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Volume 43, Issue 3, 01 August 1965

Bulk Photoconductivity of p‐Chloranil Crystals
View Description Hide DescriptionThe bulk‐photoconductivity properties of substituted p‐benzoquinone crystals with particular reference to p‐chloranil (tetrachloro‐p‐benzoquinone), are presented and discussed. While photocurrents excited by light in the fundamental absorption region of p‐chloranil can probably be considered in terms of exciton processes involving the crystal absorptionspectrum, ``anomalous'' photocurrent regions occurring below the main absorption edge can be more reasonably discussed in terms of impurity‐sensitized photocarrier production. A possible mechanism for this sensitization is presented.

Scaled Particle Theory of Fluid Mixtures
View Description Hide DescriptionAn extension of a previous one‐component theory of hard‐sphere systems (in three, two, and one dimensions) and the surface tension of real systems is made to mixtures. The theory is based on consideration of an approximate expression for the work of adding an additional hard sphere to a mixture. Comparison between theory and molecular‐dynamics calculations of the various contributions to the virial pressure (related to contact distribution functions) of such hard‐sphere mixtures is excellent. Comparison of the theory with experimental surface tensions of mixtures of simple liquids is satisfactory.

Theory of Helium Dissolution in Uranium Dioxide. I. Interatomic Forces in Uranium Dioxide
View Description Hide DescriptionKnowledge of the nature of the interatomic forces in uranium dioxide is required for theoretical treatment of phenomena such as radiation damage,adsorption, and gas solubility. The van der Waals and repulsive forces are of particular interest, for these interactions govern the behavior of neutral species in the crystal. The Kirkwood—Müller expression for the coefficients of the 1/r^{n} dispersion forces were employed, and the form of the repulsive potentials was taken from the delta‐function model of Mason and Vanderslice. The two disposable parameters in the repulsive potentials were evaluated from data on the atomic properties of the constituent ions and the lattice constant and compressibility of UO_{2}. The calculated cohesive energy of the UO_{2} lattice was in very good agreement with the value obtained from a conventional Born—Haber cycle.

Theory of Helium Dissolution in Uranium Dioxide. II. Helium Solubility
View Description Hide DescriptionThe solubility of helium in uranium dioxide was calculated directly from atomic properties and compared with experiment. The calculations were based upon a statistical‐mechanical formula which assumes dissolved helium to behave as a simple harmonic oscillator in an interstitial site in the UO_{2} lattice. Knowledge of the interactions between helium and the oxygen and uranium ions of the lattice permits computation of the heat of solution and the vibration frequency, which yield the Henry's law constant. The calculated solubility of 6.6×10^{−4} cc (STP)/g·atm at 1200°C was in good agreement with the experimental measurements, but the heat of solutions differed appreciably. This discrepancy was attributed to experimental errors, for the very large observed heat of solution (∼−30 kcal/mole) could not arise from purely physical interactions.

Calculation and Interpretation of the ^{129}I Isomer Shifts in the Alkali Iodide Lattices
View Description Hide DescriptionStarting with an ideal alkali halide lattice composed of closed‐shell ions, the overlap and electrostatic interactions are computed between the nearest and next‐nearest neighbors in the alkali iodide lattices. The electrostatic perturbation on the s electrons is found to be small relative to the overlap deformation of the free‐ion wavefunctions. Both effects predict the same correct dependence for the relative isomer shifts, however. The deformed free‐ion wavefunctions are used to compute the relative isomer shifts at ^{129}I in the alkali iodide lattices. The value of the nuclear parameter in ^{129}I is ΔR/R=0.5×10^{−4}.

Outer‐Shell Overlap Integrals as a Function of Distance for Halogen—Halogen, Halogen—Alkali, and Alkali—Alkali Ions in the Alkali Halide Lattices
View Description Hide DescriptionThe outer s‐ and p‐electron overlap integrals involving ns, np _{σ}, and np _{π} orbitals have been computed for all combinations of ion pairs in all of the alkali halide lattices. The free‐ion closed‐shell Hartree—Fock wavefunctions were used in all calculations. The halogen—alkali (H—M) overlaps are listed at the equilibrium internuclear distances. The halogen—alkali (H—M), halogen—halogen (H–H), and alkali—alkali (M—M) overlap integrals were computed at several internuclear distances and were found to follow the exponential form S _{ab}=A exp(—r _{ab}/ρ). Values of A and ρ are listed for all combinations of overlaps in the alkali halides.
Various convenient combinations of sums of squares of overlaps are also given as a function of distance for all the combinations in the alkali halide lattices.

