Franck-condon factors to high vibrational quantum numbers. iv - no band systems.
Franck-Condon factors computed to highest known vibrational quantum numbers for NO band system
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Franck-Condon factors computed to highest known vibrational quantum numbers for NO band system
Stark broadening of hydrogen lines of large principal quantum number for RF transitions by electron and ion impact approximation
Franck-Condon factors computed and tabulated to high vibrational quantum numbers for molecular oxygen band system
Approximate quantum numbers for d-band states in transition metals
Franck-Condon factors to high quantum numbers covering methods, results and tabulation
Doubly excited states of hydrogen of high quantum number and electron atom ionization
High n-alpha lines (transitions n + 1 to n) with quantum numbers n between 50 and 250 have been observed emanating from galactic H II regions where the electron density and temperature are about 1000/cu cm and 1 eV, respectively. High n-alpha lines have not previously been seen in the laboratory where fairly homogeneous plasmas may be produced and relatively precise measurements of electron densities and temperatures can be made. The present work describes experiments where the first members of the hydrogen line series with lower states n = 10, 11, 12, and 13 have been detected in a laboratory plasma. The width of the 12-alpha line at 88.7 microns could be measured and was consistent with calculated broadening from elastic electron collisions and quasi-static ion effects.
The expressions for two-center overlap integrals between angular s, p, and d Slater orbitals of arbitrary, higher principal quantum number are explicitly listed. The expressions obtained are extremely compact and independent of the coordinate system. It is further shown that the numerical values of the integrals obtained in this way are free from any numerical instability.
The high-resolution laboratory millimeter- and submillimeter-wave spectra of C-12H(3)OH and C-13H(3)OH have been extended to include transitions involving significantly higher angular momentum quantum numbers than studied previously. For C-12H(3)OH, the data set now includes 549 A torsional substate transitions and 524 E torsional substate transitions through J is not greater than 24, exclusive of blends. For C-13H(3)OH the data set now includes 453 A torsional substate transitions and 440 E torsional substate transitions through J is not greater than 24, exclusive of blends. The extended internal axis method Hamiltonian has been used to analyze the transitions to experimental accuracy. The molecular constants determined by this approach have been used to predict accurately the frequencies of many transitions through J = 25 not measured in the laboratory.
A semiclassical model of the inelastic collision between a vibrationally excited anharmonic oscillator and a structureless atom was used to predict the variation of thermally averaged vibration-translation rate coefficients with temperature and initial-state quantum number. Multiple oscillator states were included in a numerical solution for collinear encounters. The results are compared with CO-He experimental values for both ground and excited initial states using several simplified forms of the interaction potential. The numerical model was also used as a basis for evaluating several less complete but analytic models. Two computationally simple analytic approximations were found that successfully reproduced the numerical rate coefficients for a wide range of molecular properties and collision partners. Their limitations were also identified. The relative rates of multiple-quantum transitions from excited states were evaluated for several molecular types.
A semiclassical model of the inelastic collision between a vibrationally excited anharmonic oscillator and a structureless atom is used to predict the variation of thermally averaged vibrational-translational rate coefficients with temperature and initial-state quantum number. Multiple oscillator states are included in a numerical solution for collinear encounters. The results are compared with CO-He experimental values for both ground and excited initial states using several simplified forms of the interaction potential. The numerical model is also used as a basis for evaluating several less complete, but analytic, models. Two computationally simple analytic approximations are found that successfully reproduce the numerical rate coefficients for a wide range of molecular properties and collision partners. Their limitations are identified, and the relative rates of multiple-quantum transitions from excited states are evaluated for several molecular types.
As was shown earlier by Tai (1979), by using the Fourier-transform technique and properly coupling a pair of two-center exchange integrals, the multicenter molecular integrals can be cast into a simple expression upon which numerical procedures can be directly applied. In this paper, the procedure of Tai is extended to integrals involving orbitals with arbitrarily higher principal quantum number. The derivation is outlined, and the explicit expressions are presented for a three-center nuclear attraction integral and a four-center two-electron Coulomb repulsion integral of arbitrary higher states.
