Radial Coupling Research Articles

Ab initio study of spectroscopic and radiative characteristics of ion-pair states of the Cl2 molecule

Electronic structure and radiative characteristics of low-lying ion-pair states of Cl2 converging to the Cl+(3P, 1D)+Cl−(1S) limits are studied. Ab initio calculations of potential energy curves for the valence and ion-pair states and dipole moments for transitions between them are carried out employing the multireference single- and double-excitation configuration interaction (MRD-CI) method, including spin–orbit coupling. It is shown that the lowest two pairs of the Ω=0u+, 1u ion-pair states arise from an avoided crossing between the Σu−3 and Πu3 parent Λ−S states, which leads to notably anharmonic shapes of the corresponding potential curves and their mixed Λ−S nature. This causes significant radial coupling, resulting in the strongly perturbed character of the 0u+ and 1u states observed experimentally. In contrast, their gerade counterparts run parallel to one another and exhibit much less perturbation. Spectroscopic properties of the computed adiabatic curves are in very good agreement with the available experimental data. Dipole moments have been calculated for parallel ion-pair–valence state transitions and radiative lifetimes have been obtained for the adiabatic ion-pair states. A reanalysis of the experimental bound–free emission spectra from the D0u+(3P2) state [N. K. Bibinov et al., Chem. Phys. 254, 89 (2000)] is given.

State-selective single and double electron capture in the collision ofN4+with He

Ab initio potential-energy curves and rotational and radial coupling matrix elements of the S and P molecular states involved in the collision of N with He are determined by means of configuration interaction methods. In the 1–50-keV laboratory energy range, the total and the partial electron capture cross sections have been obtained using a semiclassical approach. Comparison with experiment shows the importance of the double capture channels.

Electroncapture in collisions of S4+ with atomic hydrogen

Charge transfer processes due to collisions of ground stateS4+(3s2 1S) ions with atomic hydrogen areinvestigated for energies between 1 meV u-1 and10 MeV u-1 using thequantum mechanical molecular-orbital close-coupling (MOCC),atomic-orbital close-coupling, classical trajectory Monte Carlo(CTMC) and continuum distorted wave methods. The MOCCcalculations utilize ab initio adiabatic potentials andnonadiabatic radial coupling matrix elements obtained with thespin-coupled valence-bond approach. A number of variants of theCTMC approach were explored, including different momentum andradial distributions for the initial state, as well aseffective charge and quantum-defect models to determine thecorresponding quantum state after capture into finalpartially stripped S3+ excited classical states. Hydrogentarget isotope effects are explored and rate coefficients fortemperatures between 100 and 106 K are also presented.

Nonadiabatic effects in the lowest +(3P) ion-pair states of CIF

Nonadiabatic calculations of vibrational energies and wave functions are carried out for the E(0+, 3P2) and f(0+, 3P0) ion-pair states of the ClF molecule. It is shown that strong radial coupling between these 0+ states is caused by a significant variation of their 3Σ− and 3Π Λ-S contributions with internuclear distance and results in vibrational energy shifts as well as changes in the corresponding adiabatic vibrational wave functions. Both resonance and nonresonance interactions between vibronic levels of these two adiabatic states are found to be important, but significant mixing of the adiabatic wave functions can occur only for the nearly resonant levels located around f,v=3; E,v=7 and f,v=8; E,v=13. Nonadiabatic interactions are found to be responsible for the appearance of long-wavelength maxima in the f,v=3,4 emission spectra that was the subject of the discrepancy between theoretical and experimental data discussed in the previous paper [A. B. Alekseyev, H.-P. Liebermann, R. J. Buenker, and D. B. Kokh, J. Chem. Phys. 112, 2274 (2000)]. Inclusion of nonadiabatic effects leads to notably better agreement between the calculated and measured bound-free emission spectra.

Ab-initio-based model for the charge transfer mechanisms in Ar + + H 2O collisions

The mechanism of the charge-transfer reaction between water molecules and argon ions is analysed using a two-dimensional model with the reaction and HOH bending coordinates, which maintains the C 2v symmetry of the reaction system. Potential energy surfaces and nonadiabatic coupling matrix elements are computed using ab initio Möller-Plesset perturbation theory with multiple partitioning of the full Hamiltonian. Both ab initio calculations and semiclassical simulations of the vibrational distributions of the product H 2O +(Ã) ion indicate two possible charge-transfer mechanisms. The first involves a nonadiabatic transition induced by radial coupling, whereas the second is governed by the curve crossing along the bending coordinate. The coexistence of two mechanisms agrees qualitatively with that inferred from the experimental measurements.