Molar Volume of Solid Parahydrogen along the Melting Line
View Description Hide DescriptionThe molar volume (V_{s} ) of solid parahydrogen along the melting line up to a temperature of about 24°K and a pressure of about 400 atm has been determined by two independent methods: direct measurement and computation from the heat of fusion and change in volume during melting. Results obtained by the two methods agree with each other within about ±0.2%; they are both referred to below as ``experimental.'' The empirical linear equationV_{s} =27.1788–0.283044 T reproduces the experimental results with a mean deviation of about 0.15%.

Intensity Distribution in the Electron‐Impact Spectrum of Carbon Monoxide at High‐Resolution and Small Scattering Angles
View Description Hide DescriptionAn electron spectrometer, which provides velocity selection before scattering, is described; and the results of a study of relative intensities in the carbon monoxide spectrum are reported. The vibrational levels of the fourth positive band system have been resolved and relative intensities determined for the first nine. The relative intensities are compared with calculated Franck—Condon factors. The agreement is good at low vibrational quantum numbers but noticeable discrepancies are found for high‐vibrational levels.
The problem of calculating relative oscillator strengths from a fully resolved spectrum is considered and applied to data obtained in the present research. Relative oscillator strengths are compared with those obtained previously from unresolved spectra.
If the Born approximation is valid, then the electron‐impact and ultraviolet absorption spectra should be closely similar. This is actually observed for most of the spectrum but the transition at 12.79 V is an outstanding exception. The relative oscillator strength obtained from the electron‐impact spectrum exceeds that from the ultraviolet absorptionspectrum by almost a factor of 3. The reason for this anomaly is not known.

Relative Intensities of Two Rydberg Transitions in the Electron‐Impact Spectrum of Water
View Description Hide DescriptionThe electron‐impact spectrum of water has been determined using a higher‐resolution electron spectrometer. The intensity distribution of five peaks in the spectrum which belong to two different Rydberg transitions has been investigated at zero scattering angle and electron kinetic energy of 200 V. Quantities proportional to the optical oscillator strengths for these excitations have been compared with absorption coefficients from ultraviolet spectra. The entire electron‐impact spectrum in the region below the first ionization potential shows good agreement with ultraviolet absorption.

Singlet—Triplet Exciton Absorption Spectra in Naphthalene and Pyrene Crystals
View Description Hide DescriptionSinglet—triplet excitonabsorption spectra have been measured in naphthalene and pyrene single crystals at room temperature by observing the dependence of the ``anti‐Stokes'' emission intensity resulting from mutual annihilation of triplet pairs on the wavelength of exciting light. The origin of the naphthalene spectrum is at 21 170 cm^{−1}, and the most prominent intervals in the vibrational structure are 490 and 1360 cm^{−1}. The origin of the pyrene spectrum is at 16 850 cm^{−1}, and the vibrational structure for the lowest triplet state in this crystal includes the intervals 410, 1210, 1380, and 1590 cm^{−1}.

Libration of the OH— Ion in LiOH
View Description Hide DescriptionMuch discussion and controversy has taken place in recent years on libration of the OH^{−} ion in hydroxide crystals. Recent work on the charge distribution in the OH^{−} ion makes it feasible to calculate the librational frequency and amplitude in LiOH arising from thermal agitation. A simplified model of the libration is chosen which corresponds with the Einstein model for this mode. The calculation is based on the change in lattice energy with rotation of a single OH^{−} ion, involving Madelung, van der Waals, and repulsive terms.
The results indicate considerable anisotropy of libration at thermal amplitudes at room temperature. The calculated frequency thus varies with direction so that cm^{−1} while cm^{−1}. At room temperature the calculated rms thermal displacements of the hydrogen atom arising from libration agree well with those derived from the results of neutron‐diffraction experiments. The apparent success of this simple model in LiOH suggests that it might be extended to similar layer‐lattice hydroxide crystals.

Observations of the Triplet State in Phthalocyanines
View Description Hide DescriptionThe triplet‐state lifetime of metal‐free phthalocyanine has been found to vary from 10^{−6} sec at room temperature to 150×10^{−6} sec at 77°K. Decay from the first excited state proceeds via the triplet state. Excitation by a giant‐pulse ruby laser completely empties the ground state.Luminescence is quenched in metallic phthalocyanines by the extremely rapid intersystem crossing.

Electron‐Diffraction Analysis of the Dielectric Structure of Anthracene
View Description Hide DescriptionAn electron beam was utilized for charging a dielectric object and for observing the diffraction pattern from it. Analysis of the pattern obtained permits one to see that anthracene molecules are oriented parallel to the c axis of a monoclinic lattice. The electron wavelength fluctuation method (0.0332–0.0380 Å) was applied for the present analysis.

