Radial Coupling Research Articles

Quasi-relativistic treatment of the low-lying KCs states

The potential energy curves, permanent and transition dipole moments as well as spin-orbit and angular coupling matrix elements between the KCs electronic states converging to the lowest three dissociation limits were evaluated in the basis of the spin-averaged wavefunctions corresponding to pure Hund’s coupling case ( a). The quasi-relativistic matrix elements have been obtained for a wide range of internuclear distance by using of small (9-electrons) effective core pseudopotentials of both atoms. The core-valence correlation has been accounted for a large scale multi-reference configuration interaction method combined with semi-empirical core polarization potentials. The static dipole polarizabilities of the ground X 1 Σ + and a 3 Σ + states were extracted from the closed-shell coupled-cluster energies by the finite-field method. Among the singlet and triplet Σ + states manifold the pronounced avoided crossing effect between repulsive walls of the (2,3) 3 Σ + states has been discovered and analyzed by finite-difference calculation of radial coupling matrix elements. The resulting transition dipole moments and potentials were used to predict radiative lifetimes and emission branching ratios of excited vibronic states while the calculated angular coupling matrix elements were transformed to Λ -doubling constants of the (1,2) 1 Π states and magnetic g -factor of the ground state. The accuracies of the present results are discussed by comparing with experimental data and preceding calculations.

Emergence and decay rate of the edge plasma flow shear near a critical transition

Recently, the experimental results for the emergence of the plasma shear flow layer in TJ-II have been explained as a second-order phase transition like process by using a simple model of envelope equations for the fluctuation level, the averaged poloidal velocity shear and the pressure gradient (2006 Phys. Plasmas 13 122509). Here, we extend this model by incorporating radial coupling. The model is applied to the study of the turbulence–shear flow interaction when the energy flux is low. Transition dynamics and their concomitant thresholds are examined within the context of this model. The effect of an external torque induced by electrode biasing has also been considered. In particular, we analyze the decay rate of the shear flow after switching off the biasing.

Role of secondary long wavelength structures in the saturation of electron temperature gradient driven turbulence

The dynamics of secondary long wavelength structures (LWSs) in electron temperature gradient (ETG) driven turbulence are investigated by performing gyrofluid simulations and modeling analyses in a slab geometry with an emphasis of the underlying nonlinear interaction processes. It is shown that the back-reaction of the secondary LWS on the ambient fluctuations essentially contributes to saturating ETG instability and limiting the electron transport. The LWS is nonlinearly generated mainly through the beating of the most unstable ETG modes, even a weak modulation instability. The back-reaction is identified as the enhanced stabilization of the ETG modes due to the streamer-type feature of the LWS, which dominantly produces a local poloidal mode coupling among unstable and highly damped spectral components to form a global mode, besides the suppression effect of the LWS due to the radial shearing decorrelation and/or the radial mode coupling. Finally, the correspondence between the LWS in the slab model and the quasimode observed in toroidal ETG simulation [Z. Lin et al., Phys. Plasmas 12, 056125 (2005)] and the importance of the nonlinear mode coupling in the multiscale turbulence interaction are discussed.

Culture conditions optimization of hyaluronic acid production by Streptococcus zooepidemicus based on radial basis function neural network and quantum-behaved particle swarm optimization algorithm

This study aimed to optimize the culture conditions (agitation speed, aeration rate and stirrer number) of hyaluronic acid production by Streptococcus zooepidemicus. Two optimization algorithms were used for comparison: response surface methodology (RSM) and radial basis function neural network coupling quantum-behaved particle swarm optimization algorithm (RBF-QPSO). In RBF-QPSO approach, RBF is employed to model the microbial HA production and QPSO algorithm is used to find the optimal culture conditions with the established RBF estimator as the objective function. The predicted maximum HA yield by RSM and RBF-QPSO was 5.27 and 5.62 g/l, respectively, while a maximum HA yield of 5.21 and 5.58 g/l was achieved in the validation experiments under the optimal culture conditions obtained by RSM and RBF-QPSO, respectively. It was indicated that both models provided similar quality predictions for the above three independent variables in terms of HA yield, but RBF model gives a slightly better fit to the measured data compared to RSM model. This work shows that the combination of RBF neural network with QPSO algorithm has good predictability and accuracy for bioprocess optimization and may be helpful to the other industrial bioprocesses optimization to improve productivity.

