Adiabatic theory of rotational excitation of non-sigma states
Diatomic molecules nonsigma states rotational excitation adiabatic theory
Faisal, F. H. M.↗
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Transition moments, Franck-Condon factors, and lifetimes of forbidden transitions - Calculation of the intensity of the Cameron system of CO.
Discussion of the factors affecting the intensity of forbidden transitions in diatomic molecules. It is shown that using Franck-Condon factors to predict relative band intensities is less reliable for forbidden transitions than it is for allowed transitions. The intensity of the 0,0 and 1,0 bands of the a super 3 pi-super 1 sigma Cameron system of CO are calculated using perturbation theory. The intensity arises from spin-orbit mixing of the A super 1 pi state with the a super 3 pi state. From the known spin-orbit coupling constant of the a super 1 pi state and the known intensity of the fourth positive A super 1 pi-super 1 sigma transition, the oscillator strengths of the 0,0 and 1,0 bands are calculated to be 1.63 x 10 to the minus 7th power and 1.99 x 10 to the minus 7th power. Lifetimes of various rotational levels are shown to range from 2.9 to several hundred milliseconds.-
James, T. C.↗
Application of the adiabatic-nuclei theory to vibrational excitation.
The adiabatic-nuclei theory is shown to be quantitatively applicable to vibrational excitation of diatomic molecules by electron impact. When the dependence of the fixed-nuclei phase shifts on internuclear separation is approximated by a two-term Taylor series, the resulting formulas are transparent and easily evaluated. Application to e-H2 excitation is made, phase-shift derivatives are estimated, and the theory is found to fit experimental data.
Faisal, F. H. M.↗
Post-threshold energy dependence of the cross section for endoergic processes - Vibrational excitation and reactive scattering.
The essential features of the translational energy dependence or excitation function for two types of endoergic collisional processes are deduced on the basis of information on the inverse, exoergic processes. Microreversibility is conveniently exploited via the symmetric field function, Y(E), which is uniquely determined at a given total energy, E. In the case of the vibrational excitation of diatomic molecules by atomic or molecular impact, use is made of the abundant data on the temperature dependence of the relaxation time.
Levine, R. D.↗
Diatomic predissociation line widths
Predissociation by rotation and curve crossing in diatomic molecules is discussed. The pattern of predissociation line widths is seen as providing a highly sensitive yardstick for the determination of unknown potential curves. In addition, the computation of such a pattern for given potential curves is considered a matter of routine, unless the predissociation happens to occur from an adiabatic potential curve. Analytic formulas are used to provide physical insight into the details of the predissociation pattern, to the extent that a direct inversion procedure is developed for determination of the repulsive potential curves for Type 1 predissociations.
Child, M. S.↗
Spectroscopy of Project Fire 1, April 14, 1964
The Fire 1 test was designed to study the heating of an Apollo-type reentry vehicle. The total reentry complex weighed approximately 230 kg and entered the upper atmosphere at a velocity of 11.5 km/s. The spectrum of the reentry complex has been studied in the wavelength range 3700 to 8800 A, where 102 multiplets of 21 atoms and the band systems of 5 diatomic molecules have been identified. Comparisons with meteor spectra are made.
Millman, P. M.↗
Vibrational relaxation of carbon monoxide studied by two-wavelength infrared emission
Experimental results are presented for the vibrational relaxation of pure carbon monoxide behind incident shock waves over the temperature range 4000 to 6300 K. The data were obtained as infrared emission from the fundamental and overtone vibrational band systems (in some of the experiments the two-band systems were recorded simultaneously). The data are consistent with present theories for the vibrational relaxation of diatomic molecules and can be interpreted in terms of an initial Boltzmann vibrational distribution relaxing toward final equilibrium via a continuous sequence of intermediate Boltzmann distributions.
Chackerian, C., Jr.↗
Formation of molecular lines in stellar atmospheres
Statistical equilibrium of electronic states of diatomic molecules in stellar atmospheres is examined. Atmospheres discussed are representative of the sun, Arcturus (K-giant) and Betelgeuse (M-supergiant). A comparison of the relative collisional and radiative contributions to the equilibrium of the ground electronic state shows that this state is collisionally controlled and that the line source function for vibration-rotation transitions within this state is equivalent to the Planck function. Examination of the equilibrium for excited electronic states demonstrates that the exchange between these states and the ground electronic state is most probably determined by radiative excitation. This result implies that scattering rather than pure absorption is the appropriate mechanism for the formation of lines belonging to these electronic transitions. The scattering hypothesis is given a preliminary check against solar observations. Areas for future investigations are outlined.
Hinkle, K. H.↗
Analysis of a semiclassical model for rotational transition probabilities
A semiclassical model proposed by Pearson and Hansen (1974) for computing collision-induced transition probabilities in diatomic molecules is tested by the direct-simulation Monte Carlo method. Specifically, this model is described by point centers of repulsion for collision dynamics, and the resulting classical trajectories are used in conjunction with the Schroedinger equation for a rigid-rotator harmonic oscillator to compute the rotational energy transition probabilities necessary to evaluate the rotation-translation exchange phenomena. It is assumed that a single, average energy spacing exists between the initial state and possible final states for a given collision.
Deiwert, G. S.↗
Conversion of laser energy to gas kinetic energy
Techniques for the gas phase absorption of laser radiation for ultimate conversion to gas kinetic energy are discussed. Particular emphasis is placed on absorption by the vibration rotation bands of diatomic molecules at high pressures. This high pressure absorption appears to offer efficient conversion of laser energy to gas translational energy. Bleaching and chemical effects are minimized and the variation of the total absorption coefficient with temperature is minimal.
