Frederick H. Mies

Calculated vibrational transition probabilities of OH(X2Π)

Abstract The theoretically derived dipole moment function of OH( X 2 Π) obtained by Stevens Das, Wahl, Neumann, and Krauss is used to calculate the absolute intensities of the vibrational-rotational transitions of the OH Meinel bands. The calculations take full account of the spin uncoupling and vibration-rotation coupling which markedly influence the radiative transition probabilities. The effect of lambda-doubling on the vibrational transitions is analyzed and generally found to be negligible. Results are tabulated for Δ v = v ′ – v ″ ranging from the fundamental transitions Δ v = 1 to the Δ v = 5 overtone, for v ′ = 1–9 and J ′ = 0.5 – 15.5. A comparison is made with available data, and various features of the OH spectrum are examined that are of aeronomical and experimental interest. Thermally averaged emission rates are presented for Δ v = 1–5, and the validity of the rotational temperatures commonly derived from experimental intensity distributions is questioned.

Effects of Anharmonicity on Vibrational Energy Transfer

The diagonal matrix elements of the interaction potential which enter into the quantum theory of vibrational energy transfer generally have been assumed to be identical. Apparently the assumption is based on mathematic convenience rather than on any physical model. If Morse potentials are used to describe the intramolecular forces the elements are approximately but not identically equal. The transition probability is found to decrease markedly when the ratio of the diagonal elements of the initial and final oscillator states is allowed to deviate even slightly from one. Morse potentials were chosen to reproduce the observed anharmonicities of a variety of diatomic molecules and an anharmonic correction factor to the transition probability was calculated. It is found that the generally used calculated transition probabilities should be reduced by a factor of 10—1 to 10—2.

Critical Examination of Vibrational Energy‐Transfer Theory

An accurate He–H2 interaction potential is used to test the validity of the potential that has been employed in energy transfer theory. It is found that a model based on the assumption of additive exponential potentials acting between atomic centers does not reproduce the forces, matrix elements, or transition probabilities derived from the exact potential. The cross section for vibrational excitation is critically dependent on the details of the intermolecular potential; it is particularly sensitive to small differences in the diagonal matrix elements of the interaction potential. The discrepancies that are found for the relatively simple He–H2 system raises serious concern about the general validity of the model potential, particularly in its dependence on the internal coordinate of the oscillator.

Collisions of ultracold trapped atoms

Collisions of ultracold atoms can now be investigated in the laboratory at temperatures below 0.001 K. Such collisions are qualitatively different in many ways from collisions at normal energies, where T ≫ 1 K, because of the long time and distance scales associated with such collisions. Spontaneous emission can strongly modify collision dynamics of excited-state species produced by near-resonant optical excitation if the temperature is less than the characteristic temperature TS, where the collision time is comparable with the spontaneous-emission lifetime. We also estimate the temperature TQ that is characteristic of the onset of quantum threshold behavior, where the WKB approximation fails to apply as the de Broglie wavelength becomes large. We find that TQ is generally larger than TD, the Doppler cooling limit, except for collisions controlled by long-range potentials varying as 1/R3.TQ may be larger or smaller than TS. Expressions for estimating the magnitude of rate coefficients in the T → 0 limit are given. As an example, a model for the threshold behavior of Penning ionization of two He 3S1 metastable atoms is given, and the threshold rate coefficient is estimated to be >5 × 10−10 cm3 sec−1.

Stimulated emission and population inversion in diatomic bound-continuum transitions

Exact expressions are derived for the rate of stimulated emission and the conditions for population inversion in a diatomic bound-continuum transition. The resultant formulae resemble those of a simple, homogeneously broadened, discrete transition with the Lorentzian lineshape replaced by a continuum lineshape, g C(hv = Ev ′ - e″), which is approximately equal to the square of the overlap between the initial, emitting, vibrational level v′ and the final, energy-normalized continuum state e″, i.e. g C ≈ v′|e″>2. Using the ‘reflection method’, which is most applicable to a strongly repulsive final state, equations are obtained which allow simple, but accurate, estimation of the pertinent parameters which influence lasing action. Some general conclusions are extracted, and specific results are presented for the stimulated vacuum ultra-violet emission in high pressure Xe.

Above-threshold dissociation of H+2 in intense laser fields.