Some Triplet States of the Hydrogen Molecule
View Description Hide DescriptionThe potential curves for the 2s, 3s, 3d ^{3}Σ_{ g } ^{+} states of H_{2} have been computed in the Born—Oppenheimer approximation. Some points on the potential curves for the 3d ^{3}Δ_{ g }, 3d ^{1}Δ, 3s ^{1}Σ_{ g } ^{+}, and 3d ^{1}Σ_{ g } ^{+} states were also obtained. Vibrational levels have been computed in various approximations. Lambda doubling in the 3s, 3d triplet ΣΠΔ complex is discussed. This doubling is complicated by the near degeneracy of the 3s ^{3}Σ_{ g } ^{+} and 3d ^{3}Σ_{ g } ^{+} states at the equilibrium nuclear separation.

1s3d ^{3}Π_{ g } State of the Hydrogen Molecule
View Description Hide DescriptionThe potential curve and vibrational—rotational levels for the 1s3d ^{3}Π_{ g } state of H_{2} have been computed in the Born—Oppenheimer approximation. Energy levels about 50 cm^{−1} below the experimental levels have been found. A discussion of the nature of the wavefunction is given.

Vibrational Spectra of Solutions of Zinc Oxide in Potassium Hydroxide
View Description Hide DescriptionRaman and infrared reflection spectral studies of solutions of zinc oxide in potassium hydroxide (7.5 and 15m) with OH/ZnO ratios of from 8 to 16 show that the predominant species in these solutions possesses tetrahedral symmetry (Point Group T_{d} ) and is presumably the Zn(OH)_{4} ^{2−} ion. The frequencies and assignments, neglecting the hydrogen atoms, are: ν_{1}(a _{1})=484 cm^{−1}, ν_{2}(e)=285 cm^{−1}, ν_{3}(f _{2})=430 cm^{−1}, ν_{4}(f _{2})=322 cm^{−1}.

Configuration‐Interaction Effects on the ``Free‐Ion'' Energy Levels of Nd^{3+} and Er^{3+}
View Description Hide DescriptionBy the use of three or four parameters of configuration interaction, the experimental ``free‐ion'' energy levels of Nd^{3+} and Er^{3+} have been fitted with an rms deviation of 45–55 cm^{−1}. The significance of the various parameter values is discussed. It is also shown that assignments based purely on comparison with a calculation using only F _{2}, F _{4}, F _{6}, and ζ may occasionally be in error. Several discrepancies in previous work are now cleared up.

Effects of Electron Correlation in X‐Ray and Electron Diffraction. II. Influence of Nuclear Charge in Two‐Electron Systems
View Description Hide DescriptionThe electron—electron and electron—nuclear radial distribution functionsP(r _{12}) and D(r) have been calculated for ground states of heliumlike systems (Z=2 to 8). Computations were based on the correlated and uncorrelated wavefunctions published by Roothaan et al.Elastic and inelastic scattering factors for calculating the intensities I([open phi]) of x rays scattered by two‐electron systems were determined from the distribution functions. The correction functions ΔP(r _{12}) and ΔI([open phi]) representing the differences between correlated and uncorrelated results were found to follow a simple dependency on atomic number. It was observed that universal functions could be established which closely approximated each of the functions D(r)/Z ^{*}, P(r _{12})/Z ^{*}, I([open phi]), ΔP(r _{12}), and Z ^{*}ΔI([open phi]) for all of the systems studied if the functions were expressed in terms of the reduced variables r′=Z ^{*} r and [open phi]′=2 arcsin[Z ^{*−1} sin([open phi]/2)]. The appropriate Z ^{*} was very nearly the Slater effective nuclear charge. The experimental determination of P(r_{ij} ) from x‐ray scattering and the magnitude of correlation effects to be expected are briefly discussed.

Vector Coupling Coefficients for Atomic Self‐Consistent‐Field (SCF) Calculations
View Description Hide DescriptionGeneral formulas are derived for the vector‐coupling coefficients useful in atomic self‐consistent‐field (SCF) calculations. Tables of these coefficients for all the states arising from atomic configurations consisting of any combination of s, p, and d shells and for a single f shell have been prepared and are available for atomic SCF calculations.

van der Waals Forces between Conducting Bodies
View Description Hide DescriptionThe van der Waals force of attraction between a perfectly conducting cylinder and a plane, and a sphere and a plane, was calculated. The calculations were made using first‐order electromagnetic perturbation theory coupled with the concept of zero‐point energy. In each instance the force was found to vary as the inverse fifth power of the distance of separation of the bodies. As in the case of an atom and a plane, the force between the sphere and plane was proportional to the static polarizability of the sphere.