The status of theory and experiment of electron polarization resulting from spin-orbit interaction in low-energy scattering from unpolarized targets is reviewed. Polarization effects in scattering from free atoms, molecules, and solid targets at energies between a few electron volts and a few thousand electron volts are discussed. Apart from a survey of the problems which have been solved, a perspective is given of the work which would be interesting to pursue in this rapidly developing field of research.

Vibrational relaxation data are surveyed in order to provide the rates of vibrational energy transfer for processes important in the C${\mathrm{O}}_2$-${\mathrm{N}}_2$ laser. A kinetic model is assumed for the vibrational energy transfer into and within the various vibrational modes of the molecules that make up a C${\mathrm{O}}_2$-${\mathrm{N}}_2$ laser, including the species ${\mathrm{H}}_2$O, ${\mathrm{O}}_2$, He, and ${\mathrm{H}}_2$. Experimental data are assembled and interpreted for the rate constants and the probabilities per collision for the various kinetic processes of the assumed mechanism as a function of temperature. For certain processes, the experimental data are reinterpreted in terms of more recent knowledge of vibrational energy transfer. The data are compared with theoretical calculations and various anomalies in those comparisons are discussed. The significance of the various vibrational energy transfer processes for understanding the operation of the C${\mathrm{O}}_2$-${\mathrm{N}}_2$ laser are contrasted with the state of knowledge of the rate information.

A systematic survey of the subject of the $\alpha -\alpha$ interaction is made. The early observations of $\alpha$ emission and resulting theoretical descriptions, especially the $\alpha$-particle model of nuclei, are described, as are more recent $\alpha -\alpha$ scattering experiments. The latter were designed to obtain information about the nature of the $\alpha -\alpha$ interaction and about the energy levels of ${}_{}{}^8{}_{}{}^{}\mathrm{Be}$ by studying the resonance behavior of the phase shifts. The phenomenological approach, i.e., the attempt to construct the $\alpha -\alpha$ potential which reproduces the experimental phase shifts, is described as are detailed theoretical constructions of the repulsive inner part and attactive outer part of the $\alpha -\alpha$ interaction. Studies of how the $\alpha -\alpha$ interaction provides better understanding of the structure of $\alpha$-clustered nuclei and also of the fundamental forces between the constituents of these nuclei are discussed. Suggestions for the direction of further efforts are made.

A unified treatment is given of the high-energy elastic and inelastic electromagnetic scattering of electrons and muons by hadrons in terms of the polarization density matrix of the virtual photon exchanged. It is shown that when the leptons are longitudinally polarized, the virtual photon is in a pure polarization state which is a coherent superposition of an elliptically polarized transverse state and a longitudinal state. Experiments utilizing these features are suggested and the formulas for the cross sections are obtained. The limit in which the virtual photon is almost real is investigated carefully. Finally, it is shown that the formalism is immediately applicable to neutrino scattering.

We have investigated and improved the reliability of many formulas used in the radiative corrections to elastic and inelastic electron scatterings when only the scattered electrons are detected. The radiative corrections to muon scattering are also investigated. A practical and reliable recipe for unfolding the entire inelastic spectra, including effects due to virtual photons, internal and external bremsstrahlungs, is given. Examples of actually unfolding the inelastic electron spectra are given using the experimental data obtained by the electron-scattering group at the Stanford Linear Accelerator Center.

We present a review of the literature on radiative corrections to electron scattering, a summary of the essential elements of the theory in a manner hopefully useful to experimenters, and comments on certain aspects of the subject that need further investigation.

This review of the properties of leptons, mesons, and baryons is an updating of Rosenfeld et al. [Rev. Mod. Phys. 40, 77 (1968)]. Data are evaluated, listed, averaged, and summarized in tables and wallet sheets. A data booklet is also available.

The method of self-adjoint ladder operators, developed in Parts I and II, is applied to the solution of the generalized angular-momentum problem. This reveals many interesting aspects of this approach to eigenvalue problems and, in particular, its relationship to addition of angular momentum. The complete set of irreducible unitary representations of the underlying algebra is obtained and also the corresponding Clebsch-Gordan (Wigner) coefficients for the addition of spin and angular momentum in a space of arbitrary dimension.

It is convenient to classify the impurity states in semiconductors into three groups: low, intermediate, and high. Even at high concentrations anomalous (i.e., nonmetallic) properties are observed. A simple "inhomogeneity" model is proposed in which the impurity states are regarded as spatial mixtures of metallic and nonmetallic regions. The model provides an explanation of the anomalous properties, at least qualitatively.