We present nonperturbative, time-independent calculations of the photodissociation rate of H{sup +}{sub 2} in intense laser fields. The energy distribution of the protons consists in a sequence of peaks evenly spaced by half the photon energy, all of equal width but of varying heights. They result from multiphoton absorption above the dissociation threshold, with equal sharing of the excess photon energy between H and H{sup +}. Surprisingly, the distribution of higher-energy peaks decreases with increasing intensity, due to stimulated free-free emission of the dissociating fragments. We also predict a sharp angular distribution of the protons along the electric field vector of a linearly polarized laser.

A multichannel quantum defect analysis of diatomic predissociation and inelastic atomic scattering

Given an NT×NT interaction matrix W∞(R) which describes the dissociation of a diatomic molecule into NT asymptotic atomic channel states, we can generate exact numerical solutions to the close‐coupled scattering equations. At total energies E above the highest dissociation threshold we obtain an NT×NT scattering matrix S(E) which defines the asymptotic structure of the NT‐ fold degenerate multichannel scattering or continuum wave functions. This matrix varies rapidly with energy and is nonanalytic at thresholds. However, based on a multichannel quantum defect analysis (MCQDA) of the coupled equations we find that the numerical S(E) matrix can be made to yield a real, symmetric matrix Y(E) which is analytic in E. This matrix can then be analytically continued across threshold to provide rigorous analytic descriptions of the multichannel diatomic wave functions in the predissociating and bound‐state regions of the energy spectrum. Since the extraction of Y(E) is predicated on assigning a reference potential...

Estimating Bounds on Collisional Relaxation Rates of Spin-Polarized 87Rb Atoms at Ultracold Temperatures

We present quantum scattering calculations for the collisional relaxation rate coefficient of spin-polarized 87Rb(f = 2,m = 2) atoms, which determines the loss rate of cold Rb atoms from a magnetic trap. Unlike the lighter alkali atoms, spin-polarized 87Rb atoms can undergo dipolar relaxation due to both the normal spin-spin dipole interaction and a second-order spin-orbit interaction with distant electronic states of the dimer. We present ab initio calculations for the second-order spin-orbit terms for both Rb2 and Cs2. The corrections lead to a reduction in the relaxation rate for 87Rb. Our primary concern is to analyze the sensitivity of the 87Rb trap loss to the uncertainties in the ground state molecular potentials. Since the scattering length for the a3Σ+u state is already known, the major uncertainties are associated with the X1Σ+g potential. After testing the effect of systematically modifying the short-range form of the molecular potentials over a reasonable range, and introducing our best estimate of the second-order spin-orbit interaction, we estimate that in the low temperature limit the rate coefficient for loss of Rb atoms from the f = 2,m = 2 state is between 0.4 × 10−15 cm3/s and 2.4 × 10−15 cm3/s (where this number counts two atoms lost per collision). In a pure condensate the rate coefficient would be reduced by 1/2.

Model calculation of the electronic structure and spectroscopy of Hg2

Abstract Energy curves and transition moments of the excited valence states of Hg2 were obtained in a model calculation based on calculated Mg2 energy levels and the assumption that the asymptotic spin-orbit matrix elements for the Hg atom are applicable to the molecular states. The spin-orbit and orbital-rotational interaction of the excited states of Hg2 is analyzed in both a Hunds case (c) and (a) representation. The intermediate (a) → (c) transition moments are obtained as a function of the internuclear distance. The effect of the orbital-rotational interaction which introduces Hunds case (b) and (e) couplings is found to be small for transitions among excited states under the conditions normally encountered for populating excimer states. Using the energy level positions and transition moments, the observed spectra and predicted spectra are compared for both radiative transitions including the ground state and among the excited states. The lifetime of the 1 u ( 3 Σ u + ) excimer state is calculated to be 1.4 μsec with the 335 nm band assigned to the 1 u → X 1 Σ g + transition. The 485 nm bands cannot be assigned to any Hg2 transitions. Strong bound-continuum absorptions are predicted for the 485 nm bands. On the other hand, the 335 nm emission is predicted to be absorbed by bound-bound transitions only.

A scattering theory of diatomic molecules

We present a unified theory of diatomic molecules which reconciles bound state spectroscopy and atomic scattering theory. The total wave-function is expanded in a complete set of atomic channel states which is entirely equivalent to an expansion in Hunds case (e) electronic-rotational states. An analysis of the coupled radial, that is vibrational, functions places strong constraints on the asymptotic properties of the molecular wave-functions. These are presented in terms of the reactance K and scattering S matrices of atomic scattering theory which offers a uniform treatment for open channels (inelastic scattering and continuum spectroscopy), closed channels (bound state spectroscopy) and mixtures of both (predissociation). The normalization of the total wavefunction is derived and related to the asymptotic boundary conditions both for continuum and bound states.