Vibrational Transition Rates Research Articles

On the semiclassical theory of collision-induced vibrational–rotational transitions in molecules

The ideas which were introduced in our recent theoretical work on collision-induced vibrational–rotational transitions are further developed here so that the resulting theory can be applied without any restrictions on the type of molecule. Moreover, it is shown that the original theory, in which only straight-line trajectories were considered, can be extended to include other trajectories as well. A minor error occuring in the original work is also corrected. As an application, the dependence of the vibrational transition rates of methyl halides upon the mass of the collision partner is studied.

Monte Carlo trajectory study of Ar+H2 collisions: Thermally averaged vibrational transition rates at 4500 °K

Quasiclassical trajectory calculations of vibrational transition rates in Ar+H2 collisions have been carried out. A realistic potential energy surface has been used, and the rates are averaged over rotational–translation distributions at 4500 °K. The same transition rates are calculated by eight distorted-wave-based theories which have been used by others for various applications. The present calculations provide a critical test of these theories, especially for high vibrational quantum numbers where data has been scarce. We also discuss dissociation rates, the rotational component of vibrational energy transfer, and a surprisal analysis of the vibrational transition rates.

Vibrational energy transition rates from recent sound absorption measurements in moist air and in moist nitrogen

Recent measurements of sound absorption in moist air at temperatures between 0°F and 100°F have been analyzed to extract that part of the absorption due to the vibrational relaxation of oxygen. The measurements extend to higher water-vapor concentrations than most previous measurements and show the shift in frequency of maximum relaxation absorption per wavelength with percent water vapor to be less than that extrapolated from previous measurements. The fmax versus percent-H2O curve has been analyzed in conjunction with previous measurements in binary mixtures of H2O and O2 to give more accurate values for the rate of v-v exchange between H2O and O2 and for the v-R, t rate in H2O-H2O collisions. Measurements have also been made of the vibrational relaxation absorption in moist nitrogen at 100, 200, and 300°F. In these measurements fmax was found to increase linearly with H2O concentration and a more accurate value for the v-R, t (or v) rate for H2O deexciting N2 vibration has been determined at each temperature. [Work supported NASA—Langley Research Center and NASA—Lewis Research Center.]

Theoretical evaluation of vibrational transition rates and relaxation in CO–He

An extensive set of vibrationally inelastic transition rates kn+Δn→n(T) is presented for CO–He. Calculations were performed over temperatures 100⩽T⩽3000 °K, final states 0⩽n⩽45, and transitions Δn=1,2,3. Cross sections σn+Δn→n are computed by solving sets of close coupled breathing sphere equations containing 7 to 11 vibrational states. The CO–He potential surface used was computed by the method of Gordon and Kim. Sample relaxation studies are carried out to determine the roles of the different rate constants in the relaxation process. It is shown that while the conditions of the Landau–Teller theory are not satisfied here, the relaxation of the total vibrational energy is still approximately described by a single relaxation time under usual experimental conditions. However, a detailed examination of the relaxation process shows that a canonically invariant temperature dependence generally does not hold. Anharmonic effects at high quantum numbers are shown to play a dominant effect in the relaxation.

Acoustical method of obtaining vibrational transition rates tested on CO2/N2 mixtures

Sound absorption measurements on 16% and 30% mixtures of CO2/N2 at 300 and 600°K illustrate the acoustical method of obtaining transition rates. The rate of N2 in de-exciting CO2(0110) is measured to be 8.0 × 104± 20 % and 5.0 × 105± 20 % atm−1sec−1 at 300 and 600°K, respectively.

Three-Dimensional Model of Collision-Induced Vibrational Transitions in Homonuclear Diatomic Molecules

The one-dimensional, semiclassical theory of vibrational transitions in homonuclear diatomic molecules is extended to three dimensions. Small perturbation methods are applied to harmonic-oscillator, rigidrotator wavefunctions, and the interaction potential is assumed to be a linear superposition of exponential repulsions between atomic centers. This potential is expanded to terms of first-order influence on the transition probabilities, and the spherically averaged potential is used to determine the collision trajectory and the time-dependent perturbation. Vibrational transitions (predominantly Δυ = ± 1) are found to be accompanied by simultaneous rotational transitions (predominantly Δl = 0, ± 2). The effect of coupled rotations increases the vibrational transition rates by 50% or more. Analytic approximations are derived for cross sections, rate coefficients, and relaxation rates. The three-dimensional model permits one to fit both the gradient and the magnitude of an effective exponential repulsion to observed vibrational relaxation data, whereas only the gradient can be determined using one-dimensional theories. This “effective” interaction potential for vibrational excitation is steeper and of shorter range than potentials normally responsible for pure scattering. We surmise that a multiplicity of interaction potentials exist for molecules, just as for atoms, and that the steeper inner potentials resulting from paired electron spin configurations are responsible for most vibrational transitions, whereas the outer potentials resulting from unpaired spins are responsible for most of the scattering.

