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

Wave-particle duality is an inherent peculiarity of the quantum world. The double-slit experiment has been frequently used for understanding different aspects of this fundamental concept. The occurrence of interference rests on the lack of which-way information and on the absence of decoherence mechanisms, which could scramble the wave fronts. Here, we report on the observation of two-center interference in the molecular-frame photoelectron momentum distribution upon ionization of the neon dimer by a strong laser field. Postselection of ions, which are measured in coincidence with electrons, allows choosing the symmetry of the residual ion, leading to observation of both, gerade and ungerade, types of interference.

/pdf/double-slit-photoelectron-interference-in-strong-field-2zdrt0ypsc.pdf

Double-slit photoelectron interference in strong-field ionization of the neon dimer.

This paper reviews recent experimental and theoretical progress concerning many-body phenomena in dilute, ultracold gases. It focuses on effects beyond standard weak-coupling descriptions, such as the Mott-Hubbard transition in optical lattices, strongly interacting gases in one and two dimensions, or lowest-Landau-level physics in quasi-two-dimensional gases in fast rotation. Strong correlations in fermionic gases are discussed in optical lattices or near-Feshbach resonances in the BCS-BEC crossover.

/pdf/many-body-physics-with-ultracold-gases-552s10zfdn.pdf

Many-Body Physics with Ultracold Gases

Magnetic and electric dipole transitions between levels of the 4fx configuration perturbed by a static crystalline field are treated. The expression obtained for the pure‐electronic electric‐dipole transition probability involves matrix elements of an even‐order unit tensor between the two 4fx states involved in the transition. The contributions to the transition probability from interactions, via the crystalline field, with the nd 94fx−1, 4fx−1 nd, 4fx−1 ng configurations are shown to add linearly, in such a manner as to multiply each odd k crystal‐field parameter Ak q by a constant. If ``J mixing'' in the 4fx configuration is neglected ΔJ between the upper and lower 4fx levels is restricted to six units or less. If ``L mixing'' is neglected then ΔL is also restricted to six units or less. Application is made to the fluorescence spectra of PrCl3 and EuCl3. Many of the missing and weak transitions are explained.

Intensities of Crystal Spectra of Rare‐Earth Ions

Hartree-Slater subshell photoionization cross-sections at 1254 and 1487 eV.

The interference of a discrete autoionized state with a continuum gives rise to characteristically asymmetric peaks in excitation spectra. The earlier qualitative interpretation of this phenomenon is extended and revised. A theoretical formula is fitted to the shape of the $2s2p^{1}P$ resonance of He observed in the inelastic scattering of electrons. The fitting determines the parameters of the $2s2p^{1}P$ resonance as follows: $E=60.1$ ev, $\ensuremath{\Gamma}\ensuremath{\sim}0.04$ ev, $f\ensuremath{\sim}2 \mathrm{to} 4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$. The theory is extended to the interaction of one discrete level with two or more continua and of a set of discrete levels with one continuum. The theory can also give the position and intensity shifts produced in a Rydberg series of discrete levels by interaction with a level of another configuration. The connection with the nuclear theory of resonance scattering is indicated.

Effects of Configuration Interaction on Intensities and Phase Shifts

Description of States in Quantum Mechanics by Density Matrix and Operator Techniques

Information on the spectrum of oscillator strength for neutral atoms in their ground states is surveyed with particular regard to recent progress in the far uv-soft x-ray range and to the theoretical interpretation of data from experiments and from numerical calculations. The analysis brings out numerous aspects of atomic mechanics and problems that remain unsolved. An effort is made to interconnect different theoretical approaches within the framework of the theory of atomic spectra.

Spectral Distribution of Atomic Oscillator Strengths

The ionization produced by individual fast charged particles is frequently used as a measure of their initial energy; fluctuation effects set a theoretical limit to the accuracy of this method. Formulas are derived here to estimate the statistical fluctuations of the number of ions produced by constant amounts of radiation energy. The variance of the number of ionizations is found to be two or three times smaller than if this number were governed by a Poisson distribution. An improved understanding is gained of the statistical treatment of fluctuation phenomena.

Ugo Fano

Papers

Effects of Configuration Interaction on Intensities and Phase Shifts

Description of States in Quantum Mechanics by Density Matrix and Operator Techniques

Spectral Distribution of Atomic Oscillator Strengths

Ionization Yield of Radiations. II. The Fluctuations of the Number of Ions

Irreducible tensorial sets