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.

We construct the expansion of a Bloch wave with energy E into a complete set of multipole waves around a ’’center’’ of a crystal as an analog of the expansion in spherical waves in free space. Crystal point group symmetry is used to classify the set. The density of states in a cell is then analyzed into multipole components whose magnitude depends on the cell’s distance from the ’’center.’’

Multipole expansion of the density of states about a crystal cell

Il concetto di matrice di densita ebbe origine attorno al 1930 nel corso di adattare alla meccanica quantistica la descrizione statistica di fenomeni classici, ricevendo poi nuova luce dalla formulazione dell’equazione di risonanza nucleare da parte di Felix Bloch, arricchita di effetti dissipativi. Questa equazione, apparentemente l’equazione di Schrodinger per la matrice di densita della polarizzazione di uno spin, guida in realta i valori medii di ogni quantita osservabile nel corso della sua evoluzione. Essa serve quindi come prototipo per molti e diversi fenomeni. I coefficienti di dissipazione (o «rilassamento») dell’equazione di Bloch vennero poi interpretati da Zwanzig come indici dell’informazione che sfugge per canali non osservati.

Matrici di densità come vettori di polarizzazione

Attention is called to phenomena that should serve as sensitive indicators of the field acting upon slow electrons as they traverse the edge of atoms. (auth)

Diverse manifestations of barriers to atomic electrons

Scattering geometries are represented by tensorial parameters classified according to symmetry under permutations P and Q: P changes a base set of wave functions into its Hermitian conjugate and Q interchanges the directions of incidence and scattering These parameters interlink initial and final states of projectile and target, a linkage mediated by the angular momentum j/sub t/ transferred in the collision Collision cross sections and expectation values of the observables are constructed as sums of geometrical parameters with different symmetries, weighted by dynamical parameters

New quantum numbers in collision theory. III. Symmetries of the scattering geometry.

We report recent progress toward a nonperturbative formulation of many-body quantum dynamics that treats all constituent particles on an equal footing. This formulation is capable of detailing the evolution of a system toward the diverse fragments into which it can break up. We illustrate the general concept with the simple example of the simultaneous excitation of both electrons in a helium atom. {copyright} {ital 1996 The American Physical Society.}

Ugo Fano

Papers

Multipole expansion of the density of states about a crystal cell

Matrici di densità come vettori di polarizzazione

Diverse manifestations of barriers to atomic electrons

New quantum numbers in collision theory. III. Symmetries of the scattering geometry.

Fragmentation of atomic systems