Tatsuo Tabata

Cross sections for charge transfer of hydrogen atoms and ions colliding with gaseous atoms and molecules

Analytic formulas are given for the total cross sections sigma for charge transfer collisions of hydrogen atoms and ions with gaseous atoms and molecules. The cross sections considered are sigma/sub 10/, sigma/sub 0//sub -//sub 1/, sigma/sub 1//sub -//sub 1/, sigma/sub 01/, sigma/sub -//sub 10/, and sigma/sub -//sub 11/, where the subscripts represent the initial and the final charge state of the hydrogen. The functionl forms of the formulas are modifications of the semiempirical formula for sigma/sub 10/ given by Green and McNeal. Values of adjustable parameters in the formulas have been determined by least-squares fits to a compiled set of experimental data and are given in a table. The curves given by the formulas are plotted in graphs together with the data. The root-mean-square deviation of the data from the formulas is typically about 20% except when there are large discrepancies among the measurements. Experimental data through 1982 are shown on the graphs; references through mid-1986 are listed. copyright 1987 Academic Press, Inc.

An analytic formula for the extrapolated range of electrons in condensed materials

Abstract A single analytic formula for the extrapolated range rex of electrons in condensed materials of atomic numbers from 4 to 92 is given. It has the form of the product of the continuous-slowing-down approximation (CSDA) range r0 and a factor fd related to multiple scattering detours. The factor fd is expressed as a function of incident electron energy T0 and atomic number Z of medium. Values of adjustable parameters in fd have been optimized for data on the ratio r ex r 0 , in which the Monte Carlo evaluated values of Tabata et al. [Nucl. Instr. Meth. B 95 (1995) 289] (from 0.1 to 100 MeV) and experimental data collected from literature (from 1 keV to 0.1 MeV) for rex have been used together with NIST-database values of r0. For r0 in the extrapolated-range formula, accurate database values or an approximate analytic expression developed as a function of T0, Z, atomic weight A and mean excitation energy I of medium can be used. The maximum deviation of the resultant formula from the Monte Carlo data is about 2% for either option of r0. The determination of the expression for fd at energies below 0.1 MeV is tentative. By using an effective atomic number and atomic weight, the formula can also be applied to light compounds and mixtures.

Depth profiles of charge deposition by electrons in elemental absorbers: Monte Carlo results, experimental benchmarks and derived parameters

Depth profiles of charge deposition in absorbers irradiated by electrons have been computed by using the ITS Monte Carlo system version 3.0. Plane-parallel electron beams with energies from 0.1 to 100 MeV have been assumed to impinge normally on slab absorbers of effectively semi-infinite thickness. Absorber materials considered are elemental solids of atomic numbers between 4 and 92 (Be, C, Al, Cu, Ag, Au and U). To study the accuracy of the Monte Carlo results, benchmarks at the energies of 5, 10 and 20 MeV have been generated by interpolating published experimental results. Extrapolated ranges rex, most probable depths zm of charge deposition and average depths zav of charge deposition have been determined from both the ITS and interpolated experimental charge-deposition distributions. The depth profiles and derived parameters show good agreement between calculation and experiment, except for small discrepancies for Au absorbers, where the ITS results show a slightly lower penetrability of electrons. The Monte Carlo results of rex have been compared with the semiempirical formula of Tabata et al. [Nucl. Instr. and meth. 103 (1972) 85], and some deficiencies of the latter, due to the lack of data used in determining adjustable coefficients of the formula, have been found. The use of the ratio of the continuous slowing-down approximation range r0 to zav as an estimate of multiple scattering detours is discussed.

Average depths of electron penetration: use as characteristic depths of exposure

The average depth of electron penetration is introduced as the physical quantity useful in electron beam irradiation. It is defined as the average of the maximum depths on the trajectories of electrons passing through finite, semi-infinite or infinite medium. The relation between the transmission coefficient as a function of slab thickness and the distribution of the maximum depths is analyzed, and a semiempirical equation to calculate the average depth of electron penetration is given for 0.1- to 50-MeV electrons incident on materials of atomic numbers from 4 to 92. It is shown that the quantity introduced is usable as the characteristic depths of energy and charge depositions in a target, and can possibly be generalized to the case of heterogeneous targets.

