E. Richard Cohen

The 1973 Least‐Squares Adjustment of the Fundamental Constants

This paper is a summary of the 1973 least‐squares adjustment of the fundamental physical constants carried out by the authors under the auspices of the CODATA Task Group on Fundamental Constants. The salient features of both the input data used and its detailed analysis by least‐squares are given. Also included is the resulting set of best values of the constants which is to be recommended for international adoption by CODATA, a comparison of several of these values with those resulting from recent past adjustments, and a discussion of current problem areas in the fundamental constants field requiring additional research.

Influence of the potential function on the determination of multipole moments from pressure‐induced far‐infrared spectra

The effect of the choice of the potential function on the evaluation of molecular multipole moments from pressure‐induced far‐infrared spectra is investigated. The analysis is restricted to low densities where collisions are predominantly bimolecular. The quadrupole and hexadecapole moments of N2 and O2, and the octupole and hexadecapole moments of CH4 and CF4 are evaluated from far‐infrared data using potential models consisting of a spherically symmetric part represented by the Lennard‐Jones, Kihara, and m–6–8 potentials and an anisotropic part representing the electrostatic interactions of the permanent multipole moments. In general, although different values of the multipole moments are obtained with different potentials, for similar molecular diameters the variation is not great.

The 1986 CODATA Recommended Values of the Fundamental Physical Constants

Presented here are the values of the basic constants and conversion factors of physics and chemistry resulting from the 1986 least‐squares adjustment of the fundamental physical constants as published by the CODATA (Committee on Data for Science and Technology) Task Group on Fundamental Constants and recommended for international use by CODATA. The 1986 CODATA set of values replaces its predecessor published by the Task Group and recommended for international use by CODATA in 1973.

Far infrared collision‐induced absorption in gaseous methane. II. Determination of the octupole and hexadecapole moments

The octupole and hexadecapole moments of methane are obtained by comparing the experimental and theoretical zeroth spectral moment and the integrated absorption coefficient of the collision‐induced far infrared rotation–translation spectrum. The data presented in Part I of this series and the theory summarized in this paper give the values Ω2/σ7 = 4.67×10−16 erg and Φ2/σ9 = 1.56×10−16 erg, from which we obtain the octupole and hexadecapole moments, respectively, ‖Ω‖ = (2.22±0.12) ×10−34 esu⋅cm3 and ‖Φ‖ = (4.8±0.5) ×10−42 esu⋅cm4 for σ=3.758 A. An argument is advanced as to why it is preferable to report these results in the form Ω2/σ7 and Φ2/σ9, where σ is the molecular diameter parameter appearing in the potential function.

Determination of molecular multipole moments and potential function parameters of non-polar molecules from far infra-red spectra

The quadrupole, Θ, and hexadecapole, Φ, moments of N2 and O2, and the octupole, Ω, and hexadecapole moments of CF4 and SiH4 are obtained from far infra-red collision-induced absorption in the gas phase at low densities where bimolecular collisions predominate. An accurate theory for evaluating Θ and Φ for non-polar diatomic molecules is presented here ; the theory for evaluating Ω and Φ for tetrahedral molecules has been presented previously. A reliable value of a multipole moment obtained by a direct method which does not depend on the intermolecular potential can be used to obtain an accurate value of the molecular diameter, σ. Thus using the quadrupole moment of N2 obtained by induced birefringence and the far infra-red value of Θ2/σ5, we obtain σ and with this the value of Φ.

Approximate solution of the equations for aerosol agglomeration

Abstract The integrodifferential equation for the agglomeration and settling of aerosols is reduced to a set of ordinary nonlinear equations for the moments. In general these equations do not form a closed set. By choosing a specific functional form for the distribution of particle volumes, the parameters of which are functions of time, the system is closed since all the moments are expressible directly in terms of the chosen parameters, and an n -parameter function then leads to a set of n ordinary differential equations. The specific case of a log-normal distribution for particle sizes is discussed in detail. For the case of pure Brownian agglomeration analytic solutions are obtained and the asymptotic distribution is explored. When gravitational settling and agglomeration are included, the system may be readily solved numerically.

Analysis of the far infrared H2-He spectrum

Previous measurements of the far infrared absorption due to H2–He collisions at the temperatures of 77, 195, and 292 K are analyzed. The spectra are fitted by a semiempirical line shape representing the isotropic induced overlap component and combined anisotropic quadrupolar and overlap components. The experimental spectral moments are evaluated and compared with theory for several induced‐dipole and potential models. From the isotropic contribution, the range and strength of the induced dipole is evaluated and compared with the results of ab initio calculations. Fitting parameters are obtained with physically plausible temperature dependences which allow simple and accurate representation of the spectra and of their moments at temperatures different from those of the measurements.

Fundamental Physical Constants

The periodic review of the physical constants is important for two very different reasons. One is the need to have a set of numerical values that can be used reliably in all branches of science and technology. The other is the verification of physical models inherent in the consistency of those values. This paper discusses the definition of ‘fundamental constants’ and the reasons for choosing the specific set of constants for the 1986 adjustment. It summarizes the input data included in this adjustment, the results of the analysis, and the conclusions to be drawn from them. Of particular importance is the question of the consistency of QED and the status of the experimental verification of the validity of the perturbation expansion for the electron anomalous moment and the numerical evaluation of the multidimensional integrals associated with the sixth and eighth order terms.

The 1973 table of the fundamental physical constants

Abstract The 1973 CODATA-recommended values of the fundamental constants are listed. The basis for the least-squares analysis and some of its shortcomings are discussed. Although significant modifications of some of these numbers may be indicated by more recent experimental results, the tabulation should prove useful to the general user since it provides an identifiable set of values which are internally consistent to a precision of better than 0.1 part per million.

Dielectric Relaxation at High Frequencies

A theory of dielectric relaxation is presented which is based on using an interpolation function to represent a classical correlation function which is analytic at the origin and becomes exponential at sufficiently long times. The Fourier transform of this interpolation function is a relatively simple analytical function of frequency which has the Debye character at low frequencies but decreases essentially exponentially in the high‐frequency wing. The parameters in the correlation function are discussed in terms of relaxation due to reorientational diffusion. Our model predicts practically the same absorption in the microwave region and somewhat more absorption in the far‐infrared region as theories of dielectric relaxation which include the effect of rotational inertia, but in agreement with experiment predicts very much smaller absorption in the infrared region.