The nuclear relaxation of ${}_{}{}^{29}{}_{}{}^{}\mathrm{Si}$ in phosphorus-doped silicon is studied from the metal-nonmetal transition point of view. Going from the nonmetal to the metal there is a rapid decrease of relaxation time at the transition, donor impurity ≈ ${10}^{18}$ P atoms/${\mathrm{cm}}^3$. For the insulating side of the transition the dominant process of relaxation is due to the modulation of the dipolar interaction between the impurity electron spin hopping from one impurity center to another, and the nuclear spins. This type of relaxation can only take place if the material is compensated. For the metallic side of the transition the dominant process of relaxation is due to the modulation of the hyperfine coupling between the nuclei and the highly degenerate electron gas in a narrow band. The electron density in the vicinity of the donor centers is measured in a 2.5× ${10}^{18}$ P atoms/${\mathrm{cm}}^3$ sample. The measurement shows that it remains strongly localized around the impurities. A comparison is made of our results with the $D^{-}$ band model of conductivity.

A synthesis is given of the most significant experimental features of the semiconductor-to-metal transition in group IV semiconductors. Two characteristic concentrations are discussed, the first being for a delocalization of electrons (the "Mott" transition), and the second being associated with the entry of the Fermi level into the conduction band of the host material. Experimental values are given for the two concentrations in several materials. Experimental data covering measurements of Hall coefficient, electrical resistivity and carrier mobility, NMR properties, magnetoresistance, magnetic susceptibility, and ESR properties are employed in arriving at values for the two characteristic concentrations. Si: P is taken as the model system because of the completeness of experimental measurements. Si: As is also briefly considered. Existing data for $n$-Ge are examined, as well as the more restricted evidence concerning $n$-SiC.

The magnetic-field-dependent activation energy required to explain the rapid increase in the Hall coefficient with decreasing temperature in $n$-type InSb from 2°-5°K and in fields of up to 15 kG, observed by Putley and other workers, is interpreted in terms of the energy gap between the two lowest donor levels. This gap appears to be rather insensitive to carrier screening. Further, the existence of a threshold magnetic field, below which no activation energy is found, is interpreted as evidence of a Wigner transition, in which the electrons in the lowest impurity band cease to conduct when the donor-wave-function overlap, or the effective mass for electron transport, reaches a critical value. Finally, the relation between the activation energy for conduction in the extreme high-field limit and the Yafet-Keyes-Adams ionization energy is briefly discussed. It is anticipated that this ionization energy will be more closely approached at high fields, but perhaps never quite attained in practice.

It is shown that no well-defined Fermi surface exists on the "metallic" side of the Mott transition in Hubbard's theory. An alternative approach is suggested.

A study of a narrow $s$-band model has been undertaken, pursuing an idea of Englert, which clearly shows the onset of localization. The study is based on an approximate decoupling of an appropriate two-particle Green function $〈〈{\Sigma }_{\mathrm{k}}{C}_{\uparrow }(\frac{1}{2}\mathrm{K}+\mathrm{k})C_{\downarrow }\frac{1}{2}\mathrm{K}-\mathrm{k}); {\Sigma }_{{\mathrm{k}}^{\prime }}{C_{\downarrow }}^{†}(\mathrm{K}+{\mathrm{k}}^{\prime }\left){C_{\downarrow }}^{†}\right(\frac{1}{2}\mathrm{K}+{\mathrm{k}}^{\prime })〉〉$, which is similar to a $t$-matrix approximation. In the limit of large Coulomb energy to bandwidth, these Green functions have a high-lying pole which in the first form of the approximation dominates the correlation function $N^{-1\mathrm{}}〈{\Sigma }_i{n}_{i\uparrow }{n}_{i\downarrow }〉$, but has only a temperature-independent contribution to the free energy. This approximation describes local correlation adequately except as the band approaches being half-filled. Under those conditions a single-particle distribution function must be calculated self-consistently. A simple modification of the approximation, assuming localized single-particle states, extends the above description down to the region of a half-filled band, where the avoidance of double occupancy of a lattice site implies an insulating state.

Correlation and magnetic effects in narrow bands are studied using a generalized self-consistent cluster treatment of the narrow-band Hamiltonian. Here the dynamics consists of electron hopping between nearest-neighbor sites and Coulomb interaction between electrons on the same site and nearest-neighbor sites. In the simpler case, where the neighbor interactions are neglected, i.e., the Hubbard model, the environment of the cluster is regarded as a particle reservoir, one for each spin. Hopping between the cluster and reservoirs is described by fermion source terms. It is required that the thermodynamic average of the particle currents of each spin within the cluster equal the corresponding particle exchange between cluster and reservoir. Electron motion in the system is examined for varying ratios of the strength of the hopping to the intrasite Coulomb repulsion. A discontinuous transition from an antiferromagnetic insulator to a metal is found under dynamical conditions close to those predicted by Hubbard and Kemeny. The effect of the intersite Coulomb interaction on the transition is next studied. These added terms are seen greatly to influence the transition and the magnetic properties of the cluster.