Investigation on the photofragmentation of hydrogen chloride

The photofragmentation of HCl molecules from the first absorption band has been studied. The extinction coefficients were obtained from numerical calculations, while the radial non-adiabatic transition probabilities for the excitation from the A 1Π 1 to the t 3 Σ 1 + electronic state are predicted by resorting to the Rosen–Zener–Demkov (RZD) model. The wavelength-dependent branching fraction is determined and agrees generally with experiment. The RZD coupling model is used to examine the contribution of the radial nonadiabatic transition, which causes the branching of the products. The results suggest that the foremost source of the redistribution of quantum flux is caused by radial derivative coupling, which occurs between the initially populated A state and the triplet t state. Furthermore, the interference effect is more apparent near the long-wavelength tail region of the A 1Π 1 ← X absorption profile.

Calculations of state-selective differential cross sections for charge transfer in collisions between O3+ and H2

The non-dissociative charge-transfer processes in collisions between O3+ and H2 are investigated by using the quantum-mechanical molecular-orbital coupled-channel (QMOCC) method. The adiabatic potentials and radial coupling matrix elements utilized in the QMOCC calculations are obtained with the spin-coupled valence-bond approach. Electronic and vibrational state-selective differential cross sections are presented for projectile energies of 0.1, 1.0 and 10.0 eV/u in the H2 orientation angles of 45° and 89°. The electronic and the vibrational state-selective differential cross sections show similar behaviours: they decrease as the scattering angle increases, and beyond a specific angle the oscillating structures appear. Moreover, it is also found that the vibrational state-selective differential cross sections are strongly orientation-dependent, which provides a possibility to determine the orientations of molecule H2 by identifying the vibrational state-selective differential scattering processes.

Ab initio potential energy surfaces and nonadiabatic collision dynamics in H++O2 system

The adiabatic potential energy surfaces for the lowest five electronic states of (3)A" symmetry for the H(+)+O(2) collision system have been obtained at the multireference configuration interaction level of accuracy using Dunning's correlation consistent polarized valence triple zeta basis set. The radial nonadiabatic coupling terms and the mixing angle between the lowest two electronic states (1 (3)A" and 2 (3)A"), which adiabatically correlate in the asymptotic limit to H((2)S)+O(2) (+)(X (2)Pi(g)) and H(+)+O(2)(X (3)Sigma(g)(-)), respectively, have been computed using ab initio procedures at the same level of accuracy to yield the corresponding quasidiabatic potential energy matrix. The computed strengths of the vibrational coupling matrix elements reflect the trend observed for inelastic vibrational excitations of O(2) in the experiments at collision energy of 9.5 eV. The quantum dynamics has been preformed on the newly obtained coupled quasidiabatic potential energy surfaces under the vibrational close-coupling rotational infinite-order sudden framework at the experimental collision energy of 9.5 eV. The present theoretical results for vibrational elastic/inelastic excitations of O(2) are in overall good agreement with the available experimental data obtained from the proton energy-loss spectra in molecular beam experiments [F. A. Gianturco et al., J. Phys. B 14, 667 (1981)]. The results for the complementary charge transfer processes are also presented at this collision energy.

Computed lifetimes of metastable states of the NO2+ dication

Based on the ab initio potential energy, spin-orbit coupling, electronic transition dipole moment, and radial nonadiabatic coupling functions, the energy level positions, lifetimes, and radiative transition probabilities (Einstein A coefficients) have been determined for the lowest electronic states of NO2+ using the log-amplitude-phase, stabilization, and complex-scaling methods. The calculated characteristics are in reasonable agreement to the available experimental data, thus, evidencing the reliability of the theoretical predictions for the characteristics unobserved to date. With the exception of the v<or=2 vibrational states of the B 2Sigma+ electronic state, the calculated radiative lifetimes of the excited electronic states are longer than their predissociation lifetimes, hence, accounting for the failure of the attempts which have been made so far to observe any emission from the latter states.

