Stopping Power Calculations Research Articles

Stopping power for swift dressed ions

We present theoretical calculations of electronic stopping power, including excitation and loss of both projectile and target electrons. The energy loss due to target valence and inner-shell electrons are separately evaluated: the former in the usual dielectric formalism, and the latter by employing a shell-wise local plasma approximation. Stopping power calculations of He ions in Al and Zn are presented, including the electron-electron contribution mentioned above. The agreement with the experimental data is very good, and let us conclude that, for helium ions, projectile excitation and loss contribute to the stopping power at the most in 1%, and it is reasonable for the theoretical descriptions to neglect it.

An effective single-trap-level model for the proton-induced semi-insulating substrates

To suppress the undesirable substrate couplings, a novel approach, called the /spl pi/ technology (particle-enhanced isolation), was previously proposed, in which energetic proton beams were applied on the already-manufactured mixed-mode IC wafers prior to their packaging . The results of an improvement of 25-30 dB in coupling reduction and a two-to-three folds enhancement in inductor Q values were also demonstrated. The continuing improvement of this /spl pi/ technology has shed light on the concept of a new very large-scale integration backend solution: the particle-beam stand, a brute-force that may ultimately bring general system-on-a-chip manufacturing to a common platform. However, up to this day the physics describing properties of such proton-caused defect phase has never emerged. In this paper, the possible establishment of an effective, self-consistent, single level defect model is attempted. It will be carried out by fitting the existing single-trap-level theory with experimentally obtained parameters and the data from numerical simulations using the the stopping and range of ions in matter code (a charged-particle stopping-power calculation program). It will be revealed that, more than mere simple traps of charge carriers, those proton-created defects were also intrinsically charged (carrying +e or -e) and thus all were participating in the Rutherford-like scattering of the remaining free charge carriers which had survived the defect trapping. The calculated effective single trap level (E/sub T/) is about +0.24 eV in n-Si and -0.34 eV in p-Si, measuring from the center of the energy bandgap.

Paparamborde: a software dedicated to quantitative mapping of biological samples using scanning transmission ion microscopy

Paparamborde, Programme d’Analyse des PArticules RAlenties dans la Matière de BORDEaux, a software dedicated to the scanning transmission ion microscopy (STIM) analysis of biological samples was developed. The programme includes the reconstruction of the median and/or mean energy loss image of the sample, as well as accurate calculation of sample thickness performed over the whole or a part of the scanned surface. The calculation is based on the conversion of transmitted particle energy into areal density of matter (μg/cm2) and uses SRIM code for the stopping power calculation. A new routine for the calculation of X-ray absorption correction factors (XCF), as needed for PIXE quantification of trace element, has been added in the latest version of Paparamborde, allowing the thickness heterogeneity of sample to be properly taken into account in the calculation of XCF.

Stopping Power Calculations for Partially Stripped Projectiles in High Energy Region

The electronic stopping cross-section is calculated in the spirit of the Bethe theory. Interaction potential between projectile and target is regarded to have a Coulombic character and we have modified it to take into account velocity dependences on a number of bound electrons of projectile and an effective charge of projectile and target. These velocity dependences are obtained from the Bohr adiabatic criterion using the Thomas–Fermi atomic model. We have get the electronic stopping cross-section expression using the Bethe approximation; we obtained the stopping cross-section of C and Al for C, O, and Si ions from this expression and compared our results with experiment and other theoretical calculations.

Simulations of an accelerator-based shielding experiment using the particle and heavy-ion transport code system PHITS

In order to estimate the biological effects of HZE particles, an accurate knowledge of the physics of interaction of HZE particles is necessary. Since the heavy ion transport problem is a complex one, there is a need for both experimental and theoretical studies to develop accurate transport models. RIST and JAERI (Japan), GSI (Germany) and Chalmers (Sweden) are therefore currently developing and bench marking the General-Purpose Particle and Heavy-Ion Transport code System (PHITS), which is based on the NMTC and MCNP for nucleon/meson and neutron transport respectively, and the JAM hadron cascade model. PHITS uses JAERI Quantum Molecular Dynamics (JQMD) and the Generalized Evaporation Model (GEM) for calculations of fission and evaporation processes, a model developed at NASA Langley for calculation of total reaction cross sections, and the SPAR model for stopping power calculations. The future development of PHITS includes better parameterization in the JQMD model used for the nucleus–nucleus reactions, and improvement of the models used for calculating total reaction cross sections, and addition of routines for calculating elastic scattering of heavy ions, and inclusion of radioactivity and burn up processes. As a part of an extensive bench marking of PHITS, we have compared energy spectra of secondary neutrons created by reactions of HZE particles with different targets, with thicknesses ranging from <1 to 200 cm. We have also compared simulated and measured spatial, fluence and depth–dose distributions from different high energy heavy ion reactions. In this paper, we report simulations of an accelerator-based shielding experiment, in which a beam of 1 GeV/n Fe-ions has passed through thin slabs of polyethylene, Al, and Pb at an acceptance angle up to 4°.