Empirical Formulas for the Backscattering of Light Ions from Solids

Empirical formulas have been developed for the backscattering of H, D and He ions normally incident on solid targets. The parameters considered are the number-backscattering coefficient RN, the energy-backscattering coefficient RE and the mean fractional energy rE of backscattered particles (ions and neutrals). The formulation utilizes the fact that the scaling law predicted earlier for RN and RE as a function of the Thomas-Fermi reduced energy e is improved when these parameters are multiplied by St/SeLSS. Here St is the total stopping-power, in which expressions including the Z2-oscillations are used for the electronic stopping-power, and SeLSS is the electronic stopping-power given by the LSS theory when the projectiles are much lighter than the target atoms. The formulas obtained are valid for 10-3\lesssime\lesssim102.

Simple calculation of the electron‐backscatter factor

The authors have studied the dependence of the electron-backscatter factor (EBF) on mean electron energy and on backscatterer atomic number by using the semiempirical depth-dose code EDMULT. A plane-parallel electron beam is assumed to be normally incident on a polystyrene slab, which is backed with a layer (backscatterer) of different materials of effectively semi-infinite thickness. A small air cavity to measure ionization is embedded in the polystyrene slab at the boundary facing the backscatterer. The EBF is defined as the ratio of the ionization with the backscatterer to the ionization with a full polystyrene medium, and is approximated by the ratio of the doses computed at the depth of the cavity. Values of EBF obtained show trends similar to the experimental data of Klevenhagen et al. [Phys. Med. Biol. 27, 263-373 (1982)], although the former are generally lower than the latter. When the typical energy spread of clinical electron beams is taken into account, the difference between the experimental and the calculated values is reduced. The present results also show the same trend of increase of the backscatter factor with increasing energy as observed by Klevenhagen et al. in some series of measurements for the lead backscatterer at the lowest energies. This is explained by the rapid buildup of the dose with depth for electrons of low initial energies incident on the full polystyrene medium.

Unified empirical formulas for the backscattering coefficients of light ions

Abstract Empirical formulas for the number- and energy-backscattering coefficients of light ions normally incident on elemental solid targets are given. The formulas are valid for all the light ions of atomic numbers up to two with incident energies from about 10 eV to 100 MeV. Constants in the formulas have been determined by the least-squares fit to available experimental and selected computer-simulation data. The rms deviation of the data from the formulas is 31%.

Reflection of electrons and photons from solids bombarded by 0.1 - to 100-MeV electrons

Abstract Electron and photon reflection ratios (in number and energy) for absorbers bombarded by electrons have been computed with the ITS Monte Carlo system version 3. Electrons of energies from 0.1 to 100 MeV have been assumed normally incident on an effectively semi-infinite absorber. The absorbers considered are elemental solids of atomic numbers from 4 to 92. The data on the electron reflection ratios agree rather well with the experimental data collected from literature except some discrepancies when the number-reflection ratio is small. For photons, the number-reflection ratio increases with increasing energy, but the energy-reflection ratio shows a maximum around 10 MeV. Empirical equations for the electron reflection ratios and the photon energy-reflection ratio are given (for electrons, graphs only).

SEMIEMPIRICAL ALGORITHMS FOR DOSE EVALUATION IN ELECTRON-BEAM PROCESSING

Abstract The code EDEPOS to compute the depth-dose curve of electrons normally incident on the semi-infinite absorber has been revised to improve its own output and the output of the multilayer depth-dose code EDMULT, in which EDEPOS serves as a subprogram. The values of adjustable parameters in the algorithm of EDEPOS have been determined by the least-squares fit to the depth-dose data collected from the literature. The data used cover the energies from 0.1 to 20 MeV, and the atomic numbers from 5.28 (an effective atomic number for polyethylene) to 82. The revision has removed the spurious cusp in the depth-dose curve generated by the old code, and has resulted in better agreement with a majority of the data. Illustrative results of computation by the revised version of EDMULT are given.

Mirror reversal simply explained without recourse to psychological processes

This paper proposes a simple and definitive solution to the mirror reversal problem, “Why does a mirror reverse left and right but not up and down?” The solution is given by combining the inversion caused by the optical process of mirroring and the definition of the left-right axis. Thus the left-right reversal of mirror images essentially does not involve psychological processes, in contrast to the multiprocess hypothesis recently proposed by Takano.