General method for the reduction of the effective rotational hamiltonian of molecules. Rational approximants and Padé approximants

A general method for reducing the effective rotational Hamiltonian for moleculesH _rot to the empirically constructed form in the {J_±, J_z} representation (molecules of the asymmetric-top type), applicable to Hamiltonians having improved convergence with nonpolynomial dependence on the angular momentum J, is developed. Rational forms for the reducedHrot and reduced Padé approximants for the rotational energy operator of the molecules are proposed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 32–37, August, 1985.     

Detection and analysis of new bands of O3 by CRDS between 6500 and 7300 cm

The absorption spectrum of the ¹⁶O₃ isotopologue of ozone has been recorded in the 7000-7920 cm⁻¹ region by high sensitivity CW-Cavity Ring Down Spectroscopy. This report is devoted to the analyses of the 7065-7300 cm⁻¹ region dominated by the ν₁ + 2ν₂ + 5ν₃ and ν₁ + 5ν₂ + 3ν₃ A-type bands at 7130.8 and 7286.8 cm⁻¹ respectively. 289 transitions were assigned to the ν₁ + 2ν₂ + 5ν₃ band. The corresponding line positions were modeled with an effective Hamiltonian involving Coriolis resonance interactions between the (1 2 5) upper state and the (4 4 0), (0 2 6) and (6 1 0) dark states, and an anharmonic resonance interaction with the (2 0 5) state. The very strong interaction (up to 50% mixing of the wavefunctions) between the (1 2 5) and (6 1 0) states leads to the observation of two extra lines of the 6ν₁ + ν₂ band due to a resonance intensity transfer. 213 transitions of the ν₁ + 5ν₂ + 3ν₃ band were assigned and modeled taking into account a Coriolis resonance interaction with the (3 6 0) state.We take the opportunity of the present work to report the analysis of the very weak 4ν₂ + 4ν₃ B-type band at 6506.1 cm⁻¹ which was assigned from previously recorded CRDS spectra. 286 transitions were modeled using the effective Hamiltonian approach.The dipole transition moment parameters of the three analyzed bands were determined by a least-squares fit to the measured line intensities. For the three studied band systems, the effective Hamiltonian and transition moment operator parameters were used to generate line lists provided as Supplementary Materials.     

Symmetry properties of the effective hamiltonians of some nonrigid molecules

Group-theoretical methods are used to identify the nonvanishing parameters and establish relations between them in the effective Hamiltonians which describe rotation and motion with large amplitude. The cases considered are 1) bending vibration in molecules of the type XY₂ and XYZ and 2) inversion vibration in pyramidal molecules of the type XY₃. For the latter type of molecule, the symmetry properties of the parameters in the effective centrifugal Hamiltonian for quasidegenerate inversion states are investigated. The general form of this Hamiltonian and its symmetry properties are established and studied in an arbitrary order in the small parameter.Translated from Izvestiya Vysshikh Uchebnykh Zavednii, Fizika, No. 2, pp. 22–26, February, 1981.     

Analysis of the CH3D Nonad from 2000 to 3300 cm

As part of the simultaneous analysis of line positions and intensities of the first two polyads of monodeuterated methane, the results achieved for the region 3-5 μm are reported. It involves the three highest fundamentals, (ν₁, ν₂, ν₄), overlapped by overtone (2ν₃, 2ν₅, 2ν₆) and combination (ν₃+ν₆, ν₃+ν₅, ν₅+ν₆) bands. The theoretical model was based on the global tensorial model implemented in the MIRS package. Some 10 000 line positions and 2400 line intensities have been modeled to ±0.000 88 cm⁻¹ and ±3.6% respectively, using measurements obtained at 0.0056 and 0.011 cm⁻¹ resolution with the Fourier transform spectrometer at National Solar Observatory located at Kitt Peak. The strongest band in this polyad is ν₄(E) at 3016.7 cm⁻¹ with a strength of 6.3×10⁻¹⁸ cm⁻¹/(molecule cm⁻²) at 296 K; the weakest band is 2ν₃(E) at 2597.7 cm⁻¹ with a strength of 1.9×10⁻²⁰ cm⁻¹/(molecule cm⁻²) at 296 K. The total calculated absorption arising from the CH₃D nonad is 8.95×10⁻¹⁸ cm⁻¹/(molecule cm⁻²) at 296 K.     

Analysis of High-Resolution Spectra of (18)O(3)

Using a Fourier transform spectrometer, we have recorded the spectra of the (18)O(3) species of ozone in the region 1300-3100 cm(-1), with a resolution of 0.003 cm(-1). The large product pathlength x pressure enable us to record 18 bands, 14 for the first time. The analysis has been performed using effective Hamiltonians for polyads of strongly interacting states for ozone, accounting for Coriolis and anharmonic resonances. The spectral parameters are derived for 16 vibrational states, including the two "dark" states (040) and (130). Various resonances are studied through the mixing coefficients of rovibrational wavefunctions. Systematic intensity measurements allow determination of transition moment parameters for 16 bands. Finally, a complete list of all transitions from 1300 to 3100 cm(-1), with cutoffs 10(-26) cm(-1)/mol cm(-2) (296 K), is calculated. Copyright 2001 Academic Press.     

Local field and radiative relaxation rate in a dielectric medium

The effect of macroscopic parameters of a substance on the optical characteristics of impurity particles is investigated. A generalized control equation is derived for two-level emitters forming an ensemble of optical centers in a transparent dielectric medium. In this equation, the effective values of the acting pump field and the radiative relaxation rate of an optical center are taken into account. The formalism developed here is a completely microscopic approach based on the chain of the Bogoliubov-Born-Green-Kirkwood-Yvon equations for reduced density matrices and correlation operators for material particles and modes of a quantized radiation field. The method used here makes it possible to take into account the effects of individual and collective behavior of emitters, which are associated with the presence of an intermediate medium, consistently without using phenomenological procedures. It is shown that the resultant analytic expression for the effective lifetime of the excited state of an optical center conforms with experimental data.     

Experimental study of the dynamics of penetration of a solid body into a soil medium

An experimental system is developed to determine the main parameters of the impact and penetration of a solid deformable body into a soft soil medium. This system is based on the technique of an inverse experiment with a measuring rod and the technique of a direct experiment with photo recording and the application of a shadow picture of the interaction of a striker with a soil target. To verify these techniques, the collision of a solid body with soil is studied by a numerical calculation and the time intervals in which the change of the resistance force is proportional to the penetration velocity squared are determined. The penetration resistance coefficients determined in direct and inverse experiments are shown to agree with each other in the collision velocity range 80–400 m/s, which supports the validity of the techniques and the reliability of measuring the total load.