The polarization parameter $P$ was measured at Saclay, at 7 energies, and the $C_{\mathrm{NN}}$ parameter at 3 energies. We used a polarized target and the extracted beam of the synchrotron "Saturne." The beam momentum was known at ±1%. The beam intensity was limited at ${10}^7$ protons in 400 sec.

Recent experiments at Berkeley on nucleon-nucleon systems at intermediate energies are discussed. Comparison of experimental results for measurements of parameters using polarized targets agree well with results of experiments not using polarized targets. The advantages and disadvantages of these different methods are discussed briefly.

This report presents experimental results obtained by the Orsay group in France. Firstly, experiments of differential cross-section polarization and depolarization in $\mathrm{pp}$ scattering at 150 MeV. Secondly, polarization and correlation measurements in $\mathrm{pp}$ scattering at 600 MeV.

Data bearing on the nucleon-nucleon interaction near 210 MeV are reviewed. Proton-proton elastic scattering, neutron-proton elastic scattering (both free and from neutrons bound in deuterium), nucleon-nucleon bremsstrahlung, and tests of invariance principles are discussed. Three-nucleon experiments are mentioned briefly. Some revisions to published $N-N$ scattering data are suggested, and complete tables of data are given.

The upper boundary of the unambiguous phase-shift analysis as is known, is at 310 MeV. Above the meson production threshold this unambiguity is absent. In the range from 600-650 MeV where the physicists of our Laboratory have worked during recent years the scattering amplitude has been determined ambiguously and not very reliably. In this connection all the experiments for studying nucleon-nucleon scattering being carried out at our Laboratory have two purposes: first, the more accurate determination and improvement of the phase-shift analysis and second, the discrimination of the obtained phase-shift sets for the determination of the most probable set of them. My report is a short survey of some of experiments performed with the above purpose at Dubna in recent years.

A summary is given of our state of knowledge of the nucleon-nucleon interaction as derived from the invited and contributed papers and the informal discussions. It appears that much progress has been made since 1960 and that despite the use of widely divergent formalisms current theoretical models have much of the same physical substance. The informal discussions of the conference, particularly those related to the experimental, phenomonological, and theoretical aspects of the nucleon-nucleon interaction in the elastic scattering region are summarized.

A revived interest in the Sagnac effect has recently resulted from the development of the self-oscillating laser version of the original Sagnac interferometer. The Sagnac interferometer or ring laser is an example of an electromagnetic sensor of absolute rotation, so historical and theoretical background information is useful in evaluating the possibilities of electromagnetic sensing of absolute rotation. A critical literature study of the many experimental ramifications and the older kinematical theory of the effect is presented. This geometric optical theory is then complemented and compared with more recent work that is based on a physical optical analysis using a complete electromagnetic description of the phenomenon.

The peculiarities of physical axiom systems, by contrast to the mathematical ones, are examined. In particular, the problem of attaching a physical meaning to a formalism is handled. The main views concerning meaning—formalism, operationalism, the double language doctrine, and realism—are analyzed and arguments for realism are advanced. The realistic view is illustrated by analyzing typical physical quantities and by axiomatizing a theory—special relativistic kinematics. It is argued that all the components of a physical theory—the formalism as well as the correspondence or semantic hypotheses—contribute to sketching the meaning of the theory, and that this meaning is best found out upon displaying the basic assumptions in an axiomatic fashion. The advantages and scope of the axiomatic approach are finally discussed.

Attenuation processes are examined from the viewpoint of collision theory, and the optical theorem is used to connect attenuation cross section $\sigma$ and refractive index $n$ with diagonal elements of the $T$ matrix. This approach provides resonance profiles (for "natural" lines shapes) of the form $\sigma \left(\omega \right)=C+\frac{\left(\frac{\Gamma }{2}\right)B+(\omega -{\omega }_0)A}{{(\omega -{\omega }_0)}^2+{\left(\frac{\Gamma }{2}\right)}^2},$ $n\left(\omega \right)-1=\frac{\mathrm{Nc}}{2\omega }\left[\frac{\left(\frac{\Gamma }{2}\right)A-(\omega -{\omega }_0)B}{{(\omega -{\omega }_0)}^2+{\left(\frac{\Gamma }{2}\right)}^2}-D\right],$ where the profile parameters $A$, $B$, $C$, $D$, $\Gamma$, ${\omega }_0$ are given in terms of atomic matrix elements.

