Volume 56, Issue 6, 15 March 1972

Exact Series Solution of Classical Deflection Angle for Repulsive Inverse Power Potential
View Description Hide DescriptionAn exact series solution of the classical deflection angle is developed for the potential . The series converges at all impact parameters. In addition, upper and lower bounds for θ are constructed from the series as an aid to numerical computation. Finally, the classical differential cross section is evaluated from the deflection angle.

Stress Relaxation of Solutions of Flexible Macromolecules
View Description Hide DescriptionFor stress relaxation after cessation of steady shearing flow with , the following relation has been proposed for connecting the normal stress difference during steady state flow and the shear stress during the relaxation process after t=0:It is shown here that this relation can be derived for a dilute suspension of flexible macromolecules represented as a set of N beads joined by N — 1 connectors which may be nonlinear springs; equilibrium‐averaged hydrodynamicinteraction is included in the theory. A generalization of the above formula may be derived for the stress relaxation following any steady homogeneous flow. In the derivation use is made of an expression for the stress tensor which differs from that of Giesekus in that hydrodynamicinteraction has been included. From the latter formula it is particularly easy to rederive the Lodge‐Wu constitutive equation for the Zimm model with Gaussian springs.

Effects of an Attractive Well Potential on the Atom–Diatomic Molecule Collinear Collision
View Description Hide DescriptionThe effect on the vibrational transition probability of an attractive well in the interaction potential for the collinear collision of an atom with a diatomic oscillator is investigated. Two forms of the potential are considered. For a square barrier potential, a square well introduces sharp resonances in the transition probability. It is shown that the position of these resonances may be predicted by a simple formula. For a ``soft'' Morse interaction potential no resonances are observed. It is shown in this case that the transition probability is determined more by the slope of the potential at the classical turning point than by the presence or absence of an attractive well.

Theory of Inelastic Collisions: Uniform Asymptotic (WKB) Solutions and Semiclassical Scattering Matrix Elements for Multichannel Problems
View Description Hide DescriptionThe method developed for the semiclassical solutions of two‐channel problems is generalized for a semiclassical solution of multichannel problems. The semiclassical scattering matrix elements are constructed from the solution, which are given in terms of well defined quadratures involving the Airy functions. The results obtained are valid without curve crossings and do not require the usual assumption of a sufficiently wide separation of the turning points and crossing points. It is shown that an approximate solution of an N‐channel problem can be constructed from the solutions of local two‐channel problems, if the curves cross pairwise in sequence.

Deconvolution of Molecular Beam Inelastic Scattering Data
View Description Hide DescriptionTwo deconvolution techniques and their application to large angle scattering of molecular beams are considered. The first method, an iterative unfolding (IU) technique due to Ioup and Thomas, is shown to contain an error; this error is corrected, but still further limitations are shown to exist. The second deconvolution method, which involves a folding together of apparatus and assumed scattering functions, is used to analyze some data previously analyzed by the IU method. The new results in every case show that average (vibrational) inelasticities were overestimated both by analysis of the scattering results without deconvolution and by application of the IU method. The reason for the original overestimate is quite general and is easily understood. A simple classical theory agrees reasonably well with the new energy transfer values over a wide range of collision energy.

On a Proton Magnetic Resonance Study of H_{2}S and H_{2}Se
View Description Hide DescriptionThe protonmagnetic resonance line shape and second moment have been studied in H_{2}S and H_{2}Se at 58°K. The observed second moment values indicate that the lattice of H_{2}S and H_{2}Se is essentially rigid at this temperature. The line shapes have been fitted by the method of least squares to a theoretical lineshape function having the intramolecular distance as an adjustable parameter. The distances obtained are Å for H_{2}S and Å for H_{2}Se.

Viscous Flow Past a Random Array of Spheres
View Description Hide DescriptionThe steady, slow motion of a viscous fluid past a random, uniform array of identical nonoverlapping finite spheres is studied. The expected force F acting on any given sphere is obtained by averaging over the ensemble of possible positions of all other spheres. It is shown that, if the Stokes equations hold in the fluid, then for small particle volume concentration c, F has an expansion of the formwhere F _{0} is the Stokes force on a single isolated sphere in the same flow and D is a tensor which is given in terms of the two‐sphere distribution function for the array and the Stokes solution for two spheres oriented arbitrarily in an unbounded flow. A physical model for the solution is presented and compared with the model of Brinkman.