Energy Levels ofEr16668andTm16669(7.7 h) Excited in the Decay ofHo16667(26.7 h),Ho166m(1.2×103yr), andYb16670(57 h)

The $\ensuremath{\gamma}$-ray spectra accompanying the decay of $_{67}\mathrm{Ho}^{166}$ (26.7 h), $_{67}\mathrm{Ho}^{166m}$ (1.2\ifmmode\times\else\texttimes\fi{}${10}^{3}$ yr), $_{70}\mathrm{Yb}^{166}$ (57 h), and $_{69}\mathrm{Tm}^{166}$ (7.7 h) have been examined with Ge(Li) detectors. Chemically purified sources of ${\mathrm{Yb}}^{166}$ revealed only the known 82.3-keV transition in ${\mathrm{Tm}}^{166}$. Nine transitions observed in the 26.7-h ${\mathrm{Ho}}^{166}$ activity fit known excited levels in ${\mathrm{Er}}^{166}$: 80.57 (${2}^{+}$), 786.4 (${2}^{+}$), the 1460.9-keV (${0}^{+}$) $\ensuremath{\beta}$-vibrational state, and two higher levels at 1663.0 (${1}^{+}$), and 1830.5 keV (${1}^{\ensuremath{-}}$). Forty-two of the 63 transitions observed in the spectrum of 1.2\ifmmode\times\else\texttimes\fi{}${10}^{3}$-yr $_{67}\mathrm{Ho}^{166m}$ are assigned among 14 excited states in ${\mathrm{Er}}^{166}$; these states are at 80.57 (${2}^{+}$), 265.0 (${4}^{+}$), 545.4 (${6}^{+}$), 911.2 (${8}^{+}$), 859.9 (${3}^{+}$), 956.4 (${4}^{+}$), 1075.4 (${5}^{+}$), 1216.3 (${6}^{+}$), 1376.1 (${7}^{+}$), 1556.1 (${8}^{+}$), 1666.5 (${5}^{\ensuremath{-}}$), 1693.0 (${5}^{\ensuremath{-}}$), 1787.3 (6), and 1828.1 keV (5,6). The first four levels are members of the $K=0$ ground-state rotational band. The next six states are members of the $K=2$ $\ensuremath{\gamma}$-vibrational band based on the 786.4-keV band head. Approximately 90 $\ensuremath{\gamma}$ rays are resolved in the Ge(Li) spectrum of ${\mathrm{Tm}}^{166}$. These, together with a summary of the results of internal-conversion measurements made previously by other investigators, are listed in a table containing 110 transitions believed to ocur in the ${\mathrm{Tm}}^{166}$ decay. We have placed approximately 80 of these $\ensuremath{\gamma}$ rays into 23 excited states in ${\mathrm{Er}}^{166}$. The energies (keV) of these states are 80.57 (${2}^{+}$), 265.0 (${4}^{+}$), 545.4 (${6}^{+}$), 786.4 (${2}^{+}$), 859.9 (${3}^{+}$), 956.4 (${4}^{+}$), 1075.4 (${5}^{+}$), 1375 (${2}^{+}$), 1458.9 (${3}^{\ensuremath{-}}$), 1514.5 (${3}^{\ensuremath{-}}$), 1530.1 (${2}^{+}$ or ${3}^{+}$), 1572.4 (${4}^{\ensuremath{-}}$), 1704 (${3}^{+}$ or ${4}^{+}$), 1918.6 (${3}^{\ensuremath{-}}$), 1940, 2134.4 (${3}^{+}$), 2161.2 (${3}^{+}$), 2174.4 (${3}^{+}$), 2243, 2274, 2292, 2679, and 2728. The 1530- and 1704-keV states may be the ${2}^{+}$ and the ${4}^{+}$ levels of the $\ensuremath{\beta}$-vibrational band based on the 1460.9-keV (${0}^{+}$) band head. A study of the $\ensuremath{\gamma}$-ray spectrum in coincidence with annihilation radiation (in triple coincidence) indicates that the two reported positron branches of 1932 keV (1% per disintegration) and 1210 keV (0.3% per disintegration) decay to the 80.57- and to the 786.4-keV levels, respectively. Comparison of the relative $\ensuremath{\gamma}$-transition intensities between members of the $\ensuremath{\gamma}$-vibrational band and various members of the ground-state rotational band yield a value of the mixing parameter $z=0.045\ifmmode\pm\else\textpm\fi{}0.003$. The rotational $E2$ transition rates relative to the vibrational transition rates are calculated, yielding a mean value of 45.5\ifmmode\pm\else\textpm\fi{}3 for the ratio. The energy values of the members of the ground-state and $\ensuremath{\gamma}$-vibrational bands are compared with the usual expansion in $I(I+1)$. The third-order term $C{I}^{3}{(I+1)}^{3}$ is believed necessary to describe both bands.