Energetical structure of muonic molecular ions ddµ and dtµ

The long-lived states lying below then=2 threshold in muonic molecular ions ddµ and dtµ are reviewed. We have considered all the known long-lived states both of normal and anomalous spatial parity, the bound states as well as resonant three-body states of shape and Feshbach types. It is shown that these states could be satisfactorily classified in terms of the Born-Oppenheimer adiabatic theory. We calculate some characteristic properties of the Feshbach resonances, thus obtaining that the life-time of the 3d states is greater than 10^–11 s, and the fusion rate from these states less than 10⁹ s^–1. The geometry of the 4f(J=0,v=0) state shows that it does not obey approximate ungerade symmetry. On the contrary, the low vibrational 3d states are approximately of gerade symmetry, as a result these states decay ejecting dµ atoms in the same proportion as tµ atoms.     

A variational calculation of weakly bound rotational-vibrational states of the mesic molecules ddμ and dtμ

Variational calculations of energy levels, of ϵ_Jv and λ-factors of weakly bound rotational-vibrational states (J=1, v=1) of the mesic molecules ddμ and dtμ, which are of main interest for recent muon-catalysed fusion experiments are performed. A set of about 2000 basis functions has been used in calculations which has enabled us to obtain the following extrapolated values: ϵ₁₁ (ddμ) = −1.9750 ± 0.0002 eV and ϵ₁₁ (dtμ) = − 0.6604 ± 0.0002 eV.     

Quasiresonant formation of dtμ and ddμ mesic molecules in triple collisions

The quasiresonant mechanism of mesic molecule formation, in triple collisions of the type tμ+D₂+D₂→[(dtμ)d2e]_ν¹+D'₂ is considered. It is shown that at small resonance defects and big D₂ +T₂ mixture densities φ the rate of this process is λ_qr∼φ², and it is comparable with the rate λ_r∼λ of the resonant formation of mesic molecules in reactions of the type tμ+D₂→[(dtμ)d2e]_ν¹. The observable manifestations of the process considered and its role in muon catalyzed fusion in deuterium-tritium mixtures are discussed.     

Nuclear fusion rates from resonant states of 3Hedμ molecular ion

We present new theoretical calculations of nuclear fusion rates λ _f ^J from the resonant states of the muonic molecular ion ³Hedμ ⁺⁺ with total angular momenta J=0,1. As a byproduct, new very accurate variational wave functions for these states have been obtained. Using these wave functions, the probability density |Ψ(R=0)|² in a fusion region has been calculated by extrapolating the variational solution to small internuclear distances by means of the multi-channel adiabatic solution. Calculated fusion rates for the states J=0 and J=1 are: λ _f ⁰ =1.9·10⁵s^-1 and λ _f ¹ =0.65·10³s^-1, respectively. This revised version was published online in August 2006 with corrections to the Cover Date.     

Bound states of two-dimensional relativistic harmonic oscillators

We give the exact normalized bound state wavefunctions and energy expressions of the Klein-Gordon and Dirac equations with equal scalar and vector harmonic oscillator potentials in the two-dimensional space.     

A trial wave function to study of the structure of the molecular dd μ ion

This paper provides a new effort to study of the ddμ structure. The present work is numerically performed using a new trial wave function to the ddμ system in configuration of coupled channels. The present results of energies are more accurate than those of our previous work. The obtained results of formation rates are close to results published by Yu.V. Petrov et al. and giving strong indications that the trial wave function is good enough in determining the resonance states of the mentioned ionic molecule.     

Spectroscopic factors of resonance states with the Gamow shell model

We provide an investigation of the spectroscopic factor of resonance states in A=5-8 nuclei, utilizing the Gamow shell model(GSM). Within the GSM, the configuration mixing is taken into account exactly with the shell model framework, and the continuum coupling is addressed via the complex-energy Berggren ensemble, which treats bound, resonance, and non-resonant continuum single-particle states on an equal footing. As a result, both the configuration mixing and continuum coupling are meticulously...     

Bound states of the Klein－Gordon and Dirac equations for scalar and vector harmonic oscillator potentials

We give the exact bound states of the Klein－Gordon and Dirac equations with equal scalar and vector harmonic oscillator potentials.     

Bound states of the Klein－Gordon and Dirac equation for scalar and vector pseudoharmonic oscillator potentials

The exact bound state solutions of the Klein－Gordon equation and Dirac equation with scalar and vector pseudoharmonic oscillator potentials are obtained in this paper. Furthermore, we have used the supersymmetric quantum mechanics, shape invariance and alternative method to obtain the required results.     

Theoretical study of LiCl− and LiBr− molecular ions

The molecular structures and spectroscopic constants of the ground electronic states of LiCl^? and LiBr^? are investigated with the coupled-cluster method. To improve the accuracy of our calculations, we have employed the extrapolation schemes as well as corrections of the core–valence correlation and scalar relativistic effect. The equilibrium parameters, potential energy curves, force constants, vibrational energy levels and spectroscopic parameters of both molecular ions are derived, in which those of LiBr^? are reported for the first time. The electron affinities and vertical detachment energies of neutral and anionic LiCl and LiBr are also evaluated.     

Bound states of the Klein－Gordon equation for ring-shaped Kratzer-type potential

The exact normalized bound state wavefunctions and energy equations of Klein－Gordon equation with equal scalar and vector ring-shaped Kratzer-type potential have been obtained.     

Revised molecular constants and term values for the XΣ and AΠ states of NH

The vibration–rotation spectra of NH have been reinvestigated using laboratory spectra and infrared solar spectra recorded from orbit by the ACE and ATMOS instruments. In addition to identifying the previously unobserved 6–5 vibration–rotation band in the laboratory spectra, many additional high N rotational lines have been observed. By combining the new observations with the previously published data and recent far infrared data, an improved set of molecular constants and term values have been derived for the X³Σ⁻ and A³Π states.     