Oriented chlorine atoms as a probe of the nonadiabatic photodissociation dynamics of molecular chlorine

Molecular chlorine was photolyzed using circularly polarized radiation at 310 and 330 nm, and orientation moments of the chlorine-atom Cl(2Pj) photofragment distributions were measured by resonance enhanced multiphoton ionization using circularly polarized light with Doppler resolution. The product atoms were found to be strongly oriented in the laboratory as a result of both incoherent and coherent dissociation mechanisms, and the orientation moments contributed by each of these mechanisms have been separately measured. The experimental results can be explained by nonadiabatic transitions from the C 1Π1u state to higher states of Ω=1u symmetry, induced by radial derivative coupling. Ab initio calculations indicate strong Rosen–Zener–Demkov noncrossing-type radial derivative couplings between states of 1u symmetry. The observed angular distribution (β parameter) indicates that 88% of Cl*(2P1/2) fragments produced at 310 nm originate from a perpendicular transition to the C state. The orientation measurements suggest that 67±16% of Cl*35(2P1/2) atoms dissociate via the 1u(3Σ1u+) state, and 21±6% dissociate via the 1u(3Δ1u) state.

A New Method for Solving an Eigenvalue Problem for a System of Three Coulomb Particles within the Hyperspherical Adiabatic Representation

The quantum mechanical three-body problem with Coulomb interaction is formulated within the adiabatic representation method using the hyperspherical coordinates. The Kantorovich method of reducing the multidimensional problem to the one-dimensional one is used. A new method for computing variable coefficients (potential matrix elements of radial coupling) of a resulting system of ordinary second-order differential equations is proposed. It allows the calculation of the coefficients with the same precision as the adiabatic functions obtained as solutions of an auxiliary parametric eigenvalue problem. In the method proposed, a new boundary parametric problem with respect to unknown derivatives of eigensolutions in the adiabatic variable (hyperradius) is formulated. An efficient, fast, and stable algorithm for solving the boundary problem with the same accuracy for the adiabatic eigenfunctions and their derivatives is proposed. The method developed is tested on a parametric eigenvalue problem for a hydrogen atom on a three-dimensional sphere that has an analytical solution. The accuracy, efficiency, and robustness of the algorithm are studied in detail. The method is also applied to the computation of the ground-state energy of the helium atom and negative hydrogen ion.

Conceptual design of a 42 GHz, 200 kW gyrotron operating in the TE5,2 mode

This paper deals with the conceptual design of a 42 GHz, 200 kW continuous wave gyrotron operating in the TE 5,2 mode with radial output coupling. The basic motivation and selection criteria are discussed and the design of the resonant cavity, magnetron injection gun, radio frequency (RF) guiding system, quasioptical output coupler and RF window is presented.

On the independence of nonadiabatic coupling elements on the choice of origin of the coordinate system

A finite-difference approach is employed to demonstrate the manner in which the values of nonadiabatic radial coupling matrix elements vary with the choice of origin of the nuclear coordinate system. Configuration interaction (CI) calculations for a series of excited states of the HCl molecule verify that such results do not depend on the location of the center of mass XCM as long as it is held fixed during the differentiation process. The reason that radial coupling matrix elements are found to vary with the choice of origin of the coordinate system in standard scattering formulations is that the corresponding motion is not purely internal but rather has a definite translational component, namely a linear dependence of XCM on the bond distance R is assumed. An identity which relates variations of such (mixed internal-translational motion) nonadiabatic coupling elements to the value of the electric dipole transition moment when the latter prescription is employed for choosing the origin of the nuclear coordinate system is also verified by the present CI calculations.

Microwave instability in electron storage rings

Tracking simulations, with the aim of studying the microwave regime with short and intense bunches, suggest different instability mechanisms, according to the impedance model. In order to get a better insight of the source of the instability, i.e. azimuthal or radial mode coupling, we choose to follow the Sacherer (IEEE Trans. Nucl. Sci. NS-24, 1977 1393) approach to investigate the stability of the stationnary solution. The generalized Sacherer's integral, including mode coupling and potential well distortion, is then solved by using the “step function technique” for the expansion of the radial function, as proposed by Oide and Yokoya (KEK Preprint-90-10, April, 1990). For illustration, the effect of the resonant frequency of a broadband resonator in the SOLEIL storage ring is studied. When the resonator frequency is much higher than the bunch spectrum width, azimuthal mode coupling can occur before radial mode coupling. When the resonator frequency is lower, radial mode coupling comes usually first, but two or more bunchlets are produced at relatively low current. The diffusion process between the bunchlets, which leads to the well-known “saw-tooth” behavior, originates actually from a fast-growing microwave instability. Lastly, the beneficial effect of an harmonic cavity on the microwave instability is estimated and discussed.

