Irreducible Tensor Formalism Research Articles

A model-independent irreducible tensor formalism to analyse the sequential decays of the triple strange process [formula omitted

A model-independent irreducible tensor formalism is developed to analyse Ω¯Ω production in p¯p collisions and its subsequent decay via the triple-strange decay process, Ω¯+Ω−→K+Λ¯K−Λ→K+p¯π+K−pπ−. These processes are relevant for the upcoming experiments at PANDA. We not only provide expressions for the density matrix of the ΩΩ¯ system but also for the products at each stage of the decay. The Fano statistical tensors so obtained not only completely characterize the relevant final systems but also provide expressions for joint angular distributions. Finally, we show which of the Fano statistical tensors characterizing the Ω¯Ω system can be inferred from the Fano statistical tensors characterizing the final p¯p system, wherein we also obtain the relation between the production cross sections for ΩΩ¯ and the final pp¯ system.

Thomson Scattering above Solar Active Regions and an Ad Hoc Polarization Correction Method for the Emissive Corona

Thomson-scattered photospheric light is the dominant constituent of the lower solar corona’s spectral continuum viewed off-limb at optical wavelengths. Known as the K-corona, it is also linearly polarized. We investigate the possibility of using the a priori polarized characteristics of the K-corona, together with polarized emission lines, to measure and correct instrument-induced polarized crosstalk. First we derive the Stokes parameters of the Thomson scattering of unpolarized light in an irreducible spherical tensor formalism. This allows forward synthesis of the Thomson-scattered signal for the more complex scenario that includes symmetry-breaking features in the incident radiation field, which could limit the accuracy of our proposed technique. For this, we make use of an advanced 3D radiative magnetohydrodynamic coronal model. Together with synthesized polarized signals in the Fe xiii 10746 Å emission line, we find that an ad hoc correction of telescope- and instrument-induced polarization crosstalk is possible under the assumption of a nondepolarizing optical system.

Complete analysis of beam analyzing powers in at near threshold energies

Focusing attention on the photon spin in at near threshold energies of interest to Big Bang Nucleosynthesis, a complete analysis of beam analyzing powers in reaction is carried out. A complete analysis of the reaction needs not only measurements using one state of linear polarization of photon but also measurements using another state of linear polarization inclined to the first at π/4 and the two states of circular polarization of the photon. A discussion on the complete characterization of the states of photon polarization is presented. The beam analyzing powers with respect to photon polarization are discussed theoretically, using model independent irreducible tensor formalism.

Model independent approach to photodisintegration of 7 Li at the range of energies of interest to BBN

One of the elements that was synthesized primordially in the standard Big Bang Nucleosynthesis is lithium. Lithium, being fragile gets easily destroyed at relatively low temperatures in the mixing process between stellar surface and hot internal layers. So that, at the end of the stellar lifetime the lithium content is believed to be depleted. Series of experimental measurements on lithium isotopes were carried out at High Intensity Gamma Ray Source (HIGS) at Duke Free Electron Laser Laboratory. More recently experiments [1]-[2] were performed, to measure the differential cross section of the photo-neutron reaction channel in photodisintegration of 7 Li, where the progeny nuclei is in the ground state as well as in excited states. The purpose of present contribution is to study the reaction channel 7 Li + γ → 6 Li + n using linearly polarized photons. The model independent irreducible tensor formalism [3]-[5] will be used to study the differential cross section of the reaction. We study the angular dependence of differential cross section by expressing differential cross section in terms of legendre polynomials. In view of the several theoretical and ongoing experimental studies, a detailed theoretical study of the spin structure of the amplitudes in 7 Li + γ → 6 Li + n and their expansion in terms of ’electric’ and ‘magnetic’ amplitudes is needed to analyze the measurements of spin observables as well as differential cross section, which leads to a better understanding of the problem at astrophysical energies

Model independent analysis in (γ, n) reactions using deuterium targets

Photonuclear reactions play an important role in nuclear physics, astrophysics and in various applications such as non-destructive measurement of nuclear materials (NDT). The study of (γ, n) reactions using deuterium targets i.e., photodisintegration of deuterons in addition to all the other (γ, n) reactions, is of considerable interest to these fields. In this contribution, we have studied the photodisintegration of deuterons with unpolarized photons. The angular dependence of the differential cross section is studied by expressing it in terms of Legendre polynomials. The analysis of differential cross-section is presented using the model-independent irreducible tensor formalism.

Chiral Four-Wave Mixing Signals with Circularly Polarized X-ray Pulses.

Chiral four-wave mixing signals are calculated using the irreducible tensor formalism. Different polarization and crossing angle configurations allow to single out the magnetic dipole and the electric quadrupole interactions. Other configurations can reveal that the chiral interaction occurs at a given step within the nonlinear interaction pathways. Applications are made to the study of valence excitations of S-ibuprofen by chiral stimulated X-ray Raman signals at the carbon K-edge and by chiral visible 2D electronic spectroscopy.

Magneto-optical spectroscopy with arbitrarily polarized intensity-modulated light in He4 atoms

We present both a theoretical and experimental study of the magneto-optical spectra induced with intensity-modulated resonant laser light that synchronously pumps and detects the metastable $^{4}\mathrm{He}$ atoms in the presence of a quasistatic magnetic field. We extend previous work and derive complete analytical expressions for the resonance signals by taking into account arbitrary magnetic-field directions and arbitrary light polarizations. The analytical results are derived by solving the Liouville equation using the irreducible tensor formalism on the assumption of low light power. We discuss the potential application of the derived analytical results in constructing and optimizing a dead-zone-free all-optical atomic magnetometer.