Excited states of the molecular ion (H2μ)+

The rotation-vibration spectrum of (H₂ )⁺ is computed. Radiative lifetimes of the excited states are of order 10^–4 s or more. These times can be considered infinite compared to the lifetime of ⁺. For the ion in a crystal the lifetimes are significantly decreased by interaction with polarized molecules of the lattice. Transition rates to the ground state are calculated for (H₂ )⁺ in a hydrogen crystal. The results make it possible to interpret the experimental data from SR investigations of hydrogen, deuterium and hydrogen-deuterium mixtures.     

CP asymmetry from the resonance effect of the B meson decay process with π and K final states

We present the novel V→K⁺K^-(V=φ,ρ,ω) resonance,which generates a strong phase associated with vector meson resonances,leading to significant CP asymmetry in the interference region.The φ→K⁺K^-,ρ→K⁺K^-,and ω→K⁺K^-resonances arise from the mixing of the vector mesons φ,ρ,and ω.We calculate the CP asymmetry from the decay mode of B→ KKπ(K).Meanwhile,the localized CP asymmetries are presented and a detailed analysis...     

Research on resonance and antiresonance states of free stator of traveling wave ultrasonic motors

Under the condition of high-power drive, the experimental phenomena of free stator of traveling wave ultrasonic motor takes on strong nonlinear effects. Firstly, its corresponding theories are established to analyze and compare the stator‘s performances at the resonance and antiresonance states. At the same time, some important parameters, such as resonance/antiresonance frequency, mechanical quality, electro-mechanic coupling, and the relative vibration effect, are selected elaborately to evaluate the vibrational performances of free stator. Then, some experimental schemes based on the laser vibration measurement are designed respectively. Under the different drives conditions, the experimental characterizations of free stator at the resonance and antiresonance states are analyzed systematically. Finally, The investigative results show that the performance at the antiresonance state is much better than that at the resonance state. Some conclusions of this paper can provide novel idea and guidance for the choosing of the operating states and driving modes of traveling wave ultrasonic motor.     

Bound fermion states in the field of a soliton of the nonlinear O(3) σ model

The (2 + 1)-dimensional nonlinear O(3) σ model whose n field is coupled to the fermion field by the Yukawa interaction has been examined. The cases of the isosinglet and isodoublet fermion fields with respect to the internal symmetry group have been considered. It has been shown that bound states of the fermion in the n field of a soliton of the nonlinear O(3) σ model exist for some variants of the Yukawa interaction. The absence of zeroth fermion modes in the n field of the soliton has been established. The properties of the ground state of the fermion have been numerically studied. In particular, it has been shown that an increase in the spatial size of the soliton results in a decrease in the energy of the ground state. This leads to the instability of the soliton in a certain region of the parameters of the model.     

Bound states of the Schrdinger equation for the Pschl-Teller double-ring-shaped Coulomb potential

Põschl--Teller double-ring-shaped Coulomb (PTDRSC) potential, the Coulomb potential surrounded by Põschl--Teller and double-ring-shaped inversed square potential, is put forward. In spherical polar coordinates, PTDRSC potential has supersymmetry and shape invariance in φ, θ and r coordinates. By using the method of supersymmetry and shape invariance, exact bound state solutions of Schrõdinger equation with PTDRSC potential are presented. The normalized φ, θ angular wave function expressed in terms of Jacobi polynomials and the normalized radial wave function expressed in terms of Laguerre polynomials are presented. Energy spectrum equations are obtained. Wave function and energy spectrum equations of the system are related to three quantum numbers and parameters of PTDRSC potential. The solutions of wave functions and corresponding eigenvalues are only suitable for the PTDRSC potential.     

Fast scheme for generating quantum-interference states and GHZ state of N trapped ions

We propose a fast scheme to generate the quantum-interference states of N trapped ions. In the scheme the ions are driven by a standing-wave laser beam whose carrier frequency is tuned such that the ion transition can take place. We also propose a simple and fast scheme to produce the GHZ state of N hot trapped ions and this scheme is insensitive to the heating of vibrational motion, which is important from the viewpoint of decoherence.     

The dependence of high-order harmonic generation on the laser frequency and inter-nuclear distance from multi-atom molecular ions

High-order harmonic generation from one-dimensional (1D) multi-atom molecular ions in an ultra-short laser field is theoretically investigated. The dynamics of the electron in a linearly polarized intense laser field is analyzed in terms of 1D Schrodinger equation with the Crank-Nicolson algorithm. The dependence of high-order harmonics on the laser frequency and the inter-nuclear distance is discussed. It is found that the optimum range of inter-nuclear distance should be changed to get extended harmonic generation for different laser frequency, and the lower frequency laser pulse is favorable to higher order harmonic generation as the inter-nuclear distance increases.     

Bound states in gauge theories as the Poincaré group representations

The bound-state generating functional is constructed in gauge theories. This construction is based on the Dirac Hamiltonian approach to gauge theories, the Poincaré group classification of fields and their nonlocal bound states, and the Markov-Yukawa constraint of irreducibility. The generating functional contains additional anomalous creations of pseudoscalar bound states: para-positronium in QED and mesons inQCDin the two-gamma processes of the type of γ + γ → π ₀ +para-positronium. The functional allows us to establish physically clear and transparent relations between the perturbativeQCD to its nonperturbative low-energy model by means of normal ordering and the quark and gluon condensates. In the limit of small current quark masses, the Gell-Mann-Oakes-Renner relation is derived from the Schwinger-Dyson and Bethe-Salpeter equations. The constituent quark masses can be calculated from a self-consistent nonlinear equation.