Simplified closed form expressions for irreducible tensor operators

A general closed form expression is derived which enables one to write a spherical tensor of rank L and projection k, T_uk^L, in terms of the familiar angular momentum operators, S_z and S². The simplicity of this expression results from an intriguing relationship between these spherical tensor operators (diagonal operator equivalents) and successive derivatives of Tchebichef orthogonal polynomials.     

Calculation of the intensities of the vibrational-rotational lines of polyatomic molecules using the formalism of irreducible tensor systems

The theory of irreducible tensor systems is used to obtain general formulas for the dependence of the matrix elements of the transformed vibrational—rotational dipole moment on the rotational quantum numbers. The relations obtained are valid for molecules of arbitrary symmetry and can take into account all possible intramolecular effects and interactions (resonances, vibration—rotation interactions, splitting, etc.). As illustrations we consider molecules of the type XY₄ (symmetry T_d) and XY₂ (symmetry C_2v).Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, No. 8, pp. 3–10, August, 1987.     

Magnetic circular dichroism calculations using the irreducible tensor method

The irreducible tensor method is used to derive simple expressions for the magnetic circular dichroism (Faraday Effect) parameters A/D and C/D for electric dipole allowed and vibronic transitions.     

Bi-resonance functions in the theory of collisional broadening of the spectral lines of molecules

In the model of parabolic trajectories, expressions are derived for the bi-resonance functions that appear in the theory of collisional broadening of molecular spectral lines in the case of their interference. The functions required for calculating the cross-relaxation parameters of molecular spectral lines in the case of their broadening by rare gas atoms are obtained numerically in the model of exact trajectories for the isotropic Lennard-Jones 6–12 potential. Analytic models are proposed for these functions, and the corresponding parameters are obtained.     

Irreducible tensor operators and operations over them in the theory of molecular spectra

The explicit shape of symmetrized powers of three-dimensional representations of the groups Td and Oh is found in general form. Equations are obtained for calculating the vibrational commutators and matrix elements of irreducible tensor operators. Programs have been developed (in the C and FORTRAN languages) to remove the multiple-valued property of the vibrational-rotational Hamiltonian of spherical top molecules (CH₄, SiH₄, GeH₄, SF₆, and so on).Institute of Atmospheric Optics, Siberian Branch of the Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 16–25, March, 1993.     

Classical energy-momentum tensor renormalization via effective field theory methods

We apply the Effective Field Theory approach to General Relativity, introduced by Goldberger and Rothstein, to study point-like and string-like sources in the context of scalar-tensor theories of gravity. Within this framework we compute the classical energy-momentum tensor renormalization to first Post-Newtonian order or, in the case of extra scalar fields, up to first order in the (non-derivative) trilinear interaction terms: this allows to write down the corrections to the standard (Newtonian) gravitational potential and to the extra-scalar potential. In the case of one-dimensional extended sources we give an alternative derivation of the renormalization of the string tension enabling a re-analysis of the discrepancy between the results obtained by Dabholkar and Harvey in one paper and by Buonanno and Damour in another, already discussed in the latter.     

Matrix elements of tensor operators

The Wigner-Eckart theorem for matrix elements of tensor operators transforming according to a finite-dimensional representation of a non-compact semisimple Lie group is proved. The applications of this theorem are discussed.     

Pressure broadening of hydrogen sulfide

Microwave measurements of the self-broadening parameters of four pure rotational transitions of H₂S have been carried out in the millimeter and submillimeter wavelength region. The resulting parameters are (in MHz torr^-1): 1_1.0?1_0.1, 7.18±0.5; 2_2.0?2_1.1, 6.78±0.5; 2_1.1?2_0.2, 9.10±0.5; 3_3.0?3_2.1, 7.76 ±0.5. In addition. Anderson theory calculations have been carried out for these transitions and are found to be in good agreement.     

On the structure of tensor operators in SU3

A global algebraic formulation of SU3 tensor operator structure is achieved. A single irreducible unitary representation (irrep),V, ofso(6, 2) is constructed which contains every SU3 irrep precisely once. An algebra of polynomial differential operatorsA acting onV is given. The algebraA is shown to consist of linear combinations of all SU3 tensor operators with polynomial invariant operators as coefficients. By carrying out an analysis ofA, the multiplicity problem for SU3 tensor operators is resolved.Supported in part by the National Science Foundation     

Pressure broadening of UF6 by argon

Pressure broadening of the R(6) manifold in ν₃ of UF₆ at 628.32 cm^?1 has been measured at pressures of 0–30 torr of Ar in a long-path cell at 199 ± 1 K. We obtain a pressure-broadening coefficient of 9.0 ± 1.5 MHz/torr (FWHM), which corresponds to 7.3 ± 1.2 MHz/torr at 300 K. The UF₆-Ar optical collision diameter is 7.4 ± 0.6 Å; this is larger than the hard-sphere kinetic theory collision diameter of 5.2 Å obtained from the diffusion coefficient and implies rapid rotational relaxation.     

