analyzed. Furthermore, a method developed very recently, four-particle Dalitz plots, is discussed in context of double ionization. The extraordinary power of these plots is their capability to provide a comprehensive picture of the momentum exchange between all four final-state particles in a single spectrum.     

Differential ionisation measurements for positron impact

An overview of methods being used at the University of Missouri-Rolla to measure differential ionisation for positron impact is presented. Examples of triply differential electron emission and doubly differential positron scattering and energy loss data are given and contributions to each due to binary and recoil events are discussed. In addition, angular distribution data for electron emission due to double and triple ionisation are presented.     

Convolution approximation for the energy loss, ionization probability and straggling of fast ions

In this work we describe an extension of the convolution approximation for the ionization probability and energy-loss straggling as a function of the impact parameter for swift ions. Analytical formulas for these quantities are derived and compared to full first-order Born calculations. The physical inputs of the model are the electron density and oscillators strengths of the target as well as the screening function of the projectile (in the case of dressed ions). A very good agreement is obtained for all impact parameters. In addition, we propose a general schema to add contributions from distant and close collisions. In this way physical processes arising from large and small impact parameters can be easily included into a single expression valid for all impact parameters. This model is then used to investigate the projectile-charge q dependence of ionization, stopping and straggling cross-sections.     

An indirect method to measure the electric charge deposited on insulators during PIXE analysis

Total charge deposited by a proton beam in an insulator during PIXE analysis has been indirectly determined using a Mylar film coated with cobalt. Elemental concentrations in the samples, pieces of volcanic glass, were obtained and compared to concentrations determined by ICP OES on the same samples. The strong agreement between these results shows the accuracy of the charge determined by this method.     

Energy loss and straggling of Li ions in the polymer foils

Energy loss and straggling of 0.18-0.78 MeV/amu ⁷Li ions in polycarbonate, polyethylene terephthalate and polypropylene foils were measured by means of a transmission technique with a half-covered detector. The stopping force measurements are compared with the SRIM 2006 calculation and the database of the ICRU report 73. The measured energy loss straggling are in satisfactory agreement with the results yielded using the empirical formula at the higher energy region. The obtained data also demonstrated that the validity of Bragg’s rule applied to stopping force and energy loss straggling for ⁷Li ions in polymer foils.     

Erratum to “On the gas-solid difference in stopping power for low energy ions” [Nucl. Instr. and Meth. B 262 (2007) 13]

Recently, we claimed that the gas-solid difference in stopping powers persists from high down to low ion energies. This claim was based on a comparison between experimental data and the table of ICRU Report 73. We reconsider this claim in view of a recent article by Sigmund and Schinner where the claim was rejected. We find that the apparent gas-solid difference shown in our calculations is an artifact: it really points to an inadequacy of the table of ICRU 73 for low energy ions.     

Stopping of 0.3-1.2 MeV/u protons and alpha particles in Si

The stopping cross sections ε(E) of silicon for protons and alpha particles have been measured over the velocity range 0.3-1.2 MeV/u from a Si//SiO₂//Si (SIMOX) target using the Rutherford backscattering spectrometry (RBS) with special emphasis put on experimental aspects. A detection geometry coupling simultaneously two solid-state Si detectors placed at 165° and 150° relative to each side of the incident beam direction was used to measure the energies of the scattered ions and determine their energy losses within the stopping medium. In this way, the basic energy parameter, E_x, at the Si/SiO₂ interface for a given incident energy E₀ is the same for ions backscattered in the two directions off both the Si and O target elements, and systematic uncertainties in the ε(E) data mainly originating from the target thickness are significantly minimized. A powerful computer code has been elaborated for extracting the relevant ε(E) experimental data and the associated overall uncertainty that amounts to less than 3%. The measured ε(E) data sets were found to be in fair agreement with Paul’s compilation and with values calculated by the SRIM 06 computer code. In the case of ⁴He⁺ ions, experimental data for the γ effective charge parameter have been deduced by scaling the measured stopping cross sections to those of protons crossing the same target with the same velocity, and compared to the predictions of the SRIM 06 computer code. It is found that the γ-parameter values generated by the latter code slightly deviate from experiment over the velocity region around the stopping cross section maximum where strong charge exchanges usually occur.     

