Reliability of stopping power tables and codes for heavy ions (8 ≤ Z ≤ 92) in gases

A comparative study of various stopping power tables and codes for heavy ions in gases has been made through comparison of computed values and the corresponding experimental data. Ten gaseous media: five monatomic rare gases (He to Xe), two diatomic gases (H₂, N₂) and three polyatomic gaseous compounds (CH₄, CF₄ and CO₂) have been chosen to study the stopping power investigations of heavy ions (8 ≤ Z ≤ 92) having energy ranges of ∼0.10–10.00 MeV/n and ∼20.00–57.00 MeV/n. We compare the experimental data of stopping power to values calculated using various tables and computer codes by ICRU-73, Ziegler et al (SRIM2003.26), Grande and Schiwietz (CasP3.1), Paul and Schinner (MSTAR3.12), and Bazin and Tarasov (LISE ++:2-ATIMA1.2). On the basis of statistical analysis, we estimate the reliability of these tables and codes. It has been observed that the MSTAR3.12 code shows the best agreement with the experimental data for projectile ions (8 ≤ Z ≤ 18) in the entire energy range. The SRIM2003.26 code provides good results except for some heavy projectiles (Xe, Pb and U). The values tabulated by CasP3.1 code underestimate especially at low energy region. No significant trend is observed in case of LISE++:2-ATIMA1.2 code and ICRU-73 report.     

反冲原子对低速离子轰击Si表面时电子发射产额的影响

在兰州重离子加速器国家实验室电子回旋共振离子源高电荷态原子物理实验平台上,用低能(0.75keV/u≤EP/MP≤10.5keV/u,即3.8×105m/s≤vP≤1.42×106m/s)He2+,O2+和Ne2+离子束正入射到自清洁Si表面时二次电子发射产额的实验结果.结果表明电子发射产额γ近似正比于入射离子动能EP/MP.在相同动能下,γ(O)γ(Ne)γ(He),对于原子序数ZP比较大的O2+和Ne2+离子,ZP大者反而γ小,这与较高入射能量时的结果截然不同.通过计算不同入射能量下入射离子的阻止能损S,发现反冲原子对激发二次电子的作用随入射离子能量的降低显著增大,这正是导致在较低能量范围内二次电子发射产额与较高入射能量时存在差异的主要原因.     

Reciprocity in the electronic stopping of slow ions in matter

The principle of reciprocity, i.e., the invariance of the inelastic excitation in ion-atom collisions against interchange of projectile and target, has been applied to the electronic stopping cross section of low-velocity ions and tested empirically on ion-target combinations supported by a more or less adequate amount of experimental data. Reciprocity is well obeyed (within ~10%) for many systems studied, and deviations exceeding ~20% are exceptional. Systematic deviations such as gas-solid or metal-insulator differences have been looked for but not identified on the present basis. A direct consequence of reciprocity is the equivalence of Z₁ with Z₂ structure for random slowing down. This feature is reasonably well supported empirically for ion-target combinations involving carbon, nitrogen, aluminium and argon. Reciprocity may be utilized as a criterion to reject questionable experimental data. In cases where a certain stopping cross section has not been or cannot be measured, the stopping cross section for the inverted system may be available and serve as a first estimate. It is suggested to build in reciprocity as a fundamental requirement into empirical interpolation schemes directed at the stopping of low-velocity ions. Examination of the SRIM and MSTAR codes reveals cases where reciprocity is obeyed accurately, but deviations of up to a factor of two are common. In case of heavy ions such as gold, electronic stopping cross sections predicted by SRIM are asserted to be almost an order of magnitude too high.     

Electronic stopping power of polymers for heavy ions in the ion energy domain of LSS theory

LSS based computed electronic stopping power values have been compared with the corresponding measured values in polymers for heavy ions with Z = 5–29, in the reduced ion velocity region, v_red ≤ 1. Except for limited v_red  0.6–0.85, the formulation generally shows significantly large deviations with the measured values. The ζ factor, which was approximated to be Z₁^1/6, involved in LSS theory has been suitably modified in the light of the available experimental stopping power data. The calculated stopping power values after incorporating modified ζ in LSS formula have been found to be in close agreement with measured values in various polymers in the reduced ion velocity range 0.35 ≤ v_red ≤ 1.0.     

