A survey of the existing data on the shapes of $\beta$-ray spectra is given, mostly from the experimental point of view. The majority of the empirical facts accumulated during the past 12 years is repoduced in tables. The problems of Fierz-type and energy-proportional deviations, time reversal, pseudoscalar-type interaction, conservation of vector and axial-vector currents, and neutrino degerenacy are treated.

Some basic properties of the Kelvin-Helmholtz instability are reviewed, and some papers dealing with various refinements of this phenomenon are discussed.

The principles of quantum mechanics impose certain restrictions on acceptable position operators. The probability density as derived from the position operator should agree with the fourth component of the current vector. The various relativistic wave equations are reexamined from the point of view of this consistency test. These and the group theoretical considerations lead to the conclusion that only a Dirac particle can be considered to be elementary. The position operator of the infinite-dimensional theories is investigated and the advantages of theories using the unitary representations of the Lorentz group are discussed.

A survey of theoretical and experimental methods now available for calculating, producing, and measuring high-energy coherent bremsstrahlung (HEB) and electron pair production (EPP) is presented.

After an introduction in which the historical development of the subject matter is sketched, a preliminary theoretical approach is outlined. A rough classical argument is shown, and a formal expression of the Laue-Bragg law suitable for the next calculation is deduced, together with some fundamental kinematics of the HEB and EPP processes. The structure factors for the cubic, face-centered cubic, and diamond lattice are deduced and some qualitative features of the interferential cross sections are shown.

A complete calculation of the HEB and EPP cross sections is carried out. HEB polarized and unpolarized cross sections as functions of recoil momentum are obtained and then integrated over all the reciprocal lattice space. Corresponding results for EPP cross sections are expressed and numerical calculation results are shown.

The last part of the paper deals with experimental methods and techniques used in different laboratories in order to produce and measure high-energy coherent bremsstrahlung suitable for photoproduction experiments by polarized photons. Experimental apparatus and results are described in some detail. Finally, concluding remarks are made concerning the topics omitted.

The role of beta- and gamma-ray matrix elements in the determination of wave functions for the $s^4{p}^{10}$ states of mass 14 is examined. The data considered include the Gamow-Teller (beta) matrix elements of ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{14}{}_{}{}^{}\mathrm{O}$ and the $M1\mathrm{}$ and $E2\mathrm{}$ matrix elements connecting the lowest four $s^4{p}^{10}$ states of ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$. The magnetic moment of ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ is also discussed. The shell-model wave functions considered arise mainly from the $s^4{p}^{10}$ configuration but include admixtures of the $s^4{p}^8$ ($2s, 1d$) configuration. It is found that the data, considered as a whole, cannot be explained if the $s^4{p}^{10}$ components of the wave functions are derived from a central plus spin-orbit interaction only, but that quite satisfactory agreement is obtained if the nuclear force includes a tensor part. The bulk of the cancellation of the ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$ beta decay matrix element takes place within the $s^4{p}^{10}$ configuration. In general, configuration mixing is of secondary importance; its most noticeable effect is on the $M1\mathrm{}$ decay of the first-excited state of ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$.

A review of the quantum theory of ionizing collisions is presented, with particular regard to recent theoretical developments. A discussion is given of quantal and classical approximations and their predictions compared with experimental data. Some useful empirical formulas are listed and compared, and in conclusion mention is made of the present inadequacies in the theory.

The uneasiness prevailing in thermodynamics is the inevitable result of the absence of clearly understood basic concepts. Since thermodynamics, the doctrine of equilibrium, encompasses parts of all branches of the physical sciences, its basic concepts must be explained in ordinary language, free from all references to a specific branch. Moreover, the general applicability of the concepts must be demonstrated.

Carathéodory has introduced new ideas of fundamental importance. But his shortcomings concerning basic concepts have been repeated and intensified by his successors in axiomatics.

