Rotation and vibration of diatomic molecule oscillator with hyperbolic potential function

The explicit expressions of energy eigenvalues and eigenfunctions of bound states for a three-dimensional diatomic molecule oscillator with a hyperbolic potential function are obtained approximately by means of the hypergeometric series method. Then for a one-dimensional system, the rigorous solutions of bound states are solved with a similar method. The eigenfunctions of a one-dimensional diatomic molecule oscillator, expressed in terms of the Jacobi polynomial, are employed as an orthonormal basis set, and the analytic expressions of matrix elements for position and momentum operators are given in a closed form.     

Stoletov constant and the maximum of townsend coefficient as a function of the field strength

The relation between the Stoletov constant defined as a point corresponding to the maximum of the Townsend coefficient in pressure for a given field strength and the recently introduced constant corresponding to the maximum of the Townsend coefficient as a function of the field strength for a given pressure is investigated. We propose the use of a non-self-maintained discharge for an experimental study of the recently introduced runaway curves which, as distinct from the well-known Paschen curves, characterize the electron multiplication in a gas-discharge gap rather than the discharge ignition.     

Scattering of a diatomic molecule by a stationary surface

The CCGM [N. Cabrera, V. Celli, F.O. Goodman and R. Manson, Surface Sci. 19 (1970) 67] theory of elastic scattering (diffraction) of atoms by surfaces is generalized to the case of scattering of diatomic molecules. No extensive applications of the theory are made, but an example considered by R.M. Logan [Mol. Phys. 17 (1969) 147] of the scattering of a low-energy beam of h₂ by a cold surface is re-examined in the context of the new theory. It is concluded that, because of the uncertainties in the form of the molecule-surface interaction potential and in the values of the interaction parameters, no quantitative reliance can be placed on calculations of molecule-surface scattering probabilities at the present time. Future comparisons with experimental data should help to reduce these uncertainties.     

Angle-resolved spectra of the direct above-threshold ionization of diatomic molecule in IR + XUV laser fields

The direct above-threshold ionization(ATI) of diatomic molecules in linearly-polarized infrared and extreme ultraviolet(IR+XUV) laser fields is investigated by the frequency–domain theory based on the nonperturbative quantum electrodynamics. The destructive interference fringes on the angle-resolved ATI spectra, which are closely related to the molecular structure, can be well fitted by a simple predictive formula for any alignment of the molecular axis. By comparing the direct ATI spectra for monochromatic and two-color laser fields, we found that the XUV laser field can both raise the ionization probability and the kinetic energy of the ionized electron, while the infrared(IR) laser field can broaden the energy distribution of the ionized electron. Our results demonstrate that, by using IR+XUV two-color laser fields, the angle-resolved spectra of the direct ATI can image the structural information of molecules without considering the recollision process of the ionized electron.     

Electron impact ionization of diatomic molecules

Cross sections for the ionization of N₂, CO and O₂ diatomic molecules by electron impact are calculated. The applied distorted wave model is based on our previous studies for positron impact, the molecular orbitals being described by Gaussian wavefunctions. Our study emphasizes the importance of electron exchange and of using correct distorted waves for the ejected electron.     

The effective potential and the coupling constant at high temperature

The calculation of the effective potential at non-zero temperature is considered. A method of including relevant multi-loop diagrams in the effective potential formalism avoids problems that appear in some earlier treatments. This method is then used to calculate the temperature dependence of the effective coupling constant V⁽⁴⁾ in a scalar λø⁽⁴⁾ theory. The implementation of the renormalization group at high temperature is described, and is used ti show that V⁽⁴⁾ ≈λ/ [1 - (3/16π²)λ ln (T / μ)].     

United-atom projected perturbation theory for a homonuclear diatomic molecule

It is observed that the Byers-Brown united-atom perturbation theory corresponds to a particular version of the perturbation theory for projected states. Another, more localized version of the theory is suggested and tested on a solvable model.     

Vibrational excitation of diatomic molecular ions in strong field ionization of diatomic molecules

A model based on the strong-field and Born-Oppenheimer approximations qualitatively describes the distribution over vibrational states formed in a diatomic molecular ion following ionization of the neutral molecule by intense laser pulses. Good agreement is found with a recent experiment [X. Urbain et al., Phys. Rev. Lett. 92, 163004 (2004)]. In particular, the observed deviation from a Franck-Condon-like distribution is reproduced. Additionally, we demonstrate control of the vibrational distribution by a variation of the peak intensity or a change of frequency of the laser pulse.     