Measurement of the energy deposition profile for U ions with specific energy 500 and 950 MeV/u in stainless steel and copper targets

The paper presents the results of precision measurements of the total stopping range and energy deposition function of ²³⁸U ions with specific energies E = 500 and 950 MeV/u in stainless steel and copper targets. The experiment was performed at the SIS-18 facility (GSI Darmstadt) in the experimental area Cave A in September 2004-May 2005.The measured energy deposition profiles are compared with calculations using the codes ATIMA, PHITS, SHIELD and SRIM.     

On the gas-solid difference in stopping power for low energy ions

In an earlier paper we claimed that the well-known gas-solid difference in high energy mass stopping powers persists down to low energy; this claim was essentially based on stopping powers for N ions. We now re-investigate this claim using many more experimental data, comparing them to the recent stopping power table of ICRU Report 73 which has no gas-solid difference built in, and by using our statistical analysis program. We find that, at a specific energy of 25 keV/n, the average gas-solid difference amounts to −40% for N ions and to −48% for all ions from ₃Li to ₁₈Ar taken together, the stopping power for gas being lower. It appears therefore that the agreement between experiment and theory could be improved by taking this difference into account.     

Stopping cross sections of liquid water for MeV energy protons

Cross sections for the stopping of swift protons in liquid water have been measured for the first time by using a liquid water jet target of 50 μm in diameter. The energy loss spectra of incident 2.0 MeV protons were measured at scattering angles of 5.0-50 mrad. Experimental energy loss spectra have been successfully reproduced by Monte Carlo simulation calculations (GEANT4.9.1.p02 toolkit) by taking account of multiple scattering of projectile ions inside the liquid water target. The present stopping cross sections are found to be considerably smaller than other standard stopping power data, revealing e.g. about 11% deviation from those of SRIM2003.     

Stopping power of Au for Cu ions with energies below Bragg’s peak

The stopping power of Au for Cu in the energy range 6 < E < 25 MeV was measured using a secondary beam of low velocity heavy ions produced by elastic scattering of an energetic primary beam (typically ²⁸Si or ¹⁶O) on a natural Cu target. The results were compared to predictions of the Lindhard, Scharf and Schiott (LSS) theory, the binary theory (BT), and the unitary convolution approximation (UCA) and also to semi-empirical predictions such as the Northcliffe and Schilling tables and the SRIM2003 computer program.     

The solid-gas difference in stopping powers, and statistical analysis of stopping power data

For the purpose of treating the difference in stopping power between condensed and gaseous substances, we first discuss our method of statistical analysis of published experimental data. We distinguish between a positive effect where the difference between mass stopping powers S_solid − S_gas is positive and a negative effect where the opposite holds true. Experimentally, the positive effect has been found so far with heavy ions at high energy, and the negative effect with light ions at low energy. The positive effect is due to the difference in ionic charges and can be described by the CasP program by Grande and Schiwietz. An apparent persistence of the positive effect down to low energy is found to be mainly an artifact inherent in the stopping table of ICRU Report 73. The negative effect can be described by a difference in mean ionization potentials between gases and condensed matter. It is large for metals, much smaller for compounds. It should be possible to see both effects in one projectile - target combination.     

Total bremsstrahlung spectral photon distributions in metallic targets in the photon energy range of 5-10 keV by Tl beta particles

Total bremsstrahlung spectral photon distributions produced by beta particles of the ²⁰⁴Tl beta emitter in thick targets of Al, Ti, Sn and Pb targets were evaluated at photon energies from 5 keV to 10 keV. Experimental measurements were compared with the theoretical total bremsstrahlung spectral photon distributions obtained from Elwert corrected (non-relativistic) Bethe-Heitler theory and modified Elwert factor (relativistic) Bethe-Heitler theories for ordinary bremsstrahlung, and the modified Elwert factor (relativistic) Bethe-Heitler theory which includes polarization bremsstrahlung in the stripped atom approximation. The experimental results show better agreement with the modified Elwert factor (relativistic) Bethe-Heitler theory which includes the contribution of polarization bremsstrahlung. The contributions of polarization bremsstrahlung decrease with increased photon energy, particularly for medium and high Z elements. Hence its contribution cannot be neglected while studying the total bremsstrahlung spectral photon distributions in thick targets, produced by continuous beta particles in the studied energy region.     

