Radial Coupling Research Articles

Theoretical treatment of predissociation in the A 2Σ+, B 2Π, and C 2Σ+ states of HeH

Theoretical calculations have been carried out on the predissociation of the A 2Σ+ state of HeH by radial coupling to the ground state, X 2Σ+, of the B 2Π state by rotational coupling to X 2Σ+, and of the C 2Σ+ state by radial coupling to A 2Σ+ and by rotational coupling to the B 2Π state. The results are in good agreement with experimental data regarding the predissociation of the A 2Σ+ and C 2Σ+ states, while they also predict significant predissociation of the positive rotational levels of the B 2Π state.

Theoretical spectroscopy of the NO radical. III. Λ doubling and predissociation in the C 2Π state

The Λ doubling of the C 2Π state of NO is calculated by considering the heterogeneous couplings (spin–orbit and rotational angular momentum) between the C 2Π and the first three 2Σ+ states plus the homogeneous interaction of the C 2Π with the B 2Π state. All wave functions and energies result from highly correlated configuration interaction wave functions. A transformation from the adiabatic to the diabatic basis is performed by employing the radial coupling between the two 2Π states. The perturbation matrix is solved in the diabatic basis and leads directly to the eigenvectors and eigenvalues of the Λ components. It is found that for J≥3/2 the Λ components are completely mixed and can therefore not be labeled according to their Ω values any more. Vibrational averaging leads to a calculated value of 0.019 cm−1 (J=0.5, v=0) compared to the measured value of 0.016 cm−1 for the Λ doubling. The predissociation process of the C 2Π state is calculated in the adiabatic basis; the mechanism is found to be caused solely by the spin–orbit interaction with the a 4Π state.

Structures due to the nuclear Landau-Zener effect in the 17O+12C scattering within the molecular particle-core model

Differential cross sections for the elastic scattering of 17O on 12C and the inelastic excitation of 17O to its first excited 1/2+ state are calculated within the molecular particle-core model. This model decomposes the 17O+12C system into a 12C and 16O core with an extra neutron described by molecular eigenstates of the two-centre shell-model Hamiltonian. Depending on the coupling strength the enhancement of the radial coupling due to an avoided level crossing can generate structures in the angle-integrated inelastic excitation function. These energy-dependent structures are related to resonance states of the relative motion in the elastic channels and are caused by the nuclear Landau-Zener effect.

Infrared and microwave study of angular–radial coupling effects in Ar–HCN

Microwave and infrared spectra of Ar–HCN have been obtained using an electric-resonance optothermal spectrometer. The microwave measurements extend to higher J the previous results of Leopold et al. and Klots et al., allowing the determination of higher-order centrifugal distortion constants for this quasilinear, highly nonrigid complex. A Padé approximant fit to the microwave data indicates a significant rotation-induced asymptotic increase in the zero-point center-of-mass separation between the Ar and the HCN, above that expected from pure radial distortion. This results from the large coupling between the angular and radial degrees in the intermolecular potential forcing the centrifugal alignment of the HCN. Infrared spectra are reported for the C–H streching fundamental ν1 and the combination band ν1+ν15, where ν5 is the van der Waals bending vibration. The band-origin difference between these two bands gives ν5=7.8 cm−1, in rough agreement with the 10 cm−1 harmonic value predicted from the microwave-determined nuclear quadrupole coupling constant. The complexation-induced red shift of the C–H stretching vibration is 2.69 cm−1 and the vibrational predissociation linewidths Γ are <10 MHz (FWHM). The vibrationally excited complex predissociates before striking the bolometer detector, implying that the predissociation lifetime τ<1 ms.

Molecular treatment of single-electron capture in Li3++Li collisions

The single charge exchange process in Li3++Li(2s) collisions is investigated in the impact energy range 2.25*10-4-1 keV amu-1. The adiabatic potential energies and radial coupling matrix elements of the Li23+ molecule are computed in a one-electron approximation, using a model potential method. Those are subsequently employed to solve the collision dynamics by a full quantum mechanical treatment or by using the semiclassical impact parameter approach. The results for the total electron-capture cross section present a high and broad maximum value around 220 AA2 at 0.1 keV amu-1. A disagreement of more than one order of magnitude with the theoretical results reported by Stollberg and Hai-Wong Lee (1984) is discussed.