Ab initiocross sections for low-energy inelastic H+Na collisions

We report ab initio results for the integral cross section of the process $\mathrm{H}+\mathrm{N}\mathrm{a}(3s)\ensuremath{\rightarrow}\mathrm{H}+\mathrm{N}\mathrm{a}(3p)$ for collision energies from the threshold (2.1 eV) to 600 eV. We achieve a reasonable agreement with the experimental data, which are available for energies above 10 eV. The main contributions to the cross section come from a rotational coupling mechanism in the NaH triplet molecular system and from a curve-crossing mechanism in the singlet system. At very low energy (2.1--2.4 eV), the process is governed by a centrifugal barrier in the exit channel leading to orbital resonances. The Landau-Zener model provides a reasonable qualitative description of the radial coupling mechanism at high energies, but fails below 10 eV.

Piezoelectric and structural properties of Pb(Yb 1/2Nb 1/2)O 3–PbTiO 3–PbZrO 3 ceramics

Solid solution ceramics of the system xPb(Yb 1/2Nb 1/2)O 3– yPbTiO 3– zPbZrO 3, where x=0·1–0·8, y=0·1–0·7, z=0·1–0·8, and x+y+z=1, were prepared by the solid state reaction of powder materials. Ceramic, dielectric and piezoelectric properties and crystal structures of the system were studied. The system is composed of three crystal phases at room temperature: the monoclinic, tetragonal and rhombohedral. Sintering of the system xPb(Yb 1/2Nb 1/2)O 3– yPbTiO 3– zPbZrO 3 is much easier than that of each end compositions and well sintered ceramics were obtained for the compositions near the structural transformation boundary. Piezoelectric ceramics with high electric permittivities, high radial coupling coefficient, k r , and low mechanical quality factor were obtained for the compositions near the structural transformation. The composition Pb(Yb 1/2Nb 1/2) 0·1Ti 0·48Zr 0·42O 3 showed the highest k r of 0·61.

Single and double electron capture processes in slow Ne q+-He (q=10, 6) collisions

The cross sections for single and double electron capture to the states Ne9+ n) with n=3–6 and Ne8+(3l,n′l′), Ne8+(4l,n′l′) with n′⩾4 and also the cross sections for single electron capture to the states Ne5+(3) in collisions of Ne10+ and Ne6+ with He atoms are calculated for collision energies in the interval from 10 to 150 keV. The calculation is carried out in the multichannel Landau-Zener, Nikintin, and Landau-Zener-Chaplik models with allowance for the radial coupling of the channels at crossing points of the energies of the quasidiabatic twoelectron states of the quasimolecule. The energies of the two-electron states are calculated in the effective potential method to first order in perturbation theory in the residual electron-electron interaction. The energies of the adiabatic states in the neighborhoods of the crossings of quasidiabatic terms are determined by the configuration interaction method. It is found that in Ne10+-He collisions the electron is captured mainly to the n=5 state of the Ne9+ ion. The cross section for double electron capture to the 3lnl′ state (n⩾4) of the Ne8+ ion is an order of magnitude smaller than the cross section for single electron capture. The contribution to the total cross section for double electron charge transfer from the 4l4l′ 4l5l′, and 4l6l′ states is approximately 25%. The dependence of the cross sections for double electron charge transfer on the values of l and l′ is investigated.

スカンジウムニオブ酸鉛‐チタン酸鉛‐ジルコン酸鉛セラミックスの作製と電気的性質

Solid solution ceramics of the system xPb(Sc1/2Nb1/2)O3-yPbTiO3-zPbZrO3, where x=0-0.4, y=0.3-0.6, z=0-0.7, x+y+z=1, were prepared by the solid state reaction of powder materials. The density, dielectric and piezoelectric properties and crystal structures of sintered body were studied. The system was composed of three crystal phases at room temperature: the tetragonal, rhombohedral and orthorhombic. Sintering of the system xPb(Sc1/2Nb1/2)O3-yPbTiO3-zPbZrO3 was much easier than that of each terminal compositions, and well sintered ceramics were obtained for the composition near the morphotropic transformation.Piezoelectric ceramics with high dielectric constants and high radial coupling coefficient, kr, and low mechanical quality factor were obtained for the compositions near the morphotropic transformation. Pb(Sc1/2Nb1/2)0.3Ti0.44Zr0.26O3 ceramics showed the high kr of 0.67.