Ion impact stopping cross sections for various media (Z = 3–100)

ABSTRACT

Stopping cross sections (SCS) for protons, alphas and Li ions are calculated with a modified form of our earlier work by incorporating a different electron density distribution of target materials; this involves four parameters – two projectile dependent and the rest two remain fixed. The prosed model has been tested for three stripped ion (H⁺, He^{2 +} and Li^{3 +}) projectiles and found that it describes quite satisfactorily the experimental SCS data from low energies with projectile velocities nearing v = Z₁v₀ (with Z₁ as the atomic number and v₀ the Bohr velocity) up to 100.0 MeV over a wide range of stopping media with atomic numbers Z₂ =3–100.     

Stopping powers of Al,Ti, Cu,Zr, Rh,Ag, Ta and Au for 26 MeV alpha particles and Z3 1 correction

Abstract

Stopping powers of Al, Ti, Cu, Zr, Rh, Ag, Ta and Au for 26 MeV alpha particles have been measured using a surface barrier silicon detector with an accuracy of 0.35%. The stopping powers for alpha particles divided by 4 have been compared with the stopping powers for 6.500 MeV protons of the same velocity. Experimental magnitudes of the Z ³ ₁ correction which is contained in the Bethe-Bloch stopping formula were extracted using the alpha-proton difference. Using the experimental Z ³ ₁ corrections thus obtained and the experimental Z ³ ₁ corrections of the previous paper, parameters of γ and b which appear in the theory of Ashley, Ritchie and Brandt for the Z ³ ₁ correction have been determined with exactly the same method as the previous paper as γ = 1.336 and b = 1.32. The magnitude of the Z ³ ₁ correction calculated by the theory of Ashley, Ritchie and Brandt using these parameters have been compared with those obtained by other authors.     

Investigation of radiological properties of some shielding materials on charged and uncharged radiation interaction for neutron generator

Radiation interaction parameters such as total stopping power, projected range (longitudinal and lateral) straggling, mass attenuation coefficient, effective atomic number (Z_eff) and electron density (N_eff) of some shielding materials were investigated for photon and heavy charged particle interactions. The ranges, stragglings and mass attenuation coefficients were calculated for the high-density polyethylene(HDPE), borated polyethylene (BPE), brick (common silica), concrete (regular), wood, water, stainless steel (304), aluminum (alloy 6061-O), lead and bismuth using SRIM Monte Carlo software and WinXCom program. In addition, effective atomic numbers (Z_eff) and electron densities (N_eff) of HDPE, BPE, brick (common silica), concrete (regular), wood, water, stainless steel (304) and aluminum (alloy 6061-O) were calculated in the energy region 10?keV–100?MeV using mass stopping powers and mass attenuation coefficients. Two different methods namely direct and interpolation procedures were used to calculate Z_eff for comparison and significant differences were determined between the methods. Variations of the ranges, longitudinal and lateral stragglings of water, concrete and stainless steel (304) were compared with each other in the continuous kinetic energy region and discussed with respect to their Z_effs. Moreover, energy absorption buildup factors (EABF) and exposure buildup factors (EBF) of the materials were determined for gamma rays as well and were compared with each other for different photon energies and different mfps in the photon energy region 0.015–15?MeV.     

On the use of averaging stopping power of recoiled nuclei for determining maximum neutron energy of 241Am–Be by superheated drop detectors

The average stopping power of the recoiled nuclei generated by neutron elastic interactions with the Freon-12 drops in a superheated drop detector has been used to determine the maximum neutron energy of the ²⁴¹Am–Be source. In an elastic interaction of neutrons with the Freon-12 liquid, the nuclei of ¹²C, ¹⁹F and ³⁵Cl with different values of stopping power are scattered. The stopping power of these scattered nuclei corresponding to the energy transferred to them through the head-on collision was extracted from the SRIM code. The stopping power values were weighted by considering the neutron–nucleus elastic scattering cross section and the number of each nucleus in the Freon-12 molecule and the average stopping power was calculated from known neutron energy.The maximum energy of the ²⁴¹Am–Be neutron source was estimated as 10.9 ± 3.0 MeV. The consistency between the determined energy and the other reported values confirms the validity of using the average stopping power in the superheated drop detectors. The average stopping power was also used to determine the threshold neutron energy as a function of external applied pressure at different temperatures. Knowing the threshold neutron energy as function of applied pressure, can be used in pressure scanning method for neutron spectrometry by superheated drop detectors.     