Formation of HS^{−} and DS^{−} by Dissociative Attachment in H_{2}S, HDS, and D_{2}S
View Description Hide DescriptionWe have studied the formation of HS^{−} by dissociative attachment in a total ionization chamber, with a RPD electron gun. The onset of the ionization efficiency curve ( eV) is equal to the minimum energy necessary for the formation of HS^{−} ( eV). Nevertheless the curve does not exhibit the usual shape characteristic of a vertical onset process. The cross section at the maximum is We measured the isotope effects separately, in a mass spectrometer, and we found that the cross section in D_{2}S is much smaller: . We tried to reproduce the experimental results by a semiempirical calculation, using the expression of O'Malley for the cross section and parameterizing the final state potential curve of the negative ion. We have shown that the experimental results are consistent with the assumption of a very shallow bound potential in the Frank–Condon region. Quantitative calculations are impossible because the formula of O'Malley is incorrect for that sort of potential curve.

Dielectric Relaxation of Some Aliphatic Ketones in Cyclohexane Solution
View Description Hide DescriptionDielectric constant and loss data are presented for cyclohexane solutions of 2‐hexanone, 2‐, 3‐, 4‐, and 5‐nonanone, 2‐ and 4‐decanone, 2‐, 4‐, and 8‐pentadecanone, and 2‐ and 10‐nonadecanone in cyclohexane at up to nine frequencies between 1.5 and 145 GHz at 25°C. The absorption for each system may be represented by a Cole—Cole distribution. For the 2‐alkanones, all the nonanones, and 4‐decanone, dipole orientation occurs predominantly by intramolecular motion. Rotational orientation of the molecule as a whole appears to make an appreciable contribution also when the dipole is located away from the chain end in the longer molecules.

High‐Pressure Phase Transformations in Hexagonal and Amorphous Selenium
View Description Hide DescriptionHexagonal selenium transforms to a new phase at kbar. The c/a ratio of 1.42 at the transformation corresponds to the same c/a ratio for tellurium at its transformation at 40 kbar. It has not been possible to decide unambiguously a unit cell from the diffraction pattern of the new phase. The high‐pressure phase is irreversible being retained upon releasing the pressure.Amorphous Se slowly transforms to the crystalline state under pressure and eventually develops the same unknown high‐pressure structure as the hexagonal form. The pressure‐cycled amorphous material retains its crystalline structure upon releasing the pressure. This structure appears to be identical to the irreversible hexagonal phase. It is thought that the high‐pressure structure is superconducting.

Antiferromagnetic Linear Chains in the Crystalline Free Radical BDPA
View Description Hide DescriptionThe static magnetic susceptibility from 1.6 to 300°K and the heat capacity in fields of 0 and 5 kG from 0.9 to 10.2°K have been measured on polycrystalline samples of the complex of 1,3‐bisdiphenylene‐2‐phenylallyl with benzene, commonly abbreviated BDPA. The data are shown to correspond to antiferro‐magnetic Heisenberg linear chains characterized by a nearest‐neighbor exchange integral of . Weak interchain coupling results in a paramagnetic—antiferromagnetic phase transition at 1.695°K in zero field, as evidenced by the sharp heat capacity anomaly at that temperature. Resolution of the heat capacity into a lattice T ^{3} contribution and a magnetic contribution yields a Debye temperature of 52.5°K and a magnetic entropy per mole of 101% of the expected Rln2.

Partial Charge‐Transfer Reactions at Thermal Energies
View Description Hide DescriptionThermal energy reaction rate constants are reported for the partial charge‐transfer reactions and with X as Xe, NO, O_{2}, N_{2}O, CO_{2}, CO, SO_{2}, NH_{3}, and NO_{2}. The rate constants for single electron transfer of polyatomic neutrals are often three orders of magnitude larger than the rate of electron transfer from Xe. Within a curve crossing model the molecular data yield approximate efficiencies of electron transfer from 2.5 to 14.4 Å. The difficulties of using a curve crossing model for polyatomic molecules and a simple Landau—Zener calculation at thermal energies are briefly discussed.