Optical oscillator strengths, mean excitation energy, shell corrections and experimental values for stopping power

In a recent paper, Smith, Inokuti, Karstens and Shiles discussed optical oscillator strengths (OOS) of graphite, Al and Si and compared the mean excitation energy I obtained by integration to that from stopping power measurements. They found agreement for graphite and Al, but disagreement for Si. In this paper, we discuss the OOS of Al, Si, Cu and Au and compare the stopping powers calculated from these OOS (or from a single I-value), using program CasP40, directly to experimental stopping power values for protons between 10 and 80 MeV. We find that the choice of proper shell corrections is essential: since the shell correction built into CasP is too small, we take the correction for Al, Si and Cu from the BEST program of Berger and Bichsel. For Au, better results are obtained using Bonderup’s shell correction. With these choices, we find fair agreement between experimental and calculated stopping data, both with the I-values from ICRU Report 49 and with OOS. Even in the case of Si, the stopping curve based on OOS is not in conflict with experimental data. In all cases, the curves calculated using SRIM are in good agreement with the data.     

Kinetic excitation of solids induced by energetic particle bombardment: Influence of impact angle

The kinetic excitation of a solid surface under bombardment with energetic particles is studied via internal electron emission in a metal-insulator-metal junction. In particular, the dependence of the measured tunneling yield on the projectile impact angle is studied. The resulting impact angle distribution is compared with predictions of the total excitation energy profile calculated using the SRIM 2006 Monte Carlo program package. While the calculated profiles fail to explain the experimental data, it is shown that a simple calculation of impact angle dependent projectile backscattering qualitatively reproduces the observed trends.     

Study of the electron-electron correlation via observing the two-electron cusp

In a recent experiment we found evidence for the existence of the two-electron cusp in atomic collisions, i.e. the enhanced simultaneous emission of two electrons in forward direction with velocities equal to that of the projectile. In the experiment the energies of the two electrons resulting from the mutual target and projectile ionization in 100 keV He⁰ + He collisions were measured. The strong correlation observed between the energies of the electrons was explained by an angular correlation of 180° in the projectile-centered reference system. For the interpretation of the experimental results we carried out a Monte Carlo simulation based on the Wannier theory for the two-electron break-up process at threshold. In the article we review the details of the simulation and present two extensions of the model: One takes into account the post-collisional interaction (PCI) between the outgoing electrons and the ionized target atom, while the other contains a correction for a two-center effect.     

Pure ionization cross section of helium and ionization mechanism

Pure target ionization was investigated for 0.4-6.4 MeV C^q+(q = 1-4) + He and O^q+(q = 1-4) + He collisions. The double-to-single target ionization ratios R₂₁ were measured using coincidence techniques. We compare our results with existing experimental results and find they are in good agreement. The ratio R₂₁ is nearly independent of projectile charge state. The relation of R₂₁ ∼ V is analyzed using the over barrier model (OBM) and ionization probability, which is described in our extended over barrier model. Our calculation agrees well with the experimental results.     

Electron impact single ionization of helium with large energy transfer

We report triply differential cross section (TDCS) for electron impact single ionization of helium at the incident energy of 729.6 eV for a variety of scattering angles and ejection energies. The calculations are based on two different methods, namely, the Glauber approximation (GA) and the 3C approximation, also called the BBK method. In the GA the effects of post collision interaction have been taken into account by a classical method, whereas the BBK method has been studied with and without exchange. A comparison is made of the present TDCS with the results of other calculations and the experimental data from two different laboratories. For large energy transfer we find a significant contribution from the exchange effect. Both the GA-PCI and the BBK methods show some shifts in the position of binary maxima which are in reasonably good agreement with experiment.     

Fully differential cross section for single ionization of helium by 1 KeV electrons in the eikonal approximation

We report new results for fully differential cross sections for the single ionization of helium by 1 KeV electron impact at the ejection energy of 10 eV. Investigations have been made for both the scattering and perpendicular planes. The present calculation is based on the eikonal approximation due to Glauber. Here we have also incorporated the effect of classical post collision interaction (PCI) in the Glauber approximation (GA). A comparison is made of the present calculation with the results of other theoretical methods and the recent experiment [M. Dürr, C. Dimopoulou, B. Najjari, A. Dorn, K. Bartschat, I. Bray, D.V. Fursa, Z. Chen, D.H. Madison, J. Ullrich, Phys. Rev. A 77 (2008) 032717]. The Glauber results are in good agreement with the experiment in the scattering plane, but strong discrepancies are observed in the plane perpendicular to it. The effect of PCI is not substantial in the present kinematics.