Molecular effect on interatomic potentials

Abstract

In the low energy atomic collision of ε ≤ 0.1, the energy dissipation of projectile ion is mainly by the nuclear stopping. In this energy range Z-oscillation appears on ranges and range stragglings. In order to explain this osciallation from the viewpoint of molecular effect on interatomic potentials, an extended Hückel method is adopted for potential calculation. The Z-dependence on interatomic potentials to describe respective atomic collisions is similar to that of Z ₁-range oscillation. It suggests a possibility of molecular effect on the Z ₁-range oscillation.     

Stopping power contribution due to target and projectile excitation/ionization: a comparative study

A comparative study of stopping power codes for different ions in compounds has been made by comparing the computed stopping power values using different codes with the corresponding experimental data. Two computer codes, semiempirical SRIM2006.02 and theoretical CasP3.2 have been used to evaluate and compare the stopping powers of different compounds for protons (125 KeV), helium (500 KeV) and lithium ion (175 KeV) projectiles. The energy behaviour of stopping power of various compounds for helium ion in the energy range (0.3–2.0 MeV) has been studied. The merits and demerits of the adopted formulations are highlighted. It has been observed that the calculation based on SRIM2006.02 provides the best agreement with the experimental data as compared to CasP3.2 code. The stopping power contribution due to target and projectile excitation/ionization at low energies has been evaluated and discussed with reference to CasP3.2 code. From these comparative studies it has been concluded that the target and projectile excitation-ionization increases the stopping power (>20%) at lower energies.     

Revelations from stopping power analyses

Abstract

Recent measurements of the stopping powers of various composite-material targets have been analyzed in the presence of Barkas-effect and Bloch corrections in order to extract appropriate values of Bethe-Bloch parameters. Mylar, Kapton, and Havar targets have been studied in particular, primarily using measurements with light projectiles. The present investigation focuses on results for Havar analyses, where dispersion among sets of measurements appears to separate extracted parameter-values into at least two groups. An hypothesis pertaining to target properties is advanced in explanation. In another study, analyses of experimental results for alpha particle projectiles traversing Ti and V targets have yielded parameter-values reasonably consistent with expectation. Finally, the importance of including all pertinent correction terms when analyzing data with Bethe-Bloch stopping power theory is emphasized.     

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.     

Stopping cross sections of 50- to 230-keV nitrogen ions in silicon measured by ion backscattering spectroscopy

The energy dependence of the total stopping cross section of 50- to 230-keV nitrogen ions in silicon (σ _S (E)) is measured in order to develop the diagnostics of heavy impurities in films of a nanometer thickness by heavy ion backscattering (HIBS) spectroscopy. At ion energies lower than 150 keV, this σ _S (E) dependence occupies an intermediate position between the dependences given in the SRIM and MSTAR data-bases; at higher energies, our dependence is closer to the former dependence. The estimation of the effect of inelastic processes on the stopping cross section demonstrates that the effect of these processes for nitrogen ions can be neglected when heavy impurities in such films are studied by HIBS.     

Intermediate mass fragments in the reaction6Li+46Ti atE/A=26 MeV

Intermediate mass fragment cross-sectionsσ(E, θ, 4≤Z≤11) have been measured in the reaction⁶Li+⁴⁶Ti at 156 MeV incident energy. A simple sequential binary decay model describes most of theZ>8 data as evaporation from the compound nucleus. The complete fusion cross-section is also well reproduced. An intermediate velocity source model (β=2β _CN, T=7 MeV) has been used in order to explain the small angle and Z≤8 data which indicate aZ ^?4.1 dependence.     