An experimental and theoretical study of shape resonances in CH+

A study of shape resonance energies and widths in the A 1Π state of 12CH+ and 13CH+ is reported. The experimental data were obtained by high-resolution laser photofragment spectroscopy of CH+ in a fast ion beam. Spectroscopic transitions were recorded by tunable laser excitation from levels of the X 1Σ+ state to shape resonances (quasibound rotational levels) of the A 1Π state and detection of photoproduct C+ ions. Some of the dissociation lifetimes are sufficiently short to cause broadening of the spectral lines. The linewidths are interpreted in terms of tunnelling through the centrifugal barrier and the effects of rotational-electronic and radial coupling. The e lambda-doublet component in two of the resonances is found to have a narrower linewidth than the corresponding f component. This is shown to be due to the effect of the rotational-electronic (Coriolis) interaction on the shapes of the rotationally adiabatic potential-energy curves which determine the tunnelling probability. The contributions to the predissociation rates are calculated and are in good agreement with the experimental results.

Semiclassical analysis of polarization effects in collision-induced intramultiplet mixing for Ne

We have performed new crossed-beam measurements and quantum-mechanical calculations on transitions between the short-lived Ne**{(2p)5(3p)}k={a}k states with k=4,5,6,7 (Paschen numbering), induced by collisions with ground-state He atoms at energies between 70 and 140 meV. The {a}4,5,6,7 multiplet is distinguished by the presence of several avoided crossings between the adiabatic potentials VkO(R)—a sign of strong, localized radial coupling. This has inspired a simple, semiclassical model for the Ne**-He collision process, which has the following ingredients: (i) straight-line trajectories with hard-sphere scattering at the classical turning point RT; (ii) rotational coupling for R>RL and ‘‘locking’’ of the electronic angular momentum J to the internuclear axis for R=RL, with RL the locking radius; (iii) Landau-Zener–type curve-crossing transitions near the crossing radius RC. This model goes a long way toward explaining the experimental polarization effects, i.e., differences between polarized cross sections Ql?k?Mk? for the {a}k?{a}l transition depending on the asymptotic orientation of the total electronic angular momentum J, as specified by the magnetic quantum number Mk. These polarization effects are at times very large. For example, at a center-of-mass collision energy E?100 meV, we find Ql?5?0?/Ql?5?1?=0.5 and 3.5 for l=6 and 7, respectively, Ql?6?0?/Ql?6?1?=0.41 and 1.3 for l=5 and 7, and Ql?7?0?/Ql?7?1?=0.08 and 8.9 for l=4 and 5.

On the dynamic couplings between magnetically dressed molecular states

The dynamic (radial and rotational) couplings between diatomic molecular states are considered for the case that these states are 'dressed' by a strong, external magnetic field. The explicit form of the dynamic coupling operator is derived within the classical-trajectory approximation to the internuclear motion. The radial and rotational coupling matrix elements are expressed in a form suitable for efficient numerical evaluation.

Theoretical calculations on radiative and nonradiative processes of quartet states of HeH

MRD CI calculations have been carried out on the lowest four 4Σ+ and the lowest two 4Π states of HeH. Potential energy curves, rates of radiative transitions and also rates of predissociation by radial coupling have been obtained, in order to make predictions on the possibility of observing quartet spectra in HeH.

Cross sections for charge exchange of atoms on multiple-charged ions

Charge exchange of N2+ (2p) on He(1s 2) is investigated theoretically in the eV range. The initial and final diabatic states and the radial coupling between them are calculated within the semiempirical asymptotic method. The integral cross-sections are estimated using the Landau-Zener model. Comparison is made with available experimental data.

Cooperative fluorescence in nonadiabatic dissociation of alkali diatoms.

We predict a new type of time-resolved cooperative fluorescence (CF) obtainable when a homonuclear alkali-metal diatom dissociating via a $^{1}\mathrm{\ensuremath{\Sigma}}^{\mathrm{*}}$ state evolves (by nonadiabatic radial coupling) into a superposition of two excited adiabatic states correlated to different doublet levels. CF intensity then combines ``ringing'' oscillations, caused by time variation of the interference phase between the receding emitting atoms, with quantum beats associated with fine-structure splitting. The calculated CF patterns for ${\mathrm{Li}}_{2}$ are sensitive to the amplitudes and relative phase of the two superposed adiabatic states.

