Robert C. Herman

Influence of Vibration‐Rotation Interaction on Line Intensities in Vibration‐Rotation Bands of Diatomic Molecules

The influence of vibration‐rotation interaction on line intensities in vibration‐rotation bands of diatomic molecules had been recognized and treated approximately many years ago. In the present paper matrix elements have been calculated for the P and R branches of the 0—1, 0—2 and 1—2 transitions taking into account the interaction of rotation and vibration as well as the mechanical and electrical anharmonicity. For the 0—1 and 1—2 transitions the intensities of corresponding absorption lines in the P and R branches are proportional, in first order approximation, to [1+4γθJ]J and [1—4γθ(J+1)](J+1), respectively, where J is the rotational quantum number of the initial state, γ=2Be/ωe, θ=M0/M1re and M0 and M1 are the first two coefficients in the electric dipole moment expansion about the equilibrium internuclear distance re. Corrections to the above expressions that are proportional to γ2 have also been obtained. Formulas are given for the total integrated band intensity and for the line intensities summe...

Vibrational Intensities in Diatomic Infrared Transitions. The Vibrational Matrix Elements for CO

Second‐order perturbation theory has been employed to obtain general formulas for the (rotationless) vibrational matrix elements of diatomic molecules in infrared transitions. The mechanical and electrical anharmonicities have been taken into account by expanding the potential function in a power series through quartic terms and the electric dipole moment through cubic terms in the internuclear separation. The formulas obtained in this manner are shown to be quite accurate for the fundamental and the first two overtones.These expressions were then employed to evaluate the vibrational matrix elements for CO (1Σ+) up to v′=4 using the experimental integrated absorption coefficients as auxiliary data for the determination of the electric dipole moment expansion coefficients. A comparison of the vibrational matrix elements for CO involving the use of perturbed harmonic oscillator wave functions with those obtained using Morse wave functions with both linear and quadratic expansion of the electric dipole momen...

The Calculation of Perturbation Energies in Vibrating Rotating Polyatomic Molecules

An account is presented of the calculation of the purely vibrational contribution to the eigenvalues of the vibration‐rotation Hamiltonian of a polyatomic molecule. Special attention is given to the expansion of the quantum‐mechanical Hamiltonian; and to the results of the contact transformation of the Hamiltonian which simplifies the calculation of the second‐order energy corrections. The results of the transformation theory have been presented in the form of tables. For each type of perturbation term which appears in the first‐order Hamiltonian it is possible to obtain the second‐order energy corrections by inspection. This procedure eliminates the need for applying the transformation to each specific problem. The use of these results is illustrated by working out in considerable detail the case of the X2YZ2 tetrahedrally symmetric molecular model.

The Thermoluminescence and Conductivity of Phosphors

A simple theoretical treatment is given for the emission of light and associated variations of dark current that occur on warming zinc sulphide and zinc silicate type phosphors previously irradiated with ultraviolet light at low temperatures. Reasonably good agreement is found between the calculated and observed glow curve for Willemite. The same type of treatment is applied to the case of infra‐red illumination of phosphors at low temperatures.

The Vibration‐Rotation Mechanics of the Allene Molecule. Part I. Classical Vibration Problem

Symmetry coordinates are set up from the standpoint of group theory for describing the normal modes of oscillation of the allene molecular model in such a manner that maximum factorization of the secular determinant is accomplished. The cubic and quartic portions of the anharmonic potential function are derived, and the components of vibrational angular momentum are set down. The complete valence‐type potential function is discussed. Explicit relations are derived between the force constants occurring in the secular determinant and the physical valence force constants.

Theory of Electron Retrapping in Phosphors

The set of non-linear differential equations that generally have been employed to describe the electron transfer processes in infra-red phosphors has been solved by means of a differential analyzer in the general case, and approximate solutions have been obtained for cases of practical interest. It is shown that the simultaneous measurement of the brightness and instantaneous photo-current in a phosphor stimulated by infra-red light allows a determination to be made of the ratio of the cross sections for electron capture into empty trapping centers and into empty luminescent centers. This cross-section ratio can also be determined from measurements of the light sum and the maximum instantaneous photo-current.

The Infra-Red Emission Spectra of the Oxy-Hydrogen and Oxy-Deuterium Flames*

The infra-red emission spectra of the oxy-hydrogen and oxy-deuterium flames and of hot water vapor have been studied in the LiF, NaCl, and KBr regions. The principal features of the spectrum may be accounted for by emission of H2O molecules; no unequivocal evidence for radiation from OH radicals was found with the resolving power available.

The rise in brightness of infra-red sensitive phosphors.

A phenomenological theory of infra-red sensitive phosphors is given which assumes the existence of two types of luminescent centers in order to account for the so-called “inertia” effects in the rise of brightness. The equations describing the electron transfer processes have been integrated and show under certain conditions a very rapid initial rise in brightness followed by a relatively slow attainment of the maximum. The effect of varying the intensity of the stimulating infra-red radiation is discussed.

The Tetrahedral X2YZ2 Molecular Model Part I. Classical Vibration Problem

Appropriate coordinates are set up from the standpoint of group theory for describing the normal modes of oscillation in such a manner that maximum factorization of the secular determinant is accomplished. The cubic and quartic portions of the anharmonic potential function are derived. The components of vibrational angular momentum are set down. The complete valence‐type potential function is discussed; explicit relations are derived between the generalized force constants occurring in the secular determinant and the valence force constants for CH2D2.

A Cinema-Spectrograph for Photographing Rapid Spectral Sequences*,**

A simple spectrograph designed around a 16-mm movie camera is described. The spectrograph was built for the purpose of obtaining spectrograms from light sources showing transient phenomena, in particular such light sources as the new types of rocket and jet combustion engines. The study of the light emitted from an acetylene-oxygen flame as a function of time illustrates its usefulness.