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

(1976). Nuclear Tracks in Solids (Principles and Applications) Nuclear Technology: Vol. 30, No. 1, pp. 91-92.

Nuclear Tracks in Solids (Principles and Applications)

Confined many-electron systems

The precipitation of asphaltenes in two Mexican crude oils was measured using a combination of high-pressure isothermal expansion and atmospheric titration with n-alkanes. Experiments were carried out from the live- and tank-oil type of samples of the same crude oils. For the oils investigated, compositional data, precipitation phase diagrams, and bubble point pressures are reported. A theoretical study for these systems was performed using the statistical association fluid theory for potentials of variable range (SAFT-VR) equation of state (EOS) in the framework of the McMillan–Mayer theory. By matching a single titration curve or two precipitation onset points with this EOS, a good prediction of asphaltene precipitation over wide temperature, pressure, and composition intervals is obtained. © 2004 American Institute of Chemical Engineers AIChE J, 50: 2552–2570, 2004

Asphaltene Precipitation in Crude Oils: Theory and Experiments

Intermediate Quantum Mechanics. By Hans A. Bethe. $9.00; paperback $4.95. 1964. (W. H. Benjamin, New York and Amsterdam)

We formulate the exact solution of the Schrodinger equation for systems of one electron in the Coulomb field of one or two fixed nuclei at the foci inside prolate spheroidal boxes. Numerical results are obtained for the energy eigenvalues and eigenfunctions of the lowest states of the hydrogen atom and the H+2 and HeH++ molecular ions for boxes of different sizes and eccentricities. We also evaluate the hyperfine splitting of atomic hydrogen and of H+2.

The hydrogen atom and the H+2 and HeH++ molecular ions inside prolate spheroidal boxes

A universal equation for the electronic stopping of ions in solids

The aggregation behavior of asphaltenes in asphaltene−resin mixtures within different host media is studied on the basis of the asphaltene/resin molecular structures and considering the embedding medium as a uniform background field. The approach employs models of molecular structures for both asphaltenes and resins (as derived from characterization data), and uses Molecular Mechanics (MM)/Molecular Dynamics (MD) calculations to predict the effect of the intermolecular interactions on the aggregation process as a function of composition and embedding medium. The peptizing behavior of resins is analyzed as a function of the ratio of resin to asphaltene molecules in each host medium by constructing the corresponding MD-generated radial distribution functions as well as the associated potentials of mean force (PMF). In all cases, the PMF presents repulsive barriers characteristic of aggregate systems showing a strong aggregation effect in a highly precipitant medium such as heptane. For an intermediate preci...

Molecular View of the Asphaltene Aggregation Behavior in Asphaltene−Resin Mixtures

A variational boundary perturbation method for solving Schrodinger's equation for enclosed quantum systems with infinite potential walls has been recently proposed by Gorecki and Byers Brown. Their treatment was based on the use of an input wavefunction chi =Gc0 f, where chi 0 is the wavefunction of the free system and f a non-singular function that vanishes at the boundary. The class of functions f was further used to minimize the total energy. In the present work the direct variational method is applied to the ansatz function chi by assigning the variational parameter to the free-system wavefunction, once an adequate cut-off function, f, is defined. This is in contrast to the previous authors' work. The procedure is applied to hydrogen and helium atoms within hard spherical boxes and also to a hydrogen atom confined between two impenetrable parallel walls. The results are in fair agreement with exact calculations.

Enclosed quantum systems: use of the direct variational method

The ground-state energy of excitons confined in microspherical crystallites with a finite-height potential wall is studied variationally as a function of the particle radius in the so-called strong-confinement regime. Exciton energies for dot radii in the range 5-40 A are calculated and compared with experimental and theoretical data for CdS, CdSe, PbS and CdTe crystallites. This comparison shows that the effective-mass approximation and spherical confinement geometries are appropriate for all of the particle sizes. Our results also show that the quantum dot cannot be modelled using an infinite-barrier-height potential in the strong-confinement regime.

https://iopscience.iop.org/article/10.1088/0953-8984/10/6/017/pdf

Salvador A. Cruz

Papers

The hydrogen atom and the H+2 and HeH++ molecular ions inside prolate spheroidal boxes

A universal equation for the electronic stopping of ions in solids

Molecular View of the Asphaltene Aggregation Behavior in Asphaltene−Resin Mixtures

Enclosed quantum systems: use of the direct variational method

Confinement of excitons in spherical quantum dots