A list of 193 neutral carbon lines observed in the XUV spectrum of a solar flare between 100 and 2000 A using the normal incidence spectrograph flown on Skylab is presented. Of these, 69 are newly identified lines arising from transitions from upper levels of high quantum number where the quantum number is not less than six. The new lines have allowed the determination of 63 new energy levels. Wavelengths for an additional 109 transitions were calculated by polynomial fitting using reference wavelengths of unblended neutral carbon, Si, N, and S lines emitted in the same atmospheric regions of the flare. The calculated lines falling between 1102 and 1140 A were not observed due to low instrumental efficiency at these wavelengths. The calculated wavelengths are in excellent agreement with those of Johansson (1965). It appears that in solar spectra recombination processes are dominant, enhancing the populations of the high quantum levels relative to the populations of levels with small quantum numbers.
Attention is given to the uncertainties that remain concerning the autoionization states of O2 leading to the a 4Pi(u) and A 2Pi(u) states of O2(+), as well as some of the assignments of the autoionization states and the determinations of effective quantum numbers and quantum defects. The former problems of vibrational assignments are unambiguously established in view of a study of isotopic oxygen molecules. A systematic examination of the known Rydberg series is conducted, and new assignments and interpretations for several autoionization states leading to the various states of O2(+) are suggested.
Branching ratios in hydrogen-like atoms due to electric-dipole transitions are tabulated for the initial principal and angular momentum quantum number n, lambda, and final principal and angular momentum quantum numbers n, lambda. In table 1, transition probabilities are given for transitions n, lambda, yields n, where sums have been made with respect to lambda. In this table, 2 or = n' or = 10, o or = lambda' or = n'-1, and 1 or = n or = n'-1. In addition, averages with respect to lambda' and sums with respect to n, and lifetimes are given. In table 2, branching ratios are given for transitions n' lambda' yields ni, where sums have been made with respect to lambda. In these tables, 2 or = n' or = 10, 0 or = lambda', n'-1, and 1 or = n or = n'-1. Averages with respect to lambda' are also given. In table 3, branching ratios are given for transitions n' lambda' yields in lambda, where 1 or = n or = 5, 0 or = lambda or = n-1, n n' or = 15, and 0 or = lambda' or = n(s), where n(s), is the smaller of the two numbers n'-1 and 6. Averages with respect to lambda' are given.
The transition probabilities which are given in terms of n prime k prime and n k are tabulated. No additional summing or averaging is necessary. The electric quantum number k plays the role of the angular momentum quantum number l in the presence of an electric field. The branching ratios between stark levels are also tabulated. Necessary formulas for the transition probabilities and branching ratios are given. Symmetries are discussed and selection rules are given. Some disagreements for some branching ratios are found between the present calculation and the measurement of Mark and Wierl. The transition probability multiplied by the statistical weight of the initial state is called the static intensity J sub S, while the branching ratios are called the dynamic intensity J sub D.
The branching ratios in hydrogen-like atoms due to the electric-dipole transitions are tabulated for the initial principal and azimuthal quantum numbers n prime l prime, and final principal and azimuthal quantum numbers n l. Average values with respect to l prime are given. The branching ratios not tabulated, including the initial states n prime yields infinity l prime corresponding to the threshold of the continuum, could be obtained by extrapolation.
Consideration of the mechanism of production of gravitons in the empty, anisotropic, spatially inhomogeneous Gowdy three-torus cosmology. The Gowdy cosmology is an exact solution of the vacuum Einstein equations and is obtained as a generalization of the homogeneous empty Bianchi Type I (Kasner) cosmology by permitting the metric components to depend on one of the space variables in addition to time. The Hamiltonian methods of Arnowitt, Deser, and Misner are employed to identify the dynamical variables which are to be quantized. The WKB regime solution is identical to that found by Doroshkevich, Zel'dovich, and Novikov (DZN) for a universe containing collisionless anisotropic radiation. Using a procedure similar to that of Parker (1971) or Zel'dovich and Starobinskii (1971) for defining quantum number, it is found that the DZN large-time radiation consists of quanta (gravitons) created from an initial vacuum. The quantum behavior is much like the semiclassical enhancement of quantum number with the added feature of creation of quanta from vacuum fluctuations.