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.

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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.

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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.

Resonances in the differentiai cross section for electron scattering at 72 deg by He and Ne were investigated. Measurements were made of the electron- beam current transmitted through He or Ne as a function of the incident electron energy. In He the resonance at 19.3 ev appears as a sharp increase in transmission. The transmission in Ne shows a doublet structure consisting of two sharp decreases in transmission. The resonance in He is at 16.0 plus or minus 0.1 ev. (C.E.S.)

CLASSIFICATION OF RESONANCES IN THE ELECTRON SCATTERING CROSS SECTION OF Ne AND He

The trend of various atomic properties (e.g., electron potentials, binding energies, scattering phase shifts) along the periodic system is examined utilizing available evidence from experiments and computations. Properties that depend primarily on different layers of the atomic structure are seen to attain extreme values at different columns of the periodic table. From this plausible connection, one can see where and how to search for additional striking variations of properties from one element to the next; e.g., experiments on elastic scattering of slow electrons are thus indicated. The analysis also contributes to the interpretation and correlation of various atomic properties.

Atomic Potential Wells and the Periodic Table

High-resolution measurements of ${\mathrm{S}}^{\ensuremath{-}}$ photodetachment near threshold are interpreted on the basis of an intermediate $[{p}^{4}(^{3}P)+e(l=0)]^{2}P$ complex which dissociates into $\mathrm{jj}$-coupled constituents. The $e\ensuremath{-}\mathrm{S}$ interaction is represented by doublet and quartet scattering lengths ${a}_{d}$ and ${a}_{q}$. Relative cross sections are calculated in terms of electron energies, and of ${a}_{d}$ and ${a}_{q}$. Thereby we generalize to a multichannel process the scattering-length theory of cross sections near $s$-wave thresholds. Many features of the experimental data are accounted for. Predictions are made on the spin-polarization effects of circularly polarized light.

Theory of Photodetachment near Fine-Structure Thresholds

Eigenfunctions of a collision complex branch into different channels when propagating from a condensed-complex to a fragmented-complex limit. The branching ratios depend on separate processes localized where propagation becomes nonadiabatic. The cumulative effect of branching is represented by Jost matrices, which consist of the coefficients of the asymptotic expansion of a base set of eigenfunctions and serve to construct scattering matrices and cross sections. The formulation presented here blends theoretical elements of different origin and includes resonant and bound states of the complex.

Unified treatment of collisions

We present a unified discussion and illustrations of the electron-optical aspects of electron penetration into, or escape from, the inner region of atoms Both processes may focus or defocus the amplitudes of wavefunctions and shift their phases, as manifested in countless phenomena ranging from level shifts to $\ensuremath{\beta}$-decay rates A background survey begins by discussing the Fermi-Segr\`e formula for hyperfine splittings and emphasizes the interplay of hydrogenic and WKB approximations The Phase-Amplitude Method, which determines amplitude ratios and phase shifts directly, proves useful for interpreting the systematics of these parameters along the Periodic System We present results of survey calculations, carried through the Periodic System using Hartree-Slater potential fields, of: (a) $\frac{{\ensuremath{\alpha}}_{l}(0)}{{\ensuremath{\alpha}}_{l}(\ensuremath{\infty})}$, the ratio of the wavefunction's amplitude at $r=0$ to that outside the atom; (b) ${\ensuremath{\delta}}_{l}(E=0)$ and ${\frac{d{\ensuremath{\delta}}_{l}}{\mathrm{dE}}|}_{E=0}$, the phase shift and its energy derivative at $E=0$, and (c) the changes in ${\ensuremath{\delta}}_{l}(E=0)$ and $\frac{{\ensuremath{\alpha}}_{l}(0)}{{\ensuremath{\alpha}}_{l}(\ensuremath{\infty})}$ induced by either a unit perturbation localized near $r=0$ or a relativistic correction Thus we provide a broad mapping of certain fundamental parameters based on rather crude but realistic calculations These results are meant to serve as a bench mark in surveying problems and in checking new results, while standard methods are preferable for working out specific applications accurately

Ugo Fano

Papers

CLASSIFICATION OF RESONANCES IN THE ELECTRON SCATTERING CROSS SECTION OF Ne AND He

Atomic Potential Wells and the Periodic Table

Theory of Photodetachment near Fine-Structure Thresholds

Unified treatment of collisions

Electron-optical properties of atomic fields