The stopping and range of ions in matter is physically very complex, and there are few simple approximations which are accurate. However, if modern calculations are performed, the ion distributions can be calculated with good accuracy, typically better than 10%. This review will be in several sections: 

a)

A brief exposition of what can be determined by modern calculations.




b)

A review of existing widely-cited tables of ion stopping and ranges.




c)

A review of the calculation of accurate ion stopping powers.

The stopping and range of ions in solids

We report calculations of electron inelastic mean free paths (IMFPs) of 50–2000 eV electrons for a group of 14 organic compounds: 26-n-paraffin, adenine, β-carotene, bovine plasma albumin, deoxyribonucleic acid, diphenylhexatriene, guanine, kapton, polyacetylene, poly(butene-1-sulfone), polyethylene, polymethylmethacrylate, polystyrene and poly(2-vinylpyridine). The computed IMFPs for these compounds showed greater similarities in magnitude and in the dependences on electron energy than was found in our previous calculations for groups of elements and inorganic compounds (Papers II and III in this series). Comparison of the IMFPs for the organic compounds with values obtained from our predictive IMFP formula TPP-2 showed systematic differences of ∼40%. These differences are due to the extrapolation of TPP-2 from the regime of mainly high-density elements (from which it had been developed and tested) to the low-density materials such as the organic compounds. We analyzed the IMFP data for the groups of elements and organic compounds together and derived a modified empirical expression for one of the parameters in our predictive IMFP equation. The modified equation, denoted TPP-2M, is believed to be satisfactory for estimating IMFPs in elements, inorganic compounds and organic compounds.

Calculations of electron inelastic mean free paths. III. Data for 15 inorganic compounds over the 50–2000 eV range

The computer code system PENELOPE (version 2008) performs Monte Carlo simulation of coupled
electron-photon transport in arbitrary materials for a wide energy range, from a few hundred eV to
about 1 GeV. Photon transport is simulated by means of the standard, detailed simulation scheme.
Electron and positron histories are generated on the basis of a mixed procedure, which combines
detailed simulation of hard events with condensed simulation of soft interactions. A geometry package
called PENGEOM permits the generation of random electron-photon showers in material systems
consisting of homogeneous bodies limited by quadric surfaces, i.e., planes, spheres, cylinders, etc. This
report is intended not only to serve as a manual of the PENELOPE code system, but also to provide the
user with the necessary information to understand the details of the Monte Carlo algorithm.

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PENELOPE-2006: A Code System for Monte Carlo Simulation of Electron and Photon Transport

We report calculations of electron inelastic mean free paths (IMFPs) for 50–2000 eV electrons in a group of 27 elements (C, Mg, Al, Si, Ti, V, Cr, Fe, Ni, Cu, Y, Zr, Nb, Mo, Ru, Rh, Pd, Ag, Ta, W, Re, Os, Ir, Pt, Au and Bi). This work extends our previous calculations (Surf. Interface Anal. 11, 57 (1988)) for the 200–2000 eV range. Substantial variations were found in the shapes of the IMFP versus energy curves from element to element over the 50–2000 eV range and we attribute these variations to the different inelastic scattering properties of each material. Our calculated IMFPs wee fitted to a modified form of the Bethe equation for inelastic electron scattering in matter; this equation has four parameters. These four parameters could be empirically related to several material parameters for our group of elements (atomic weight, bulk density and number of valence electron per atom). IMFPs and those initially calculated was 13%. The modified Bethe equation and our expressions for the four parameters can therefore be used to estimate IMFPs in other materials. The uncertainties in the algorithm used for our IMFP calculation are difficult to estimate but are believed to be largely systematic. Since the same algorithm has been used for calculating IMFPs, our predictive IMFP formula is considered to be particularly useful for predicting the IMFP dependence on energy in the 50–2000 eV range and the material dependence for a given energy.

Calculations of electorn inelastic mean free paths. II. Data for 27 elements over the 50–2000 eV range

We present new calculations of electron inelastic mean free paths (IMFPs) for 200–2000 eV electrons in 27 elements (C, Mg, Al, Si, Ti, V, Cr, Fe, Ni, Cu, Y, Zr, Nb, Mo, Ru, Rh, Pd, Ag, Hf, Ta, W, Re, Os, Ir, Pt, Au and Bi) and four compounds (LiF, SiO2, ZnS and Al2O3). These calculations are based on an algorithm due to Penn which makes use of experimental optical data (to represent the dependence of the inelastic scattering probability on energy loss) and the theoretical Lindhard dielectric function (to represent the dependence of the scattering probability on momentum transfer). Our calculated IMFPs were fitted to the Bethe equation for inelastic electron scattering in matter; the two parameters in the Bethe equation were then empirically related to several material constants. The resulting general IMFP formula is believed to be useful for predicting the IMFP dependence on electron energy for a given material and the material-dependence for a given energy. The new formula also appears to be a reasonable but more approximate guide to electron attenuation lengths.

Calculations of electron inelastic mean free paths for 31 materials

Since the appearance of the title paper, a number of new developments have occurred which need to be included in that body of material. We present additional remarks and clarifications which supplement and update numerous aspects of the Bethe theory discussed in the earlier paper. We also bring the bibliography up to date. Plasma stopping power, the ${z}^{3}$ effect, and stopping power for particles at extreme relativistic energies are among the new topics included. We make several comments on Fano's earlier review article, Ann. Rev. Nucl. Sci. 13, 1 (1963).

Mitio Inokuti

Papers

Inelastic Collisions of Fast Charged Particles with Atoms and Molecules-The Bethe Theory Revisited

Inelastic collisions of fast charged particles with atoms and molecules the Bethe theory revisited