Ab initio ro-vibrational Hamiltonian in irreducible tensor formalism: a method for computing energy levels from potential energy surfaces for symmetric-top molecules

A theoretical approach to study ro-vibrational molecular states from a full nuclear Hamiltonian expressed in terms of normal-mode irreducible tensor operators is presented for the first time. Each term of the Hamiltonian expansion can thus be cast in the tensor form in a systematic way using the formalism of ladder operators. Pyramidal XY₃ molecules appear to be good candidates to validate this approach which allows taking advantage of the symmetry properties when doubly degenerate vibrational modes are considered. Examples of applications will be given for PH₃ where variational calculations have been carried out from our recent potential energy surface [Nikitin et al., J. Chem. Phys. 130, 244312 (2009)].     

The effect of tensor correlations on isovector operators

Very simple relations between renormalization factors and corrections to the GT-type-decay operator, isovector magnetic moment and coulomb energy differences between mirror nuclei due to tensor correlations are obtained.     

The effect of tensor correlations on isovector operators

Very simple relations between renormalization factors and corrections to the GT-typeΒ-decay operator, isovector magnetic moment and coulomb energy differences between mirror nuclei due to tensor correlations are obtained.     

Correlations in the quantum theory of plasma line broadening

A unified theory of plasma line broadening is obtained from a quantum kinetic equation, paralleling existing results for a classical plasma. The atom-electron interactions are shielded by equilibrium electron correlation functions and a frequency dependent dielectric function. A “ring” approximation is used to replace the classical plasma parameter expansion, for typical laboratory conditions. Atom-electron correlations are included as well as electron-electron correlations.     

Studies of scattering theory using numerical methods

Abstract

Numerical simulations, using both exact and approximate methods, are used to study rough surface scattering in both the smd and large roughness regimes. This study is limited lo scattcring lrom rough one-dimensional surfaces that obey the Dirichlet boundary condition and have a Gaussian roughness spectrum. For surfdces with small roughness (kh?1, where k is the radiation wavenumber and h is the root-mean-square (RMS) Surface height), perturbation theory is known to be valid. However, it is shown numerically that when kh?1 and kl?6 (where I is the surface correlation length) the Kirchhoffapprorimation is valid except at low grazing angles, and one must sum the first three orders of perturbation theory obtain the correct result. For kh?1 and kl?1, first-order perturbation theory is accurate. In this region, the accuracy of the first two terms of the iterative series solution of the exact integral equation is examined; the first term a1 this series is the Kirchhoff approximation, It is shown numerically that lor very small kh these first two terms reduce to first-order perturbation theory. However, lor this reduction to occur, kh must be made smaller than necessdry lor first-order perturbation theory to be accurate. In the regime of large roughness (kh?1) backscattering enhancement occurs when the RMS slope is on the order of unity. Several investigators have recently shown that the second term of the iterative series solution (the double-scattering term) replicates the properties of backscattering enhancement reasonably well. However, the double-scattering term has a lundamental flaw: predictions lor the scattering cross section per unit length based on the double-scattering term increase as the surfdce length is increased. This is shown here with numerical simulations and with an approximate analytical result based on the high frequency limit. The physical significance of this finding is also discussed. The final topic is the use of the double-scattering approximation to study the mechanism for backscattering enhancement with the Dirichlet boundary condition. This mechanism is usually assumed to be interference between reciprocal scattering paths. When the interlerence between reciprocal scattering paths is removed, the enhancement is eliminated. This shows that interference between reciprocal paths is almost certainly the dominant mechanism for backscattering enhancement in the scattering regime studied.     

Pressure broadening of millimeter lines of carbon monoxide

We report measurements on self-, N₂-, O₂-, and He-broadened widths of the 230-GHz line of carbon monoxide. The temperature dependence of the broadening parameters has been studied in the range 220–300 K. The results are compared with values previously obtained for the 115-GHz line and with published infrared data on the J = 1 ← 0 and J = 2 ← 1 transitions of carbon monoxide.     

Pressure broadening of OCS in the 10μm region

We report diode laser heterodyne measurements of pressure-broadening coefficients of OCS in the 020°–00°0 vibrational band of OCS and compare these measurements and previously reported microwave measurements with calculations performed with a recent cutoff-free impact technique.