Stopping energetic heavy-ions in one-bar helium: broad incident momentum distributions

Various tests for stopping energetic 32 P fragments in a 50 cm gas cell filled with helium were performed. The fraction of ions stopped in the gas was measured as a function of the width of the incident beam momentum distribution. The use of a shaped degrader placed in a dispersive plane before the gas cell significantly improves the stopping efficiency in gas. A stopping efficiency of 35% was obtained for fragments with the broadest momentum distribution, which was an improvement of approximately 80%. Qualitative agreement between the experimental results and stopping power calculations was obtained.

Allegria: a new interface to the ERD program

As a new PC-based acquisition system has been installed to replace the VAX-based system of the elastic recoil detection by time-of-flight (ERD-TOF) and gas-counter ERD setups at University of Montréal, a new analysis software has been developed. It includes a calculation of the energy calibration involving pulse height defects corrections for each element. It has been further improved to process a number of different ERD or Rutherford backscattering spectrometry (RBS) spectra in a single run and now incorporates stopping power calculations based on SRIM-2003 parameters. The application comes with a graphical interface that is used to extract mass separated spectra from event-list files. A second application allows the user to input the experimental parameters and prepares a command file that is passed to the ERD program. The latter iteratively converts the energy spectra into depth profiles for each mass. Resulting atomic fractions are normalized to one of the elements, typically the substrate or one of its components. Some examples of analysis for both TOF and gas counter ERD measurements are presented and discussed. The program and source code will be made available to the ion beam analysis community under GNU licensing conditions.

Modifications to a universal electronic stopping power equation for ions

Modifications to a universal electronic stopping power equation for nonrelativistic heavy ions in solids have been made. Some calculations of electronic stopping power for protons are performed using the new equation for a variety of targets with different atomic numbers. The results are close to that of the TRIM program.

Stopping energetic heavy ions in one-bar helium: narrow incident momentum distributions

Various tests for stopping energetic, 100– 150 MeV /amu, heavy ions with narrow momentum distributions in a 50 cm gas cell filled with helium at 0.5– 2 bar pressure were performed. The fraction of ions stopped in the gas was measured as a function of absorber thickness, gas pressure and length of ion path within the gas cell. Information on the range distribution was obtained and the residual energy distribution of ions was measured under different conditions. The experimental results for various beams are compared with stopping power calculations in the literature. The results are discussed in the context of the proposed RIA facility.

Atomic effects of stopping power in planar channeling

Using the method of a dielectric function ε in nonuniform many-electron systems, we derive the formula of stopping power for randomly distributed atomic systems under high frequency response. We show the theoretical standpoint of the local density approximation [K. Dan. Vidensk. Selsk. Mat. Fys. Medd. 27 (15) (1953)] precisely, in which there appear the modified Bethe type formula. Using results mentioned above and taking into account of atomic effects of planar channeling, we also develop the theory of stopping power in planar channeled ions. In this approach, channel walls are constructed by discrete lattice atoms. We perform numerical calculations of stopping power for 3 MeV He ions passing through Au atomic planes, and show weaker impact parameter dependences of stopping power from channel plane than results obtained from usual planar continuum model, which have been pointed out by Robinson [Phys. Rev. 179 (1969) 327] since 1969. Through numerical calculations, we show that the modified Bethe type formula gives reasonably quantitative values in planar channeling although those from the usual Bethe type one are overestimated.

Effective stopping charges and stopping power calculations for heavy ions

In this study the model suggested by Sugiyama has been developed and applied for the calculation of the stopping powers for nonrelativistic heavy ions in various target materials. Sugiyama's model has been expanded to low and high energy regions in our work. Analytical expressions are obtained in the modified BB stopping power formula for the effective charge and effective mean excitation energies. In the modified LSS formula, a quasi-molecule criterion has been applied to both the projectiles and the target atoms. Electronic excitation contribution, S e0, and quasi-molecule contribution, S ei , to stopping power were found for a wide energy region. It is observed that in intermediate energy region both contributions have maxima. The stopping power due to excitation-ionization in the intermediate and higher energy region is found to be dominant, whereas quasi-molecule contribution is dominant in the lower energy region. The calculated results of stopping power are in good agreement with experimental data for various ions and targets within a few percent in a wide projectile energy range.

Channeling effects observed in energy-loss spectra of nitrogen ions scattered off a Pt(110) surface

We present measured energy-loss spectra of nitrogen ions, which are scattered off a $(1\ifmmode\times\else\texttimes\fi{}2)$ missing row reconstructed Pt(110) single-crystal surface. The primary energy is varied from below 1 keV up to above 1 MeV, i.e., ${0.04v}_{0}&lt;v&lt;{2v}_{0}$ with ${v}_{0}$ the Bohr velocity. We use grazing angles low enough in order to have surface channeling at all energies. Experimental results are compared with theoretical energy-loss values obtained from trajectory and stopping power calculations of charged particles scattered under grazing incidence conditions from metallic surfaces. The stopping power is calculated using the scattering theory formalism. Different trajectory classes are found by the calculations and assigned to different contributions in the energy-loss spectra. Regarding the simplicity of the presented model the agreement with the experiment is good.