Angular Correlation of Annihilation Photons in Frozen Aqueous Solutions
View Description Hide DescriptionLinear‐slit angular correlation curves were obtained at about for frozen aqueous solutions of HF, HCl, HBr, HI, NH_{3}, FeCl_{2}, FeCl_{3}, NaI, H_{2}SO_{4}, NHO_{3}, MnSO_{4}, KMnO_{4}, K_{2}Cr_{2}O_{7}, NaOH, and LiOH. We found no appreciable influence of a 4% concentration of the last seven impurities. Only halide‐containing impurities strongly changed the form of the curves; ppm concentrations of HCl and HF could be seen. The main change was a broadening of the part of the curve where the narrow and broad components meet. This fact is interpreted as being caused by trapping of para‐positronium in holes in the structure created by the impurities. No evidence of any chemical reactions of positronium and the impurities was found. The annealing of a fast frozen FeCl_{2} solution was studied. The strongest changes in the curves occurred on annealing from to .

Linewidths and Spin Densities in the ESR Spectra of Electrogenerated Radical Anions of Sterically Hindered and 1,8‐Dinitronaphthalene
View Description Hide DescriptionThe ESR spectra of the radical anions of and 1,8‐dinitronaphthalene generated by electroreduction in anhydrous dimethylformamide (DMF) have been recorded in the temperature range 20 to . Interesting linewidth effects are observed in the ESR spectra of these two radical anions at lower temperatures. From the linewidth data, the spectral densities for the modulations of isotropic splittings and anisotropic intramolecular interactions have been computed making use of the complete expressions for linewidths derived from relaxation matrix theory and a two‐jump model. Using the spectral densities and the measured dynamic frequency shifts, correlation times for modulations of isotropic splittings are evaluated. It is noticed that the two‐jump model with out‐of‐phase correlation of nitrogen splittings in the two nitro groups explains the observed trends in the spectral densities satisfactorily for both the radical anions. The details of the modulating motions are investigated next, and spin densities calculated for some geometries of the radical anions. Experimental splitting constants are compared with those computed from spin density values obtained by McLachlan and UHFAA (unrestricted Hartree—Fock method of Amos and Snyder with annihilation of quartet component) methods. In radical anion, satisfactory agreement is obtained between experimental and calculated splittings for the geometry in which the two planes of the phenyl rings make an angle of 40° when they are twisted from the trans—planar configuration with respect to the nitro groups. In order to explain the out‐of‐phase correlation and the observed couplings, it is suggested that the modulating motions are such that when one of the nitro groups is in the plane of the phenyl ring, the other one is out‐of‐plane. In the case of 1,8‐dinitronaphthalene radical anion also, similar results have been obtained thus leading to the model of a ``seesaw'' type of motion of the nitro groups in these radical anions.

Dynamics of Dissociation. I. Computational Investigation of Unimolecular Breakdown Processes
View Description Hide DescriptionAn explicit method for the exact calculation of unimolecular linewidths and line shapes, using an adaptation of known numerical techniques, is presented. The method renders feasible the calculation of decay from one composite ``bound'' subspace, into another composite ``continuum'' subspace. The eigenvalues of the Hamiltonian for the whole ``bound'' subspace are also obtained to a high degree of accuracy. Two specific examples are studied: (a) A single closed channel (containing four bound states) coupled to a single open channel, and (b) three closed channels corresponding to eight bound states, interacting with a single open channel. The exact line shapes for the first of these cases are computed. Interference effects, due to overlapping resonances, are clearly demonstrated and discussed in terms of Fano's theory. Line‐widths and resonance energies are calculated for the second case. The results are contrasted to those of the related scattering problem and discussed in terms of the different boundary conditions.

Computational Approach to the Construction of the Optical Potential
View Description Hide DescriptionAtom—diatomic molecule scattering is considered in the close coupling approximation. It is shown how a local optical potential matrix can be constructed such that scattering from this optical potential re‐produces exactly a specified submatrix of a given multichannel (and arbitrarily accurate) transition matrix (T). However, these two requirements on the optical potential (that it be local and reproduce a given submatrix of T) do not define it uniquely. For the special case of open channels a T (R) is defined such that T(∞) =T. Requiring the optical potential to be local and reproduce a specified submatrix of T(R) at every R does lead to a unique (and quite simple) result capable of trivial generalization to closed as well as open channels. rotationally inelastic scattering, neglecting exchange, is considered as an example.

