A generalized approach to the calculation of ro-vibrational spectra of triatomic molecules

A generalization of the well known atom-diatom scattering hamiltonian to a coordinate system of two lengths and an angle is derived, another special case of which is a previously known bond angle-bond length hamiltonian. Different axis embeddings are also considered. The formalism is applied to the ro-vibrational levels of D₂H⁺, CH⁺ ₂ and HDHe (A ¹ A′) and the advantage of a judicious choice of coordinates demonstrated. The vibrational band origins for HDHe*, the first predictions for this system for which previous calculations had failed, are obtained using a new geometrically defined coordinate system. It is suggested that these coordinates might be used to represent isotopically substituted van der Waals complexes.     

Convergence properties and theoretical implications of a scattering theory calculations of molecular structure

The non-hermitian wave function formalism of the channel coupling array theory of many-body scattering has been tested through exact calculations on the H⁺₂ molecular ion. Numerical methods, convergence properties and theoretical implications of the results are discussed.     

4HeH+核间距的实验测定

用MeV量级⁴HeH⁺在超薄无衬碳膜中的库仑爆炸,获得高频离子源产生⁴HeH⁺核间距的实测值为0.094±0.003nm.发现⁴HeH⁺与H⁺₂,H⁺₃不一样,其核间距大小和离子源种类及离子源参数有密切关系,并从⁴HeH⁺的形成机理与形成条件,解 关键词：     

Effects of the internuclear vector on the photoelectron angular distributions of H<Subscript>2</Subscript><Superscript>+</Superscript>

We study the photoelectron angular distributions (PADs) of diatomic molecule H₂ ⁺ irradiated by intense laser fields using a nonperturbative scattering theory. We find that the internuclear vector may change the PADs. The PADs have qualitative changes with the increasing of the internuclear distance. The molecular orientation affect the symmetry of the PADs. When the internuclear vector is vertical or parallel to the laser polarization vector, the PADs are four-fold symmetric; for other case the PADs are two-fold symmetric. Due to the modulation effect resulting from the molecular multi-core nature, the size of the jet and the main lobe can be enlarged or reduced. The molecular modulation effect become obvious for large internuclear distance.     

One-centre multipole calculation of second-order perturbation energies for H+ 2

A knowledge of the H(1s) pseudospectrum allows one to calculate the one-centre second-order perturbation energies for the H(1s)-H⁺ interaction. The efficiency of such calculations is tested in detail for induction, exchange-induction, first-order overlap and Murrell-Shaw-Musher-Amos second-order energies for the ground and excited state H₊ ² at different internuclear distances. It is found that a large number of STO functions accounting for at least the first sixteen non-expanded multipoles is needed to obtain three figure accuracy in the short to medium range of internuclear separations. Higher accuracy can be obtained only in terms of a sensibly smaller number of two-centre functions which automatically satisfy the electron-nucleus cusp requirement.     

Enhanced dissociation of H2+ into highly excited states by UV pulses

We theoretically study the dissociation of H₂⁺ by UV laser pulses as a function of the photon energy ω of the pulse. Our results show that pronounced enhancements of the dissociation into highly excited electronic states can be achieved at some critical ω. This is found to be attributed to a consecutively resonant excitation mechanism where the population is first transferred to the first excited state by absorbing one photon and then to higher states by absorbing another one or more photons at the same internuclear distance. This study indicates that the strong coupling between the lowest two states of H₂⁺ can significantly affect the dissociation through higher lying states.     

An expansion method for calculating molecular properties IV.

The energies of the 2pσ and 2sσ states of H₂ ⁺ and HeH²⁺ and those of the a ³, A ¹, b ³, B ¹Σ⁺ states of HeH⁺ are calculated up to second order in the heavy nuclear charge. For the one-electron systems the first-order equation is solved analytically employing a special separation technique for degeneracies. The consideration of screening enables a recently proposed interchange result for the degenerate case to be tested. The results for the 2sσ states are good while those for the 2pσ states are only good at small internuclear distances.

For the two-electron systems the method employed is a single perturbation approach for two perturbations in the presence of degeneracy. The results for HeH⁺ appear to be good only at small internuclear distances. The corresponding results for the excited states of H₂ are omitted since an interesting problem arises at first order.     

Strings in the CP2N−1 model

The CP₂^N?1 model is discussed using strings as collective variables in the hamiltonian formulation. The large N limit is obtained as a semiclassical approximation. The mass gap and β-function are computed. In the limit N → ∞, it is shown that the singlet spectrum contains both bound states and scattering states whose energies and wave functions are calculated.     

Experimental and theoretical study of charge transfer in hydrogen ion scattering from a graphite surface

Ion scattering spectrometry (ISS) with time of flight (TOF) analysis is employed to measure the ion fraction of positively charged hydrogen (H⁺) projectiles scattered from a well characterized highly oriented pyrolitc graphite (HOPG) surface at a 45° scattering angle, various ingoing/outgoing angles and two different incoming energies (4 and 5 keV). In the theoretical approach, the negative ionization probability is calculated by employing a Green's function formalism to solve the dynamic collisional process. Both theoretical and experimental results are analyzed and contrasted. The theoretical negative ion fraction evolution during the collisional process is described in detail.     

Quasimolecular or kinematical broadening of autoionization electron spectra from Li+/He collisions? a coincidence study

We have measured energy- and angular distributions of autoionization electrons from Li⁺/He collisions in coincidence with the scattered Li⁺ projectiles. The coincident energy spectra do not exhibit the broad structures that are observed in the non coincident spectra and which in the past were attributed to quasimolecular autoionization of the (LiHe)⁺ system. We show that these broad structures are caused by kinematical shifts of electron spectra from pure atomic autoionization following different scattering events. With an exploitation of published inelastic differential scattering cross sections and with the assumption that the angular electron distribution with respect to the asymptotic internuclear line is nearly independent of the scattering angle we are able to reproduce the non coincident electron spectra satisfactorily.     