Non-adiabatic interactions between the C 2Σ + and D 2Σ + electronic states of HeH

Off-diagonal coupling matrix elements have been calculated between vibrational levels of the C 2Σ + and the D 2Σ + states of HeH, using published potential energy curves and radial coupling matrix elements. The theoretical off-diagonal matrix element between ν= 0 of D 2Σ + and ν=3 of C 2Σ + is 39 cm −1, which is comparable to a reported experimental value of 43.4 cm −1.

Nuclear Landau-Zener effect in17O+12C scattering within the molecular particle-core model

Coupled channel calculations for elastic scattering of 17O on 12C and excitation of the first 1/2+ state of 17O were carried out in the molecular particle-core model. In this model the extra neutron of 17O occupies molecular single-particle states of the two-centre shell model. The enhancement of the radial coupling strength due to an avoided level crossing leads to structures in the differential cross sections in agreement with measured data. These structures are understood as the signals of a Landau-Zener-type nuclear transition, uniquely proving the existence of nuclear molecular orbitals and consequently of nuclear molecules.

Collision-induced intramultiplet mixing for Ne

We have investigated fine-structure--changing collisions of short-lived (20-ns) ${\mathrm{Ne}}^{\mathrm{*}\mathrm{*}}$ atoms in the {\ensuremath{\alpha}}\ensuremath{\equiv}{(2p${)}^{5}$(3p)} multiplet with ground-state He atoms. A newly designed cross-beam apparatus allows the measurement of accurate polarized cross sections ${Q}_{l\ensuremath{\leftarrow}k}^{\ensuremath{\Vert}{M}_{k}\ensuremath{\Vert}}$ for the {\ensuremath{\alpha}${\mathrm{}}}_{k}$\ensuremath{\rightarrow}{\ensuremath{\alpha}${\mathrm{}}}_{l}$ transition. In the experiment, the initial {\ensuremath{\alpha}${\mathrm{}}}_{k}$ state is prepared with a well-defined asymptotic orientation ${M}_{k}$ of its electronic angular momentum J, through excitation of metastable ${\mathrm{Ne}}^{\mathrm{*}}$ atoms with a polarized laser. The reported transitions are mainly between states in the {\ensuremath{\alpha}${\mathrm{}}}_{4}$,5,6,7 group (Paschen numbering), at approximately 100 meV center-of-mass energy. Some of these exhibit very strong polarization effects, with differences between ${Q}_{l\ensuremath{\leftarrow}k}^{\ensuremath{\Vert}{M}_{k}\ensuremath{\Vert}}$ and ${Q}_{l\ensuremath{\leftarrow}k}^{\ensuremath{\Vert}{M}_{k}^{\mathcal{'}}\ensuremath{\Vert}}$ of up to a factor 4. Fully quantum-mechanical coupled-channel calculations on a diabatic basis, with the ${\mathrm{Ne}}^{\mathrm{*}\mathrm{*}}$-He model potentials of Hennecart and Masnou-Seeuws as input, prove successful in reproducing experimental results. Cross-section behavior may be qualitatively understood from the presence of avoided crossings between the adiabatic potentials, indicative of strong radial coupling. The restraint of reflection symmetry is strongly felt here. In addition, the effects of rotational coupling can be readily identified.

Uniform semiclassical treatment of the radial coupling term in the adiabatic basis: Application to the excitation transfer He(1S)+Ne2+(1D)-->He(1S)+Ne2+(1S).

We present a uniform semiclassical analysis of the radial coupling A(r)(d/dr) in the adiabatic basis. Various approximations are tested for solving the perturbative form of the probability integrals. Our model is applied to the excitation transfer He(/sup 1/S)+Ne/sup 2/+(/sup 1/D)..-->..He(/sup 1/S)+Ne/sup 2 +/(/sup 1/S). The results we obtain are in good agreement among themselves and provide an alternative model in the adiabatic frame to complete the current Landau-Zener-Stueckelberg--like calculations. The dominating role of the turning points in such curve-crossing problems is also demonstrated.