Translational and rotational motions of a diatomic molecule enclosed in a solid matrix

The hamiltonian for a molecule enclosed in a cavity may be written H = H ^R(θ) + H ^T(r) + U ^RT(θ, r), where θ and r denote the molecular orientation and the displacement of the centre of mass. The crystalline potential seen by the guest molecule can be explicitly calculated on the basis of atom-atom and electrostatic multipolar interactions, by using an nth-order gradient formula in the spherical representation. We take a N ₂ molecule encaged in β-quinol clathrate as our model system, and solve variationally the Schrödinger equation for H to clarify the translation-rotation coupling. Energy levels of H are obtained as a function of the height of the hindering potential for rotation, by modifying the strength of the electrostatic multipolar interaction. Three limiting cases of H ^R are important: (a) libration around the Z-axis, (b) free rotation, and (c) an oscillational rotation whose equilibrium orientation is perpendicular to the Z-axis. The constrained translation under consideration is an anharmonic and almost spherically symmetric oscillation. The Pauli principle must be applied to the eigenstate of H. Excepting the case (a), translational states of H are different for different nuclear spin species, and higher-order effects of U ^RT on these states are significant. For p-N₂, some modes of motion interchange if the rotational motion changes from case (a) to case (c). If the constraining potential for translation is steeper, the effect of U ^RT will become smaller. The anharmonicity involved in H ^T is not negligible in discussing this effect.     

Cooling of a nanomechanical resonator in presence of a single diatomic molecule

We propose a theoretical scheme for coupling a nanomechanical resonator to a single diatomic molecule via microwave cavity mode of a driven LC$LC$ resonator. We describe the diatomic molecule by a Morse potential and find the corresponding equations of motion of the hybrid system by using Fokker–Planck formalism. Analytical expressions for the effective frequency and the effective damping of the nanomechanical resonator are obtained. We analyze the ground state cooling of the nanomechanical resonator in presence of the diatomic molecule. The results confirm that presence of the molecule improves the cooling process of the mechanical resonator. Finally, the effect of molecule’s parameters on the cooling mechanism is studied.     

非Born-Oppenheimer近似一对双原子分子振动光谱的修正

为提高Born-Oppenheimer(BO)近似的精确度,修正BO近似所得到的令人不太满意的结果,此文在电子与原子核之间引入一个位相差,并利用小参数微扰法推导出了双原子分子核振动的波函数及红外能谱的计算公式,由修正后的结果得到的双原子分子红外振动光谱线的位置应更接近于实验观测值.     

Conditional stability of diatomic molecule driven by a weak laser field

Using a direct perturbation method, we investigate the stability of a diatomic molecule modelled by a weakly laser-driven Morse oscillator. It is shown that stationary state solution of the system is stable in the sense of Lyapunov and the periodical one possesses conditional stability, namely its stability depends on the initial conditions and system parameters. The corresponding sufficient and necessary conditions are established that indicate the stable states associated with some discrete energies. The results reveal how a diatomic molecule can be stabilized or dissociated with a weak laser, and demonstrate that the mathematical conditional stability works in the considered physical system.     

Vibrational analysis of nitrosamine,a molecule with an almost constant potential along the inversion coordinate

ABSTRACT

The fundamental vibrational transitions of nitrosamine and its doubly deuterated isotopologue have been computed by vibrational configuration interaction theory including up to 6-tuple excitations. The potential energy surface has been represented by an n-mode expansion up to 4-mode couplings terms obtained from explicitly correlated coupled-cluster theory, CCSD(T)-F12a. Very good agreement with experimental data has been been achieved and a number of new assignments is provided.     

在位势对于一维双原子链晶格振动长声学波的影响

根据声学模的定义,明确了具有在位势的一维双原子链的晶格振动不存在声学模,讨论了具有在位势的一维双原子链晶格振动的低频支长波模振动图像,得到原胞中两种原子运动的振幅不再一致,低频支长波模不再是原胞质心的运动,且两种原子运动的振幅比随在位势的增大而单调增大.