A properly constructed basis of thermodynamics elucidates the fundamental distinction of generalized coordinates and generalized forces from each other and from other properties. As an accessorial result one notices a unique quality of the generalized forces (and the temperature): They can be measured only if equilibrium has been established.

The so-called "zeroth law" is neither a law nor a generalized observation. The clarification of its significance contributes to the epistemological understanding of thermodynamics.

The effects of the isotropic, anisotropic, and vibrational intermolecular forces on the rotation-vibration energy levels in solid parahydrogen are investigated theoretically. The main part of the shift of the rotation-vibration levels is due to the stretching of the molecules by the isotropic intermolecular forces. These shifts are calculated using a vibrating-rotor model for the hydrogen molecule, containing four anharmonicity constants determined from the spectroscopic data on gaseous hydrogen. The next most important interaction is the quadrupole-quadrupole interaction. For the matrix elements of the quadrupole moment between the rotation-vibration states we take the theoretical values calculated by Karl and Poll for an isolated molecule. On this basis a satisfactory account can be given of the shifts and splittings of all the zerophonon features in the infrared and Raman spectra of solid parahydrogen and of ortho-para mixtures at low orthohydrogen concentrations. Of particular interest is the verification of the predicted shifts of the $S_1\mathrm{}\left(0\right)\mathrm{}$ and $S_2\mathrm{}\left(0\right)\mathrm{}$ lines, arising from the imperfect localization of the $J=2\mathrm{}$ excitation on the vibrating molecule in the upper states of these transitions, and of the self-energy shifts of the rotational states due to the interaction with the lattice vibrations. The fine structure of the $S_1\mathrm{}\left(0\right)\mathrm{}$ line at low ortho concentrations, and the splitting of the $S_1\mathrm{}\left(0\right)+S_1\mathrm{}\left(0\right)\mathrm{}$ doublet in the overtone infrared spectrum can also be understood using the unperturbed quadrupole moments and taking into account the imperfect localization of the rotational excitations. The complete frequency analysis yields empirical values of the vibrational coupling constant (${\epsilon }^{\prime }=0.49\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$) and the crystalline field constants (${\epsilon }_{2c}=-0.03\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$, ${\epsilon }_{4c}=-2.60\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$), and leads to predictions concerning the frequency of the $S_0\mathrm{}\left(0\right)\mathrm{}$ infrared line, the splitting of the $S_1\mathrm{}\left(0\right)\mathrm{}$ Raman triplet and the position of the as yet unobserved third component, and the frequency of the $Q_1\mathrm{}\left(0\right)+Q_1\mathrm{}\left(1\right)\mathrm{}$ line. For the remaining three unknown interaction parameters, six relations are derived of which the consistency is discussed in relation to the available experimental data.

The quantum-mechanical study of the motion of a charged spin-½ particle in a uniform magnetic field has a number of features which are of interest to theorists. Not only can the Dirac equations be solved completely and analytical solutions be obtained, but unlike the Coulomb problem, the expressions for absorption and emission of radiation can be evaluated exactly with these exact Dirac wave functions without resorting to a multipole expansion of the usual sort that is made in the theory of the hydrogen atom. In the ultrarelativistic limit, reasonably simple, closed expressions can be obtained for synchrotron radiation, or photoproduction of electron-positron pairs in a magnetic field. The latter expression allows one to associate an absorption coefficient with the magnetic field in vacuo, and through the use of dispersion theory, to obtain the real (dispersive) part of the index of refraction. The use of exact wave functions, rather than plane waves, to describe the electron may simplify the anomalous-moment calculations and shed some light on the computation of the complete power series in $\alpha$.

In this paper, the second-quantized theory of free particles and antiparticles, with any spin and with internal $\mathrm{SU}\left(2\right)\mathrm{}$ or $\mathrm{SU}\left(3\right)\mathrm{}$ symmetry, is developed. All spins and both statistics are treated in a uniform way in terms of well-defined complete sets of functions that are orthonormal with respect to a Lorentz-invariant positive-definite inner product. Explicit formulas for field operators of energy, momentum, etc., are given, including three-vector, four-vector, and tensor operators for polarization. It is shown that causal space densities of physical quantities exist when the correct spin-statistics connection is used. The field operators for systems self-conjugate under $C$, $G$, and $\mathrm{GP}$ are treated and self-conjugate multiplets of $\mathrm{SU}\left(3\right)\mathrm{}$ are set up.