Structure and Phase Transitions of Solid Heavy Methane (CD_{4})
View Description Hide DescriptionThe orientational structures and the phase transitions (27.0 and 22.1°K) of solid CD_{4} are investigated by coherent neutron scattering from powder samples as well as from single crystals. In its high temperature phase, CD_{4} is found to crystallize within the space group Fm3m with four molecules per unit cell and a lattice constanta _{0}=5.96 Å at 77°K. The molecular orientations are completely disordered at 35°K, while an indication of partial order was detected at 77°K. The transition to phase II is accompanied by critical fluctuations with a correlation length of about 24 Å (at 27.7°K) and appears to be of second order (critical exponent . In phase II six of eight molecules order with a local symmetry , while the remaining two are orientationally disordered. The space group is cubic Fm3c with 32 molecules per unit cell and a _{0}=11.64 Å at 24.5°K. The transition to phase III is predominantly of first order. With the present data the structure of phase III cannot be determined unambiguously. Superlattice reflections can be indexed cubic primitive. The number of molecules per unit cell remains 32, with a _{0}=11.61 Å at 17.5°K. The data suggest, that the low temperature structure is to be understood by an ordering within the sublattices of molecules disordered in phase II together with slight distortions of the other sublattices. The structures of phases I and II agree with the ones predicted by James and Keenan under the assumption of octupole—octupole interaction between nearest neighbour molecules. For phase III the model of James and Keenan, as well as other predictions, hitherto published, must be ruled out.

Measurement of Low Energy Scattering Cross Sections for the System
View Description Hide DescriptionTotal elastic scattering cross sections for the system were measured for relative velocities from to utilizing the crossed beam technique. An orbiting resonance below the j=0 to 2 transition was observed. Two collimated, aerodynamically intensified molecular beams intersecting at 10° were used. Each beam had a speed distribution comparable to that obtained from mechanical velocity selectors. The scattering center density was determined from a calibration of the detector utilizing a thermal beamsource, carefully considering the geometry of the system. Attenuation of the scattering signal due to the background gas was determined without recourse to pressure‐gauge readings. One beam was modulated and integrating techniques were used to recover the signal. The time‐of‐flight technique was used to determine the initial conditions in each beam. The measurements were compared with quantum mechanical calculations performed at the University of Bonn using a LJ (12,6) potential. Generally, the measurements were larger than these calculations, but one resonance was partially resolved.

Collision‐Induced Light Scattering in Liquids
View Description Hide DescriptionThe isolated binary collision model of light scattering in liquids has been developed to obtain an analytical expression for the spectral intensity in the wings of the Rayleigh spectrum. The expression shows the dependence of the spectral intensity on the nature of the interaction potential energies between the collision pair, on the frequency shift, and on the temperature. The exponential part of the intensity appears in the formwhere ω is the frequency shift and T is the temperature. The pre‐exponential part is shown to be weakly dependent on ω and T. Numerical studies for Xe, Ar, and CCl_{4} show that the calculation agrees quantitatively with experiment. Both the ω and T dependence of the spectra have been investigated.

ESR Study of the Chlorofluoroacetamide Radical in Irradiated Dichlorofluoroacetamide Single Crystals
View Description Hide DescriptionThe electron spin resonance spectra of single crystals of dichlorofluoroacetamide and N, N‐dideutero‐dichlorofluoroacetamide irradiated with x‐rays at 77°K and later warmed to 170°K, have been assigned to and respectively. A tensor Hamiltonian fit to the spectra have yielded either complete or partial hyperfine splittingtensors for fluorine‐19, chlorine‐35, carbon‐13, and nitrogen‐14 in addition to the chlorine‐35 quadrupole coupling and the gtensor. These results along with a CNDO/2 molecular orbital calculation indicates that the radical is a planar π radical. An INDO molecular orbital calculation was carried out for the and radicals in order to interpret the experimentally observed amide nitrogen and proton splitting variations.