Caledonia, G. E.↗
Electronic energy states
One-electron wave functions are reviewed and approximate solutions of two-electron systems are given in terms of these one-electron functions. The symmetry effects associated with electron spin are reviewed and the effects of electron exchange on energy levels of the two-electron system are given. The coupling of electronic orbital and spin angular momentum is considered next and the Lande interval rule for Russell-Saunders or LS coupling is derived. The configurations possible for various multi-electron LS couplings are enumerated (examples from the first two rows of the periodic table are given), and the meaning of the spectroscopic nomenclature is discussed, particularly with respect to the degeneracies of the electron states involved. Next the nomenclature, symmetries, and degeneracies for electron states of diatomic molecules are discussed, and some examples for N2, O2, and NO are presented. The electronic partition functions and derivative thermodynamic properties are expressed in terms of these energies and degeneracies, and examples are given for some of the simple gas species encountered in the earth's atmosphere.
Source record↗
Partition function corrections
The vibration-rotation interaction coupling in diatomic molecules is analyzed and first-order expressions for the energy levels are deduced. Corrections to the partition function to account for this coupling are derived. The effects of long-range intermolecular forces due to induced dipole-induced dipole interactions, dipole-induced dipole interactions, charge-dipole interactions, and charge-charge interactions are considered. London's quantized oscillator model of the induced dipole-induced dipole interaction is developed. The partition function including effects of such dispersion forces is derived and is shown to lead to the virial equation of state. For a model combining the hard sphere and long-range attractive type potentials, this is found to lead to the van der Waals equation of state. The equation of state near the critical point is presented in reduced form (thermodynamic variables expressed in units of critical point values). Finally, approximate corrections to the electronic partition functions are derived to account for perturbations of excited electronic states induced by neighboring neutral particles, heavy ions, and fast electron collisions.
Source record↗
Tables of the coefficients A
Numerical coefficients required to express the angular distribution for the rotationally elastic or inelastic scattering of electrons from a diatomic molecule were tabulated for the case of nitrogen and in the energy range from 0.20 eV to 10.0 eV. Five different rotational states are considered.
Chandra, N.↗
Calculation of rotational transition probabilities in molecular collisions - Application to N2 + N2
A computational method is proposed to obtain rotational transition probabilities in collisions between two diatomic molecules. The potential method of Rabitz and an exponential approximation are used to solve the semiclassical coupled equations without invoking any perturbational technique. The collision trajectory is determined in the classical modified-wave-number approximation. The method can treat systems involving strong interactions and provide probabilities for transitions even with a multiquantum jump. A simultaneous transition in the rotational states of both molecules, i.e., the rotational-rotational energy transfer, is taken into account. An application to the system N2 + N2 is presented.
Itikawa, Y.↗
The influence of molecular rotation on vibration-translation energy transfer
A three-dimensional vibration-rotation collision model is formulated within a semiclassical framework to study the effect of coupled rotational motion on the rate of vibrational energy transfer for collisions between anharmonic diatomic molecules and structureless atoms. Emphasis is on the net rates of vibrational energy transfer summed over all final rotational states rather than those for individual vibration-rotation transitions. The corresponding three-dimensional rate parameters are cast into forms that may be identified with equivalent parameters associated with the collinear approximation. Their comparisons allow the validity of a collinear model to be evaluated and some constraints on its application to be implied. The mechanisms of vibrational energy transfer including rotational transitions are shown to be separable into three classes which are identified and discussed
Mckenzie, R. L.↗
Electron impact cross sections for v = 0-1 vibrational excitation in CO at electron energies of 3 to 100 eV
The paper discusses the measurements of normalized, absolute differential cross-sections for electron-impact vibrational transition in CO. Integral and momentum-transfer cross-sections were obtained from these differential results; incident electron energies were in the 3 to 100 eV range, and the scattering angles were 10 to 135 deg. A comparison of these results with measurements made with pure vibrationally elastic cross-sections in N2, and with the data based on a two-potential theory for electron scattering from diatomic molecules showed that the present CO cross-sections are similar to those in N2. This indicates that the long-range effect of the small CO dipole moment is negligible in promoting vibrational excitation; moreover, a significant peak in the integral and momentum-transfer cross-sections is observed at 20 eV. Finally, the low-energy integral cross-sections are compared with a recent set of swarm data for vibrational excitation.
Chutjian, A.↗
Solar-pumped gas laser development
The direct conversion of solar radiation into an inverted population for extraction in an optical cavity holds promise as a relatively simple system design. Broad-band photoabsorption in the visible or near-UV range is required to excite large volumes of gas and to ensure good solar absorption efficiency. The state excited must be a metastable state which is not quenched by the parent gas. The emission bandwidth must be less than approximately 10 A. The system should show chemical reversibility and an insensitivity to increasing temperature. Other properties such as good quantum efficiency and kinetic efficiency are also implied. A search of electronic-vibrational transitions in diatomic molecules satisfying these conditions is now in progress. A photodissociation-pumped atomic iodine laser is now being tested under solar pumping conditions. Photodissociation studies for thallium spin-flip metastable formation will begin in the near future.
Wilson, J. W.↗
Systematics of ground-state potential minima between two main-group atoms or ions
A diagram is presented illustrating the internuclear separations between diatomic molecules or quasi-molecules with the exception of those containing transition metal and rare-earth atoms. As plotted as a function of the atomic numbers of the constituent atoms, the ground-state separations are observed to exhibit dramatic periodicities, as well as a gradual rise with increasing atomic number. The data for van der Waals molecules are not sufficient to predict the results of future experiments, although it is noted that the greatest internuclear separations are those of the alkali earth-rare gas molecules. Finally, it is found that to within the resolution of the diagram, isoelectronic molecules or quasi-molecules along the homonuclear direction have a constant internuclear separation.
Hefferlin, R.↗