Quantum-mechanical calculations of vibrationally resolved cross sections for non-dissociative charge transfer of O3+ with H2

Charge transfer due to collisions of ground state O3+(2s22p 2P) ions with molecular hydrogen is investigated using the quantum-mechanical molecular-orbital close-coupling (MOCC) method，and electronic and vibrational state-selective cross sections along with the corresponding differential cross sections are calculated for projectile energies of 100，500，1000 and 5000eV/u at the orientation angles of 25°，45° and 89°. The adiabatic potentials and radial coupling matrix elements utilized in the QMOCC calculations were obtained with the spin-coupled valence-bond approach. The infinite order sudden approximation (IOSA) and the vibrational sudden approximation (VSA) are utilized to deal with the rotation of H2 and the coupling between the electron and the vibration of H2. It is found that the distribution of vibrationally resolved cross sections with the vibrational quantum number v′ of H+2(v′) varies with the increment of the projectile energy; and the electronic and vibrational state-selective differential cross sections show similar behaviors: there is a highest platform within a very small scattering angle，beyond which the differential cross sections decrease as the scattering angle increases and lots of oscillating structures appear，where the scattering angle of the first structure decreases as E-1/2p with the increment of the projectile energy Ep; and the structure and amplitude of the differential cross sections are sensitive to the orientation of molecule H2，which provides a possibility to identify the orientations of molecule H2 by the vibrational state-selective differential scattering processes.

Nonadiabatic coupling in cold collisions of spin-polarized metastable hydrogen atoms

Previous calculations of low-temperature cross sections for collisions between spin-polarized metastable hydrogen atoms are improved to include nonadiabatic radial and angular coupling at large interatomic separations. The electrostatic dipole-quadrupole interaction produces nonadiabatic radial coupling between (2s,2p) and (2p,2p) states, while the Coriolis interaction produces nonadiabatic angular coupling. Both of these long-range contributions are handled in a space-fixed atomic gauge that is particularly convenient for a spin-polarized system. The improved theoretical results are compared with an existing experiment.

POTHMF: A program for computing potential curves and matrix elements of the coupled adiabatic radial equations for a hydrogen-like atom in a homogeneous magnetic field

A FORTRAN 77 program is presented which calculates with the relative machine precision potential curves and matrix elements of the coupled adiabatic radial equations for a hydrogen-like atom in a homogeneous magnetic field. The potential curves are eigenvalues corresponding to the angular oblate spheroidal functions that compose adiabatic basis which depends on the radial variable as a parameter. The matrix elements of radial coupling are integrals in angular variables of the following two types: product of angular functions and the first derivative of angular functions in parameter, and product of the first derivatives of angular functions in parameter, respectively. The program calculates also the angular part of the dipole transition matrix elements (in the length form) expressed as integrals in angular variables involving product of a dipole operator and angular functions. Moreover, the program calculates asymptotic regular and irregular matrix solutions of the coupled adiabatic radial equations at the end of interval in radial variable needed for solving a multi-channel scattering problem by the generalized R-matrix method. Potential curves and radial matrix elements computed by the POTHMF program can be used for solving the bound state and multi-channel scattering problems. As a test desk, the program is applied to the calculation of the energy values, a short-range reaction matrix and corresponding wave functions with the help of the KANTBP program. Benchmark calculations for the known photoionization cross-sections are presented.