Ab initio study of charge transfer in low-energy collisions with helium

Charge transfer cross sections for collisions of ground state and excited state ) with atomic helium are presented for energies less than 250 eV . Using a fully quantum mechanical, molecular-orbital, close-coupling approach, the cross sections are calculated in a diabatic representation. Completely ab initio adiabatic potentials and nonadiabatic radial coupling matrix elements obtained with the spin-coupled valence-bond method are utilized. Rate coefficients for temperatures between 100 and 100 000 K and cross sections for collisions with isotopic are presented. Results for the reverse process, , are also given.

Non-adiabatic wavepacket dynamics for charge-exchange processes in ion-atom collisions: application to

The collisional system is studied as a test case to assess the efficiency of a full quantum time-dependent method to calculate charge-exchange cross sections. The molecular diabatic electronic channels are calculated at the CASSCF level from the adiabatic potential energy curves and the radial coupling matrix. The elements of the collision matrix are extracted, for each value of the total angular momentum K, by Fourier transforming the post-collisional amplitudes of the wavepackets which are prepared in the entry channel and propagated on the coupled effective channels for each value of K. The results are compared with previous calculations of cross sections obtained by solving the stationary scattering equations and with recent experimental results. The close-coupling wavepacket method also provides a time-dependent picture of the collision dynamics for any K value. The kinematic isotopic effect is also examined.

Quantum Charge Transfer Study of Triply Charged Ions in the Adiabatic Representation: the (BHe)3+ System

Full quantum charge transfer study of the process B3+ + He ® B2+ + He+ has been investigated in the collision energy range 1-102 eV using an ab-initio interaction potential. A new method to solve the Schrodinger equation in an adiabatic basis was used, where the radial and rotational coupling were taken into account, and the importance of the coupling between states of different symmetry was discussed. Moreover, by using the well known Landau-Zener model, it was concluded that the two state model cannot be applied for the present system, and this might indicate that such a model should be applied carefully for other systems when a charge transfer process is considered. Finally, the quantum total cross sections were compared with the previous published work of Gargaud and co-workers and a fair agreement was achieved.

Charge Transfer in Collisions of C+with H and H+with C

Charge transfer rate coefficients for collisions of C+ with H and H+ with C are presented for temperatures from 30,000 to 107 K and from 10 to 107 K, respectively. The rate coefficients were calculated from recommended cross sections deduced in a recent theoretical and experimental investigation that took into account previous measurements. Nonadiabatic radial coupling is the dominant mechanism for both reactions above ~50,000 K, but for lower temperatures the reaction of H+ with C proceeds primarily by radiative charge transfer. Implications, due to the magnitude of the rate coefficients, for various astrophysical environments are discussed.

Ab initio study of charge transfer in low energy collisions with atomic hydrogen

Charge transfer cross sections for collisions of ground state and excited state with atomic hydrogen are presented for energies less than . The cross sections are calculated in a diabatic representation using a fully quantum-mechanical, molecular-orbital, close-coupled method. Completely ab initio adiabatic potentials and nonadiabatic radial coupling matrix elements obtained with the spin-coupled valence-bond method are incorporated. Inclusion of the and closed-channels results in oscillations in the charge transfer cross section for collision energies above the separated-atom energy of the lowest closed-channel . Rate coefficients for temperatures between 500 and 100 000 K and cross sections for collisions with isotopic D are presented. Results for the reverse process, charge transfer ionization, are also given.

イッテルビウムニオブ酸鉛‐チタン酸鉛‐ジルコン酸鉛セラミックスの作製と電気的性質

Solid solution ceramics of the system xPb (Yb1/2Nb1/2) O3-yPbTiO3-zPbZrO3, where x=0.1-0.7, y=0.2-0.7, z=0.1-0.7, and x+y+z=1, were prepared by the solid state reaction of powder materials. Ceramic, dielectric and piezoelectric properties and crystal structures of the system were studied. The system is composed of three crystal phases at room temperature: the monoclinic, tetragonal and rhombohedral. Sintering of the system xPb (Yb1/2Nb1/2) O3-yPbTiO3-zPbZrO3 is much easier than that of each terminal compositions and well sintered ceramics were obtained for the compositions near the morphotropic transformation. Piezoelectric ceramics with high dielectric constants and high radial coupling coefficient, kr, and low mechanical quality factor were obtained for the compositions near the morphotropic transformation. The composition Pb (Yb1/2Nb1/2)0.1Ti0.5Zr0.4O3 showed the highest kr of 0.46.