Final Energy Distribution Research Articles

A classical analysis of the ionization threshold vicinity

The classical trajectory method has been used for investigating electron-hydrogen-atom excitation and ionization regions close to the ionization threshold. Final energy and angular momentum distribution functions have been computed with the total angular momentum equal to zero, both below and above the ionization threshold. Combining the analytical result of Vinkalns and Gailitis (1967) with the computed energy distribution function, the threshold behaviour of the high n excitation function has been derived, which is subsequently confirmed by ab initio numerical calculations. The results show that the Wannier theory (1953) is applicable below the threshold, too. The numerical results show that each electron acquires large angular momentum in the threshold vicinity, as predicted by Fano (1974).

Monte Carlo trajectories: The reaction H + Br2 → HBr + Br

A quasiclassical trajectory study of the electronically adiabatic exothermic reaction H + Br2 → HBr + Br using 13 different semiempirical and empirical potential energy surfaces has been conducted. Detailed results are reported for 8035 reactive trajectories using Monte Carlo selection of initial conditions drawn from six different sets of distributions. For all the surfaces examined, the reaction is dominated by sideways collisions. The differential cross section for unit plane angle is sideways peaked but the differential cross section per unit solid angle peaks for molecular scattering angles (measured relative to the direction of the incident atom) in the range 156°–180°, i.e., backward scattering. There is a good correlation of scattering angle and initial orientation of the intermolecular axis, but it was not possible to use this correlation to guess a potential energy surface which yields a differential cross section in quantitative agreement with experimental results. The trajectory results, however, do indicate that a surface which has a low barrier or no barrier for collinear collisions yields too much forward scattering as compared to experiment. We find the computed angular distribution is not a strong function of atomic temperature in the range 300° to 5600°K or molecular temperature in the range 100° to 900°K. Under 300°K conditions the final state internal energy distributions are in good agreement with chemiluminescence results and at an atomic temperature of 2800°K the final translational energy distribution is in good agreement with molecular beam results. The reaction cross section is calculated to be a decreasing function of translational energy, in agrement with White and Su's interpretation of the hot atom studies; and the room temperature energy of activation is calculated to be only 0.2 kcal/mole which agrees with experiment within experimental error. The absolute values of the cross section and the room temperature rate constant are about a factor of 3 larger than experimental values. Many other details of the results are given and these may serve as a model study for the important mass combination where a light atom reacts with a heavy homonuclear diatomic molecule.

Planck distribution in a classical nonlinear coupled harmonic-oscillator system

A system ofN harmonic oscillators having a quadratic nonlinear coupling was numerically analysed. Solutions of the nonlinear problem are decomposed in terms of the normal modes of the linear system. A number of initial conditions were considered. We computed the energy in a mode as a function of time and the corresponding average energy. We found that, when initially all the energy of the mode system was in the lowest-frequency mode and the oscillators were at rest, the final time-averaged energy distribution showed that, as we increased the number of oscillators, the first fewlow odd modes received more energy on the average than neighboring even modes. When the energy was initially equipartitioned among the modes and the oscillators were initially at rest, we found that the time-averaged energy distribution of approximately the firstN/4 modes fell off monotonically with increasing frequency, with the other 3N/4 modes keeping essentially all of their energy. Finally, when the energy was initially distributed in a «Planck-like» distribution, the final time-averaged energy distribution was also a «Planck-like» distribution which was quite similar to the initial distribution. In fact, there was very little energy sharing among the modes in this case. When the space-time variation of the actual string was analysed, we found that the «Planck-like» distribution with the oscillators initially at rest was, at least to a good approximation, a «normal mode» of the nonlinear system.

Computer simulated finite-length turbulent heating experiment

A computer code has been used which was designed to allow for finite length effects found in real plasmas in order to study turbulent heating in a plasma where boundary conditions might be important. An electric field was applied to an initially quiescent plasma, and it was found that the final energy distribution (after saturation occurs) favors ions and electrons equally (Ti≃Te). This is in contrast to the infinite length simulations where the electrons become much hotter than the ions Ti≃(me/mi)1/3Te. It was also found that the saturation level depends critically upon the length of the system as well as the mass of the ions and the applied electric field.

Derivation of the DIPR model for reactive scattering

The classical model for reactive scattering proposed by Kuntz, Mok, and Polanyi is derived from the viewpoint of a pseudo-hard-sphere model which satisfies conservation of momentum constraints. Derivation of the DIPR equations is considerably simplified by (a) viewing the model in an impulsive framework and (b) casting it in a coordinate system different from the original derivation. The model admits analytical expressions for the angular distribution of products and the final translational energy distribution. A method for introducing potential information is described in terms of net momentun transfer and weighting collision configurations.

Inelastic Neutron Scattering from Pressurized Ethane

Motions of the ethane molecule have been investigated at room temperature by inelastic neutron scattering techniques. Ethane targets were observed both in the gas and liquid phases by means of pressure variation. The University of Michigan four-rotor mechanical monochromator was used to obtain data at scattering angles of 90 and 22 deg for neutron energies in the range 0.046 to 0.020 eV. Triple-axis-crystal spectrometer measurements were also made at 0.035 and 0.064 eV as verification. These data indicate that there is no significant difference in the scattering properties of ethane in the gas and liquid state. Effects of the torsional motion of the two methyl groups about the C–C bond can be seen in the forward-angle data. Comparison of experiment with theory indicates that a Krieger—Nelkin model which includes a harmonic-oscillator representation of the torsional motion approximately predicts the observed data. The influence of multiple scattering on the final energy distribution has been observed and is discussed.

An Analysis of the Absolute Energy Distribution in the Spectrum of Eta Aquilae.

view Abstract Citations (50) References (16) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS An Analysis of the Absolute Energy Distribution in the Spectrum of Eta Aquilae. Oke, J. B. Abstract Photoelectric spectrum-scanning instruments have been used to obtain the absolute energy distribution in the spectrum of,' Aquilae as a function of phase High-dispersion spectra were used to correct the scans for the effects of low resolution; the final energy distributions refer to the continuum seen on high-dispersion spectra. The red and infrared magnitudes of the six-color photometry were put on the same scale. The observed energy distributions were corrected for interstellar reddening of 0.14 in B - V. The energy distributions were compared with fluxes computed from model atmospheres to obtain effective temperatures Spectral classification of ,` Aquilae gives a range from F6.5 Ib to G2 Ib; the corresponding temperatures found in this paper are 6140 K at maximum light and 5320 K at minimum These temperatures are substantially higher than those given by Keenan and Morgan; the rate of change of temperature with spectral class is lower than that given by Keenan and Morgan. Using fluxes from the model atmospheres and the monochromatic light-curves, the radius-displacement curve was computed. This curve is in good agreement, both in shape and in phase with the displacement-curve obtained from radial- velocity data. Comparison of the curves gives a mean radius, in solar units. of 63 6 + 2.6. Bolometric and blanketing corrections were determined. Using these, a mean absolute visual magnitude for ,` Aquilae of -4.05 was obtained. The estimated mean error is 0.3. Publication: The Astrophysical Journal Pub Date: January 1961 DOI: 10.1086/147005 Bibcode: 1961ApJ...133...90O full text sources ADS | data products SIMBAD (1)