Long-range intermolecular potentials for the metastable rare gas-rare gas systems Ar*, Kr*( 3P 0,2)+Ar, Kr, Xe

In a crossed beam experiment with a calibrated supersonic secondary beam the absolute value (rms accuracy 2.5%) and the velocity dependence of the total cross section Q have been measured in a wide range of relative velocities 500<g<5000 m s −1 for the title systems. The data have been analysed with the ion-atom Morse-Morse-spline-van der Waals potential of Gregor and Siska for the Ne*-Xe system as a reference, resulting in accurate values for the well depth ϵ, well position R m and long-range pure van der Waals constants C 6 (without the influence of C 8 and C 10). These long-range pure C 6 values are in excellent agreement with the calculated values of Dalgarno for the corresponding alkali atom-rare gas systems when scaled with the ratio of polarisabilities. The major difference in comparison with the alkali systems is the larger influence of the higher-order dispersion terms C 8 and C 10 (due to the ( np) −1 core hole), as reflected in the velocity dependence of the attractive contribution Q a ∝ (2ϵ R m/ ħg) 2/( s−1) with s=6.5–7 for high velocities and in the large amplitude of the glory contribution Q gl. For all systems the interesting N=1 glory maximum has been observed, with the glory range extending to the N=1.5 minimum for Ar*-Ar and to the N=6 maximum for Kr*-Xe. For the homonuclear systems only the glory oscillations due to the van der Waals-type potentials are observed. The glory damping due to the scattering on multiple potentials is described in terms of a rms spread Δ(ϵ R m) in the ϵ R m product, e.g., for Ar*-Ar we find Δ(ϵ R m)/ϵ R m=0.13. These measurements are fully complementary to the high-energy differential cross section measurements of Gillen et al., which only probe the chemical type potential with a deep well. For the heteronuclear Kr*-Xe system a strong velocity-dependent damping of the glory oscillations is observed, which can be described quantitatively by an excitation transfer process to a near-resonant short-lived Xe**((5p) 5 (6p)) state. The characteristic velocity dependence is used to calculate the radial coupling matrix element for this transition.

Alignment and orientation of the excited H(2p) orbital following H

A systematic theoretical study of alignment and orientation of the excited H(2p) orbital in H+He collisions in the energy range from 0.8 to 8 keV is carried out with use of a molecular-orbital representation. The present model takes the active electron in the H atom explicitly into account, while treating the He atom as a frozen core. Calculated alignment and orientation agree very well with recent measurements, implying that the dominant excitation mechanism for H(2p) excitation is the strong X /sup 2/..sigma..-A /sup 2/..sigma.. radial coupling for all energies studied. Hence, the integral alignment A/sub 20/ is negative and slowly varying with energy. Present partial excitation cross sections for H(2s) and H(2p) agree well with the corresponding measurements, except at energies below 1--2 keV.

Translational diffusion in liquids: Specific features of the spectral densities for isotropic intermolecular interactions

In theories of electron spin exchange and diffusion-induced direct proton tunnelling in solution, one has to calculate the spectral densities J(ω) of a purely radial intermolecular coupling resulting from a translational diffusion. By using the exact solutions of the diffusion equation, it is shown that at low frequencies, J(ω) = J(0)− Aω 1 2 , where J(0) and A are independent of the procedure used to incorporate the molecular impenetrability. On the other hand, at high frequencies, J(ω) strongly depends on the boundary conditions, decreasing as ω −2 in the presence of a reflecting wall at the molecular contact.

Ferropiezoelectricity of calcium modified lead titanate ceramics

When a ceramic with grain Boundaries rich in OPb is poled Beyond 4O kV cm−1 at ferroelectric phase, the highest anisotropy of electromechanical coupling factor is obtained. An attempt to explain this Behaviour is made in terms of domain switching and the strains and cracks generated during cooling down poling. Apart from composition, two more factors are revealed as contributing to the disappearance of radial coupling in Ca-modified lead titanate ceramics: microtexture and electric poling strategy.

Theoretical dipole transition moments for transitions between bound electronic states and non-adiabatic coupling matrix elements between2Σ+of HeH

Dipole transition moments and radial non-adiabatic coupling matrix elements between electronic states of HeH are presented. The estimated radiative lifetimes of the excited states of HeH are in good agreement with the available experimental data.