Calculation of proton stopping power in the region of its maximum value for several organic materials and water

The stopping powers (SP) for 10 solid organic materials and water have been calculated in the range of proton energies 50–500 keV. Most of the presented results are new and are in good agreement with existing experimental data. The calculated data might be useful for applications in radiobiology and space research.

Stopping power for heavy ions (3⩽ Z⩽35) in solids at energies ∼0.5–2.5 MeV/n

The Hubert et al. formulation for stopping power calculations has been extended below its recommended range of validity, i.e. 2.5–500 MeV/n. It has been established that the extended formulation for projectiles with Z=3–35 provides a good agreement with the experimental data for elemental targets (6⩽ Z⩽79) and complex materials e.g. CR-39, LR-115, Mylar, Kapton, polycarbonate and Havar in the energy range 0.5–2.5 MeV/n.

Improvement of low-energy stopping power algorithms in the FLUKA simulation program

Monte Carlo methods are actually the best tools to perform the detailed dosimetric and radiobiological calculations required in conformal radiotherapy. In this work we focus our attention on the FLUKA simulation program and on the electronic stopping power calculations for protons and α particles in materials of interest for therapy. We discovered large inaccuracies (>10%) with respect to the values suggested by ICRU (standard reference) for protons in compounds and α particles both in elements and compounds below 1 MeV/ amu . These deviations, due to the standard approach based on additivity and scaling rules, could indeed affect radiobiological evaluations for primary charged hadron and neutron beams. Therefore, we developed new algorithms based on proper parametric formulae and inserted them in the FLUKA code. The new approach allows an agreement with ICRU data much better than 1% in the entire energy range 1 keV – 100 MeV/ amu spanned by the old one.

Stopping power of Mylar for heavy ions up to copper

The stopping powers of Mylar for several heavy ions covering Z=11 to 29 in the energy range ∼0.3 to 2.3 MeV/n have been measured using the elastic recoil detection technique and twin detector system. The technique provided a unique method to generate a variety of variable energy ion species utilizing a fixed energy 140 MeV Ag 13+ primary beam from the Pelletron accelerator facility at Nuclear Science Center, New Delhi, India. Most of these measurements are new. The experimentally measured stopping power values have been compared with those calculated using LSS theory, Ziegler et al. formulation and Northcliffe and Schilling tabulations. Merits and demerits of these formulations are highlighted. Stopping power calculations using the Hubert et al. formulation have been extended successfully beyond its recommended range of validity, i.e. 2.5–500 MeV/n down to energies as low as 0.5 MeV/n.

Stopping power of some elemental and complex SSNTD media at low energies

Stopping power calculations using Hubert et al. formulation have been extended beyond its recommended range of validity, i.e. 2.5–500 MeV/n. It has been established that, for elemental targets up to copper and for complex polymeric SSNTD materials, e.g. CR-39, LR-115, Mylar and Kapton, the formulation provides good agreement with experimental data for projectiles with Z≤29 down to energies as low as 0.5 MeV/n.

Fragmentation of fast positive and negative C $\mathsf{_{60}}$ ions in collisions with rare gas atoms

The fragmentation of anions and cations resulting from 50 keV collisions with rare gas targets is studied. Positive ion fragment patterns are recorded, and dramatic changes in these patterns are observed as a function of target atom number. The fragment pattern dependence on the target atom size is investigated within a simple model, normally used for stopping power calculations. Fair agreement is obtained between calculated and experimental spectra. From these comparisons we conclude that the range of the screened atomic potentials, as e.g., the Thomas-Fermi potential, is an essential parameter in the collisional induced fragmentation process.

Nonlinear effects in stopping of partially ionized swift heavy ions

We present stopping power calculations for swift heavy ions in a hydrogen gas target. The point-like model is reviewed and compared to a new theory which includes the projectile elastic form factor. It is shown that, even for highly ionized ions, the projectile form factor yields a substantial modification over the standard stopping results.

Multiple scattering effects on stopping power of large clusters in solids

We study the effects on the electronic stopping power of large clusters in solids, resulting from multiple elastic scattering of each particle in the cluster by the target atoms, in the small-angle approximation. Evaluation of the cluster vicinage self-energy at the entrance of the target shows that large clusters may stabilize against the Coulomb explosion for a range of cluster sizes and speeds, so that the change of the cluster structure, due to multiple scattering, may have a noticeable influence on the vicinage, or interference, energy losses of clusters due to collective electronic excitations in the target. Stopping power calculations are presented for ${\mathrm{C}}_{60}$ and $({\mathrm{H}}_{2}{)}_{50}$ clusters in an Al target, together with the results on stabilization conditions against the Coulomb explosion for $({\mathrm{H}}_{2}{)}_{{N}_{m}}$, based on self-energy considerations.