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.

The quantum-mechanical description of phase and angle variables is reviewed, with emphasis on the proper mathematical description of these coordinates. The relations among the operators and state vectors under consideration are clarified in the context of the Heisenberg uncertainty relations. The familiar case of the azimuthal angle variable $\varphi$ and its "conjugate" angular momentum $L_z$ is discussed. Various pitfalls associated with the periodicity problem are avoided by employing periodic variables ($sin\varphi$ and $cos\varphi$ to describe the phase variable. Well-defined uncertainty relations are derived and discussed. A detailed analysis of the three-dimensional harmonic oscillator excited in coherent states is given. A detailed analysis of the simple harmonic oscillator is given. The usual assumption that a (Hermitian) phase operator $\phi$ (conjugate to the number operator $N$) exists is shown to be erroneous. However, cosine and sine operators $C$ and $S$ exist and are the apprópriate phase variables. A Poisson bracket argument using action-angle (rather $J$, $cos\phi$, $sin\phi$) variables is used to deduce $C$ and $S$. The spectra and eigenfunctions of these operators are investigated, along with the important "phase-difference" periodic variables. The properties of the oscillator variables in the various types of states are analyzed with special attention to the uncertainty relations and the transition to the classical limit. The utility of coherent states as a basis for the description of the evolution of the density matrix is emphasized. In this basis it is easy to identify the classical Liouville equation in action-angle variables along with quantum-mechanical "corrections." Mention is made of possible physical applications to superfluid systems.

Techniques for the determination of rotational and vibrational excitation cross sections of molecules by low-energy electrons are reviewed. The results of experiment are then compared with theory. High-energy resolution electron beam techniques are most useful for the measurement of the details of resonance-type, vibrational excitation cross sections. Cross section determinations from analyses of electron transport coefficients are most successful at energies near the threshold of vibrational excitation and for rotational excitation. High-frequency energy relaxation studies provide data on rotational excitation. A comparison of presently available experimental and theoretical results shows that some of the excitation processes, e.g., rotational excitation of ${\mathrm{N}}_2$ and CO and vibrational excitation of CO near threshold, are accurately described by the longest-range forces and Born approximation. In other cases, e.g., vibrational excitation of ${\mathrm{N}}_2$ and CO near 2 eV, the excitation is best described in terms of an electron resonance with the molecular potential.

A survey on the new theoretical and experimental results in the field of electron capture processes, first since the Warsaw Conference, 1963, is given.

Evidence is reviewed which demonstrates that the recently observed low-temperature electron state arising from the Kondo effect in metals containing small numbers of transition element impurities is present over a much wider temperature range than is generally appreciated. The possibility that this state forms a link between magnetic and nonmagnetic impurity states in metals as suggested by Schrieffer is discussed.

A review is given of the theory of magnetic groups and of their unitary corepresentations. Particular application is made to magnetic space groups, this part of the work being set in the framework of little-group theory. The symmetry problems in physics which lead to magnetic groups are analyzed and various applications of the theory to such problems are pointed out. Finally a method is given for obtaining the Kronecker products of corepresentations of magnetic groups, and an example is presented in which the unitary subgroup of the magnetic group is the point group ${\mathrm{C}}_{2v}$.

Proofs that closed-shell molecules must be diamagnetic are shown to be restricted to two-electron systems. An exact nonrelativistic ground-state wave function having four or more electrons is shown to possess a nodal structure which arises from the Pauli principle. These nodes cause the proofs that a closed-shell molecular wave function is necessarily diamagnetic to be invalid when more than one pair of electrons is present. The physical situation is examined with special reference to the diatomic BH molecule.