Part I reviews the notion of resonances. Part II summarizes the relevant results of collision theory, stressing physical interpretation, and gives a definition for excited (or resonance) states based on a simple partition of basis states into two classes. Part III applies perturbation theory to the calculation of resonance profiles. Part IV applies these results specifically to the attenuation and refraction of photons by tenuous gases, with particular attention paid to the profiles of autoionizing lines. The effects of degeneracy (the extension of the bound-state $Z^{-1\mathrm{}}$ expansion theory) are noted.

This paper provides a theoretical background for, and some interpretation of, recent measurements of the infrared optical properties of fluorite crystals particularly Ca${\mathrm{F}}_2$, Sr${\mathrm{F}}_2$, Ba${\mathrm{F}}_2$, and Cd${\mathrm{F}}_2$. A quantum-mechanical derivation of the optical properties in the harmonic approximation is given. The most reasonable procedure for the phenomenological treatment of damping effects is described. The physical origin of damping effects is discussed and it is shown how the perturbation theoretic results may be simplified in the low-frequency limit. Damping functions for the above materials are presented as a function of frequency and temperature.

This paper compares theory and experiment for behavior very near critical points. The primary experimental results are the "critical indices" which describe singularities in various thermodynamic derivatives and correlation functions. These indices are tabulated and compared with theory. The basic theoretical ideas are introduced via the molecular field approach, which brings in the concept of an order parameter and suggests that there are close relations among different phase transition problems. Although this theory is qualitatively correct it is quantitatively wrong, it predicts the wrong values of the critical indices. Another theoretical approach, the "scaling law" concept, which predicts relations among these indices, is described. The experimental evidence for and against the scaling laws is assessed. It is suggested that the scaling laws provide a promising approach to understanding phenomena near the critical point, but that they are by no means proved or disproved by the existing experimental data.

An examination is made of the evidence which led to the idea of the existence of solid layers in the adsorbed helium film at low temperatures. The experimental evidence from adsorption isotherm, specific heat, and flow measurements on the helium film is reviewed and the interpretation of this evidence as supporting the idea of a solid layer structure near the adsorbing surface is critically discussed. This discussion includes some evaluation of the applicability of the B.E.T. and other adsorption models used to describe helium adsorbed at very low temperatures. As a result of these considerations the author is of the opinion that the concept of a solid layer, or so, existing in an adsorbed helium film, is not nearly as well founded as is usually supposed. One particular inference from the solid layer picture; that the helium film at near monolayer coverages be considered immobilized is particularly questioned. The model of Dzyaloshinskii, Lifshitz, and Pitaevskii which considers no density variation with depth is discussed and a suggestion is also made for using some early calculations of Lennard-Jones and Devonshire to show that adsorbed helium at very low coverages should be quite mobile on the adsorbing surface.

The jump rate $k$ for atomic diffusion via the vacancy mechanism in crystals is evaluated by treating a jump as the result of a particular type of thermal fluctuation in a crystal. The occurrence rate of this fluctuation is found (a) using a dynamical method similar in content to that of Rice and Manley, and (b) using statistical mechanics directly as was done by Vineyard. If the jumps are effected only when the surrounding atoms take up one single distorted configuration (the first approach being limited to describing one configuration only) then both methods are exactly equivalent and give the same $k$ (Sec. II)

The total $k$ is then obtained by summing the contributions to $k$ from the most significant configurations using a saddle point integration (Sec. III). This is done without introducing new (incalculable) "saddle-point" frequencies which in the Vineyard theory, leaves the pre-exponential factor imprecisely defined. In $k$, all parameters are well defined in terms of the force constants and its mass dependence is always exactly $m^{-\frac{1}{2}}$ [Eq. (27)].

In the discussion, contact is made with earlier forms of the frequency factor, and, by way of example, the expression for $k$ is used to evaluate the self-diffusion coefficient in solid argon giving a value in agreement with experiment (Sec. IV)

This article presents a simplified treatment of the high density, collisionless, free-electron gas, based on the ideas of a wave number and frequency-dependent conductivity and dielectric constant. The formalism is applied to solve a number of problems: the screening of the electrostatic potential of a foreign point charge placed in the electron gas, the rate of energy loss of a charged particle moving through the electron gas, plasma oscillations, the reflection of electromagnetic waves from the electron gas, and ultrasonic attenuation in metals due to the interaction of the sound waves with the conduction electrons. In a final section it is indicated how the methods may be generalized. Explicit expressions for the conductivity of the electron gas are obtained in an appendix.