Energy values for the H+2 ion in superstrong magnetic fields using the adiabatic approximation

Energy values, equilibrium internuclear separations, and zero-point energies of nuclear vibrations parallel to the magnetic field are calculated for the lowest states of the H⁺₂ ion in magnetic fields B?10⁶ T (characteristic of neutron stars) using numerical wave functions that are products of Landau states and arbitrary z-dependent functions, thus improving on previous estimates of variational or LCAO type, which have been obtained in the high-field regime.     

Properties of the adiabatic energy curves for the ground states of H2+, HD+, and D2+

Equilibrium internuclear distances, energies, and force constants are reported for the diatomic molecules H₂⁺, HD⁺, and D₂⁺ at the adiabatic level of approximation. The differences between these values and those calculated previously at the Born-Oppenheimer level of approximation are analyzed.     

Application of symmetry coupling coefficients in zero-field splitting of d5 ion complexes

Symmetry coupling coefficients and symmetry reduced matrix elements are used in calculating the minimum required matrix elements required to determine the analytical expressions for the three ⁶ A ₁ ground-state energy levels for a d⁵ ion in a weak crystal field of tetragonal symmetry. Expressions for the spin hamiltonian parameters a, D, F and G are derived, from which the effect of spin-orbit coupling and the tetragonal component of the crystal field are examined. The parameters describe the form of the hamiltonian and consequently the spin eigenfunctions and eigenvalues of the ground state where a is a measure of the isotropic component whereas D, F and G measure the tetragonal component of the interaction giving rise to the zero-field splitting. Some experimental results are examined.     

Strong coupling limit of the gφ4 theory

The strong coupling limit of the gφ⁴ theory in the framework of the path integral formalism. An expansion of the Green's functions in negative powers of the coupling constant is obtained; at each order the dependence on the external momenta is of polynomial type. A renormalization procedure is proposed; the asymptotic behaviour of the Callan-Symanzik β function is studied and the existence of a stable ultraviolet fixed point is established.     

Dissociative ionization of molecules in intense laser fields

Accurate and efficient grid based techniques for the solution of the time-dependent Schrödinger equation for few-electron diatomic molecules irradiated by intense, ultrashort laser pulses are described. These are based on hybrid finite-difference, Lagrange mesh techniques. The methods are applied in three scenarios, namely H₂ ⁺ with fixed internuclear separation, H₂ ⁺ with vibrating nuclei and H₂ with fixed internuclear separation and illustrative results presented.Received: 19 November 2002, Published online: 24 April 2003PACS: 02.60.Cb Numerical simulation; solution of equations - 02.70.Bf Finite-difference methods - 33.80.Rv Multiphoton ionization and excitation to highly excited states (e.g., Rydberg states) - 33.80.-b Photon interactions with molecules     

The H—H+, H+—H+ and H—H fragmentation in the collision-induced dissociation of H 2 + ions

The collision-induced dissociation of 10 keV H ₂ ⁺ ions incident on H₂ has been studied in this paper. Total cross sections and angle distributions for the H⁺-H, H⁺-H⁺ and H-H fragmentations are given. Distributions over both angle and velocity have been measured for the H-H⁺ and H-H fragmentation.     

An operator approach to the strong coupling transmutation of a Yukawa interaction

It is shown that the transmutation mechanism introduced in our earlier papers is both necessary and sufficient to ensure the equivalence of the Lee model and the attractive separable potential model in all sectors when the bare coupling constant of the Lee model is taken to infinity. It is demonstrated that the hamiltonian operator for the Lee model reduces to that for the separable potential. It is further demonstrated that in the same limit the finite energy eigenfunctions, and hence the scattering amplitudes and the S-matrix calculated from the two theories coincide in all sectors.     

Zur Gültigkeit von Hypervirialsätzen bei Variationsfunktionen

It is shown that the so-called hypervirial theorems found byHirschfelder and coworkers (Sect. 1) are satisfied for a large class of variational trial functions (Sect. 2). The results are applied to several variational approximations to the eigenfunctions of the H ₂ ⁺ molecule (Sect. 3).     

The isotope chemical shift of μ+ in HBr

The isotopic change of the magnetic shielding for a ⁺ in HBr is computed from first principles, using a cellular cluster multiple scattering method, for condensed matter, and for the free molecules.The isotope shift and the chemical shift in liquid Br₂ is evaluated with the obtained eigenfunctions and eigenvalues using Ramsey formalism. The computed isotope chemical shifts are comparable with the results of breskman and Kanofsky and of Williams and the solvent effect has the correct sign and order of magnitude.     

Asymptotic method for determining the amplitude for three-particle breakup: Neutron-deuteron scattering

The process of neutron-deuteron scattering at energies above the deuteron-breakup threshold is described within the three-body formalism of Faddeev equations. Use is made of the method of solving Faddeev equations in configuration space on the basis of expanding wave-function components in the asymptotic region in bases of eigenfunctions of specially chosen operators. Asymptotically, wave-function components are represented in the form of an expansion in an orthonormalized basis of functions depending on the hyperangle. This basis makes it possible to orthogonalize the contributions of elastic-scattering and breakup channels. The proposed method permits determining scattering and breakup parameters from the asymptotic representation of the wave function without reconstructing it over the entire configuration space. The scattering and breakup amplitudes for states of total spin S = 1/2 and 3/2 were obtained for the s-wave Faddeev equation.