Influence of nondipolar effects on the photoelectron angular distribution upon photoionization of 2p and 3d atomic shells

Relativistic calculations of the angular distribution of photoelectrons upon photoionization of 2p and 3d shells in the range of photoelectron energies from 1 to 10 keV are carried out for unpolarized and linearly polarized radiation. An exact expression for the angular distribution of photoelectrons that takes into account nondipolar terms of the order of O[(kr)²] (k is the photon energy and r is the radius of the ionized shell) is obtained in the case of unpolarized radiation. It is shown that the contribution of the O[(kr)²] terms to the differential cross section can be considerable, reaching 24% at the maximum energy considered. Accounting for such terms in the calculation of the ratio of differential cross sections, which is experimentally measured at a certain geometry of angles in the case of linearly polarized radiation, can change this ratio twofold. The parameters of the angular distribution, which are necessary for the conduction of a quantitative x-ray photoelectron analysis, are given for the 2p _1/2 and 2p _3/2 shells of elements with 11≤Z≤29 and for the 3d _3/2 and 3d _5/2 shells of elements with 30≤Z≤54.     

Investigation of the passage of 100–1000-MeV/nucleon superheavy ions through homogeneous media

This work is a continuation of the experimental and theoretical investigations of the effect of the Z ₁ ³ correction to the stopping power of ions on the passage of heavy ions ⁴⁰Ar, ⁵⁶Fe, ¹⁹⁷Au, ¹³¹Xe, and ²³⁸U with energies of about 1 GeV/nucleon through a homogeneous medium. The previously observed systematic deviations of the calculations based on the first Born approximation to the scattering of a particle by the atomic electrons in the medium from the experimental values of the total ionization ranges of the nuclei and their stopping powers is confirmed. The discrepancy increases with the atomic number of the projectile nucleus. It is shown that the Z ₁ ³ correction in the form proposed by Jackson and McCarthy eliminates, especially for ions with Z ₁>50, the systematic discrepancy between the computed and experimental values. For the experimental energy range relativistic Mott scattering of a particle by the atomic electrons in the target makes the dominant contribution to the observed Z ₁ ³ effect. Zh. éksp. Teor. Fiz. 115, 404–415 (February 1999)     

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.     

A large‐volume gas cell for high‐energy X‐ray reflectivity investigations of interfaces under pressure

A cell for the investigation of interfaces under pressure is presented. Given the pressure and temperature specifications of the cell, P≤ 100 bar and 253 K ≤T≤ 323 K, respectively, high‐energy X‐rays are required to penetrate the thick Al₂O₃ windows. The CH₄(gas)/H₂O(liquid) interface has been chosen to test the performance of the new device. The measured dynamic range of the high‐energy X‐ray reflectivity data exceeds 10^?8, thereby demonstrating the validity of the entire experimental set‐up.     

Binary stopping theory for swift heavy ions

The Bohr theory treats charged-particle stopping as a sequence of interactions with classical target electrons bound harmonically to their equilibrium positions. We demonstrate that equivalent results can be derived on the assumption of free binary collisions governed by a suitable effective potential. This kind of mapping is rigorous in the limits of distant and close collisions and therefore provides a tool to evaluate energy losses via binary-scattering theory. This model was developed with the aim of calculating stopping forces for heavy ions at moderately high velocities, where a classical-orbital calculation is typically superior to the Born approximation. The effective potential employed holds equally well for dressed as for stripped ions. Unlike the Bohr theory, the present evaluation avoids a formal division into regimes of close and distant collisions that do not necessarily join smoothly. Moreover, no perturbation expansion is necessary. For these reasons the overall accuracy as well as the range of validity of the Bohr model are significantly enhanced. Extensive tests have been performed, including comparisons with rigorous evaluations of the Z ₁ ³ effect, with excellent agreement even where such was not necessarily expected. Moreover, credible results have been obtained under conditions where the perturbation expansion shows poor convergence. A comparison with experimental data on O–Al is encouraging, even though shell corrections and projectile excitation/ionization have not yet been incorporated and input has not yet been optimized. Received 21 April 2000 and Received in final form 16 June 2000 An erratum to this article is available at .     

Relativistic correction to the dipole polarizability of a hydrogenic ion

The first relativistic correction of orderα ² to the dipole polarizability of a hydrogenic ion has been investigated by using mean excitation energy of the ion within the second-order perturbation theory. The density-dependent mean excitation energy is estimated via Bethe theory for the stopping cross section for a moving point charge interacting with the hydrogenic ion. In this approach only the unperturbed Dirac wavefunctions are required to evaluate the appropriate matrix elements. The first relativistic correction turns out to be − (13/12)(αZ)². This has the correct sign and is within 5% of the exact result which is −(28/27)(αZ)².