A general theory is developed for the linear response of an interacting molecular system to an external field. The exact ground state of the system is expressed in terms of the uncoupled molecule (zeroth-order) state by means of adiabatic time-dependent perturbation theory. Including the external field to first order in the time-development operator leads to an infinite-order expansion of the linear response function for physical quantities such as current-charge density and electric-dipole polarization. Two basic approximations involving partial decorrelation of charge motion and spatial separability of the molecules allow the response function to be determined by a simplified Dyson-type equation, which can be put into closed form by further approximations. The approximate linear response function (susceptibility) so obtained is given in terms of the isolated molecule susceptibility and corresponds exactly to the results of classical, local field theory. Emphasis throughout is placed on the effect of molecular interaction on absorption spectra. Comparisons among theories of hypochromism show clearly that all previously reported theories are mutually compatible and are either equivalent to, or are contained in, the theory developed here. The relation of the present theory to a coupled equivalent oscillator model is discussed and the results are applied to a simple physical model.

The theory of angular distributions of $\gamma$ rays is developed systematically, aiming at a phase consistent derivation of angular distribution formulas for gamma rays emitted in the decay of an aligned initial state. The development starts from first principles, that is, the angular distribution formulas are derived directly from perturbation theory and all quantities introduced are carefully and explicitly defined. In particular the mixing ratios are phase consistently related to reduced matrix elements of interaction multipole operators which again are well defined in phase. Hence the mixing ratios become physical quantities which can be extracted from angular distribution measurements and then compared in both magnitude and sign with the predictions of nuclear models (especially the independent particle model). Critical stages in the theoretical development at which either a choice of phase convention has to be made or transformation properties enter are emphasized.

As a first step, the transition probability for emission of gamma radiation with wave vector k and polarization $\varepsilon$ from an initial state $|\lambda 〉$ to a final state $|\mu 〉$ is calculated using time-dependent perturbation theory. This step makes no specification of the angular momentum of the initial and final states and no multipole expansion of the interaction. Particular attention is paid to the relation between emission and absorption. In the second step of the calculation the angular momentum of the initial and final states is specified, the interaction is expanded in a series of multipoles and the final angular distribution formula is derived. In order to describe emission of gamma radiation a definite and well-defined part of the interaction Hamiltonian must be expanded. This part of the Hamiltonian is determined by the order in which the initial and final states are written in transition matrix elements. The expansion yields a set of interaction multipole operators which are well defined in phase and transformation properties. There is no uncertainty in the relative phase of the electric and magnetic interaction multipole operators due to an arbitrariness in the phases of the vector potentials. These interaction multipole operators must be used to define the mixing ratios appearing in angular distribution formulas in this paper. It is shown that care must be taken when using Siegert's theorem and "effective" multipole operators.

In the last section, reduced matrix elements of the interaction multipole operators are given explicitly for one- and two-particle states and one- and two-holes states of the independent particle model.

A graphical method is presented allowing the representations of $``j-m\text{'}\text{'}$ and $``3nj\text{'}\text{'}$ coefficients, spherical harmonics, irreducible tensor operators, and rotation matrices. Rules are established which permit calculations on expressions with the above elements. As the main difficulty of using $``3j\text{'}\text{'}$ Wigner coefficients is the construction of the phase, an algorithm is proposed which simplifies this problem. Concrete examples are given for this general method.

The symmetry group of the Hamiltonian plays a fundamental role in quantum theory in the classification of stationary states and in studying transition probabilities and selection rules. It is here shown that the properties of the group may be given a condensed and transparent description in terms of the convolution algebra, and that Schur's lemma immediately leads to the construction of the fundamental set of projection and shift operators. The projection operators form a resolution of the identity which may be used to split the Hilbert space into orthogonal and noninteracting subspaces of infinite order. The question of the splitting of the conventional secular equations is discussed, and the explicit form of the decomposed equation is derived in terms of the convolution algebra and the characters. The theory is here discussed only for finite groups, but the results may be generalized to the compact infinite groups having a well-defined "invariant mean."