Strong Isotope Effects on the Charge Transfer in Slow Collisions ofHe2+with Atomic Hydrogen, Deuterium, and Tritium

Probabilities and cross sections for charge transfer by He2+ impact on atomic hydrogen (H), deuterium (D), and tritium (T) at low collision energies are calculated. The results are obtained using an ab initio theory, which solves the time-dependent Schrödinger equation. For the H target, excellent agreement is achieved between the present and previous results. Differences by orders of magnitude are observed between the cross sections for H, D, and T. A method is introduced to separate the contributions of charge-transfer mechanisms due to radial and rotational coupling. The large differences observed for H, D, and T are attributed to isotope effects in the rotational coupling mechanism.

Temperature stability of the piezoelectric properties of Li-modified KNN ceramics

Presently, the most promising family of lead-free piezoelectric ceramics is based on K 0.5Na 0.5NbO 3 (KNN). Lithium doped KNN ceramics show high piezoelectric properties at room temperature. An issue of particular interest for medical applications is the temperature stability of the properties because of the need for repeated sterilization process at around 140 °C. A concern with Li-doped KNN is that the properties may not be thermally stable because the orthorhombic–tetragonal phase transition temperature is close to the room temperature. We report on electromechanical properties of KNN-modified with 3–6 atomic % Li, measured by resonance technique in function of temperature from 20 to 140 °C, during two heating and cooling cycles. The piezoelectric coefficients d 31 and radial coupling coefficients k p are decreased up to 30% of their initial value after the first heating cycle. However, after the second cycle, the properties stabilize. The depoling is smaller in compositions that do not undergo a phase transition in the examined temperature interval.

Charge transfer and ionization in collisions ofSi3+with H from low to high energy

Charge transfer processes due to collisions of ground state ${\mathrm{Si}}^{3+}(3s\phantom{\rule{0.3em}{0ex}}^{1}S)$ ions with atomic hydrogen are investigated using the quantum-mechanical molecular-orbital close-coupling (MOCC) and classical-trajectory Monte Carlo (CTMC) methods. The MOCC calculations utilize ab initio adiabatic potentials and nonadiabatic radial coupling matrix elements obtained from Herrero et al. [J. Phys. B 29, 5583 (1996)] which were calculated with a full configuration-interaction method. Total and state-selective single-electron capture cross sections are obtained for collision energies from $0.01\phantom{\rule{0.3em}{0ex}}\mathrm{eV}∕\mathrm{u}$ to $1\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}∕\mathrm{u}$. Total and state-selective rate coefficients are also presented for temperatures from $2\ifmmode\times\else\texttimes\fi{}{10}^{3}\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ to ${10}^{7}\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. Comparison with existing data reveals that the total CTMC cross sections are in good agreement with the experimental measurements at the higher considered energies and that previous Landau-Zener calculations underestimate the total rate coefficients by a factor of up to two. The CTMC calculations of target ionization are presented for high energies.

Theoretical spectroscopy of the calcium dimer in the AΣu+1, cΠu3, and aΣu+3 manifolds: An ab initio nonadiabatic treatment

Nonadiabatic theory of molecular spectra of diatomic molecules is presented. It is shown that in the fully nonadiabatic framework, the rovibrational wave functions describing the nuclear motions in diatomic molecules can be obtained from a system of coupled differential equations. The rovibrational wave functions corresponding to various electronic states are coupled through the relativistic spin-orbit coupling interaction and through different radial and angular coupling terms, while the transition intensities can be written in terms of the ground state rovibrational wave function and bound rovibrational wave functions of all excited electronic states that are electric dipole connected with the ground state. This theory was applied in the nearly exact nonadiabatic calculations of energy levels, line positions, and intensities of the calcium dimer in the AΣu+1(1S1+1D1), cΠu3(1P3+1S1), and aΣu+3(1P3+1S1) manifolds of states. The excited state potentials were computed using a combination of the linear response theory within the coupled-cluster singles and doubles framework for the core-core and core-valence electronic correlations and of the full configuration interaction for the valence-valence correlation, and corrected for the one-electron relativistic terms resulting from the first-order many-electron Breit theory. The electric transition dipole moment governing the AΣu+1←XΣg+1 transitions was obtained as the first residue of the frequency-dependent polarization propagator computed with the coupled-cluster method restricted to single and double excitations, while the spin-orbit and nonadiabatic coupling matrix elements were computed with the multireference configuration interaction wave functions restricted to single and double excitations. Our theoretical results explain semiquantitatively all the features of the observed Ca2 spectrum in the AΣu+1(1S1+1D1), cΠu3(1P3+1S1), and aΣu+3(1P3+1S1) manifolds of states.

