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.

The coupling between adiabatic channels can be partially transformed away. The transformation need not induce any transition between channnels; but it correlates the radial wave functions and their gradients with the channel functions and it depresses the lower effective potentials, as the energy increases, in accordance with empirical evidence. (AIP)

Post-Adiabatic Analysis of Atomic Collisions

Results of Sauter are expressed in the form of a transition matrix which determines the photoelectric effect cross section for arbitrary x-ray polarization and arbitrary initial and final orientations of the electron spin. The structure of the matrix elements accounts for curious properties of the cross section in terms of interference between orbital and spin currents. Expansion of the wave functions into powers of $\frac{Z}{137}$ simplifies the calculation of the transition matrix, reduces it to a special case of the bremsstrahlung theory in Born approximation, and explains discrepancies between results of earlier calculations. Analytical and graphical data are given on the photoemission of polarized electrons by circularly polarized x-rays.

Sauter theory of the photoelectric effect

The occurrence of resonant states in regions of high potential, inferred from experiments over two decades, is traced to a familiar aspect of the diagonalization of finite Hamiltonian matrices. The diagonalization generates two sets of eigenstates localized in regions of high and low potential, respectively. These sets are related by a conjugation transformation that determines the relative numbers of set elements and the scale ratio of their eigenvalue spectra. The residual eigenstates are not localized.

Semianalytic study of diamagnetism in a degenerate hydrogenic manifold

The bremsstrahlung matrix element at the short-wavelength limit of the spectrum is calculated to lowest order in $\ensuremath{\alpha}\ensuremath{\equiv}\frac{Z}{137}$, for an unscreened Coulomb field. The result, valid for relativistic incoming electrons, is shown to be exactly ${\ensuremath{\alpha}}^{\ensuremath{-}1}{m}^{\ensuremath{-}\frac{1}{2}}$ times the complex conjugate of Sauter's relativistic matrix element for the $K$-shell photoelectric effect. These matrix elements are the leading terms in an expansion of the exact matrix elements in powers of $\ensuremath{\alpha}$, and they are found to be derivable from the first two terms of the expansions in powers of $\ensuremath{\alpha}$ of the electron wave functions. In this sense their structure is completely analogous to that of the Bethe-Heitler bremsstrahlung matrix element.

Ugo Fano

Papers

Post-Adiabatic Analysis of Atomic Collisions

Sauter theory of the photoelectric effect

Semianalytic study of diamagnetism in a degenerate hydrogenic manifold

Bremsstrahlung and the photoelectric effect as inverse processes

Interference of Orbital and Spin Currents in Bremsstrahlung and Photoelectric Effect