Evaluation of the adiabatic correction for LiH, RbH and CsH molecules

The evaluation of the first and second derivative of the non adiabatic coupling between the several 1Σ + adiabatic states of LiH, RbH and CsH molecules, is considered from accurate diabatic and adiabatic data. Such derivatives of the electronic wave function are determined through a numerical differentiation of the rotational matrix connecting the diabatic and adiabatic representations. The first as well as the second derivative presents many peaks, related to ionic–neutral and neutral–neutral coupling between the 1Σ + states. Such radial coupling has been exploited to calculate the first adiabatic correction, which corresponds to the diagonal term of the second derivative divided by the reduced mass, for the ground and some excited states of the three molecules. The second adiabatic correction has been determined using the Virial theorem. The first adiabatic correction was added to the adiabatic potential energy curves to re-determine the corrected spectroscopic constants and vibrational energy levels. The vibrational shift, which is the difference between the corrected and the adiabatic levels, has been calculated for X, A, C and D 1Σ + states of the three molecules. A shift of some 10 cm −1 is observed for some vibrational levels showing the breakdown of the Born–Oppenheimer approximation.

An ab initio study of the excited states of the vinoxy radical

Ab initio potential energy surfaces and radial coupling matrix elements of the vinoxy radical have been calculated in a subspace of two active angles involved in the photodissociation process. A quasidiabatic scheme has been developed in the vicinity of the conical intersection and some implications on the possible photodissociation mechanism of vinoxy from different formation path have been discussed.

Dielectric Permittivity Enhancement in PZT by Light Doping with Gd

ABSTRACTPbZr0.53Ti0.4703 doped with 0.6% at. of Gd2O3 has been produced following the traditional solid state reaction technique. The ferro-paraelectric transition temperature is reduced from 386 °C to 352 °C. Remnant polarization and coercive field measurements were made from the hysteresis loops obtained at 23 °C and at different applied electric fields up to a maximum of 17 kV/cm. Piezoelectric performance was studied in the 4 Hz to 4 MHz frequency range at 25 °C and the radial electromechanical coupling factor was determined. A detailed electrical conductivity study in the 30-450 °C temperature range is performed in a wide frequency interval. The different participating transport mechanisms are elucidated and the corresponding activation energies were determined by fitting the experimental data. In particular, in the 30 to 300 °C temperature interval, the ac conductivity follows Jonscher universal relaxation law.

Dynamical single-particle effects in the threshold fission cross section

A new formalism intended to simulate the cross section of the threshold neutron induced fission is proposed. The barriers corresponding to excited intrinsic single-particle states are taken explicitly into account. The radial coupling damping is treated within the Landau–Zener effect while the second-well damping due to re-emission in other channels is treated within an imaginary potential. In this context, the excitations are strongly dependent on the internuclear velocity between the two nascent fragments, and therefore managed by the dynamics of the system. An example of the neutron induced fission cross section of 234U is given.

An absolute coordinate formulation for three-dimensional flexible pipe analysis

A rather general absolute coordinate formulation is presented for the analysis of flexible pipe structure. The present formulation uses a similar line of approach adopted by Paulling and Webster (1986), which avoids the need of having to use infinitestiminal or finite rotations as nodal variables at the local floating frames of reference by expressing the structural response characteristics in terms of globally based position coordinate and its derivative to allow an accurate non-linear description of the pipe kinematics to be made, and extend the idea to include bending–torsion coupling, axial–radial coupling and bend restriction effect. The present formulation is also capable of handling internal flow effect, pre-bent section and irregular seabed interaction with friction effect, thus allowing an alternative general tool to be developed for riser, pipeline and flexible hose analyses.