Generalised descriptions on orientational order parameters and mean field theory for uniaxial and biaxial nematic liquid crystals

ABSTRACTWe present a complete set of the orientational and pseudo-vector (or polar) order parameters and a general potential of mean torque responsible for the formation of a lowest symmetry of triclinic biaxial nematic phases. By adopting the irreducible spherical tensor formalism, twenty-five orientational and nine pseudo-vector (or polar) order parameters are explicitly expressed in terms of both the Saupe ordering supermatrix and the Wigner rotation matrices. For various biaxial nematic phases and molecules, the corresponding independent order parameters are uniquely classified, including the orthorhombic monoclinic , and triclinic symmetries as well as the uniaxial nematic phase. These works could also describe the order parameters for the smectic C phases and the polar biaxial phases composed of symmetry.

Accurate first-principles calculations for 12CH3D infrared spectra from isotopic and symmetry transformations

Accurate variational high-resolution spectra calculations in the range 0-8000 cm(-1) are reported for the first time for the monodeutered methane ((12)CH3D). Global calculations were performed by using recent ab initio surfaces for line positions and line intensities derived from the main isotopologue (12)CH4. Calculation of excited vibrational levels and high-J rovibrational states is described by using the normal mode Eckart-Watson Hamiltonian combined with irreducible tensor formalism and appropriate numerical procedures for solving the quantum nuclear motion problem. The isotopic H→D substitution is studied in details by means of symmetry and nonlinear normal mode coordinate transformations. Theoretical spectra predictions are given up to J = 25 and compared with the HITRAN 2012 database representing a compilation of line lists derived from analyses of experimental spectra. The results are in very good agreement with available empirical data suggesting that a large number of yet unassigned lines in observed spectra could be identified and modeled using the present approach.

Translational transformations of tensor solutions of the Helmholtz equation and their application to describe interactions in force fields of various physical nature

Using group theory and irreducible tensor formalism we derive formulas for translational transformations of the tensor solutions of the Helmholtz equation. These formulas can be used to solve different problems in theoretical and mathematical physics, where it is necessary to relate boundary conditions for two or more spatial bodies. We show that these formulas can be used to perform invariant expansions of the interaction energy of the bodies in force fields of different physical nature. These expansions have a number of advantages and are very efficient and convenient to study force interactions. Examples from celestial mechanics, space vehicle dynamics and electric current interactions are given.

Nonstationary theory of polarized light pulse propagation through a four-level resonant medium with allowance for nonlinear complex refractive index of medium

Nonstationary theory of polarized light pulse propagation through the medium with resonant transition 1/2 -1/2 is developed with taking into account complexity of the medium nonlinear refractive index. The theory is developed based on the irreducible tensor formalism which allows diagonalizing relaxations matrix and introducing effective decay times associated with the population relaxation, as well as relaxation of coherence between magnetic sublevels of the resonant system. It is shown that as a result of interference of magnetic sublevels in the polarized radiation field the inversionless amplification of radiation occurs due to optical pumping process. The dependence of inversionless amplification on the line broadening and resonance detuning is studied.

Ground-state Hanle effect based on atomic alignment

We have studied the ground-state Hanle effect (GSHE) excited by linearly polarized laser light on the $D$${}_{1}$ line of cesium atoms. We have solved algebraically the Liouville equation using the irreducible tensor formalism, and derive an analytical expression for the resonance line shapes in a magnetic field of arbitrary direction. The model predictions are in excellent agreement with experimental observations in various field geometries. Our model is valid for arbitrary $F\ensuremath{\rightarrow}{F}^{\ensuremath{'}}$ transitions in the low-power limit. We discuss the relation between the GSHE and electromagnetically induced transparency or absorption. Our approach allows a full understanding of the mechanism of the GSHE and provides tools for quantifying the resonance contrast, a crucial parameter for metrological applications of level crossing resonances.

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)].

Collision-induced absorption byCO2in the far infrared: Analysis of leading-order moments and interpretation of the experiment

The diagrammatic theory, developed recently by the authors [Phys. Rev. A 74, 012732 (2006)], is applied to binary collision-induced properties, with emphasis on induced dipole moments. Assuming rototranslational dynamics to be classical and using irreducible spherical tensor formalism, exact analytical formulas are worked out for the two leading order spectral moments of a collision-induced band by two interacting linear molecules. The formulas are applied to the far infrared absorption by ${\text{CO}}_{2}{\text{-CO}}_{2}$, and permit interpretation of the experiment. This study provides evidence of the adequacy of the electrostatic induction mechanism, provided that hitherto missing vibrational terms of static polarizability are considered.

Quantum state tomography for quadrupolar nuclei using global rotations of the spin system

In this paper, we describe a quantum state tomography method based on global rotations of the spin system which, together with a coherence selection scheme, enables the complete density matrix reconstruction. The main advantage of this technique, in respect to previous proposals, is the use of much shorter rf pulses, which decreases significantly the time necessary for algorithm quantum state tomography. In this case, under adequate experimental conditions, the rf pulses correspond to simple spatial rotations of the spin states, and its analytical description is conveniently given in the irreducible tensor formalism. Simulated results show the feasibility of the method for a single spin 72 nucleus. As an experimental result, we exemplify the application of this method by tomographing the steps during the implementation of the Deutsch algorithm. The algorithm was implemented in a (23)Na quadrupole nucleus using the strongly modulated pulses technique. We also extended the tomography method for a 3-coupled homonuclear spin 12 system, where an additional evolution under the internal Hamiltonian is necessary for zero order coherences evaluation.

Relaxation of diatomic molecules by isotropic collisions: application to depolarizing collisions of CS by He atoms

An irreducible tensor formalism is applied to isotropic collisions of diatomic molecules with 1S atoms. Explicit expressions of the generalized spectroscopic relaxation cross sections are given, including pressure broadening cross sections as well as collisional transfer and destruction cross sections of the k-component of the target density matrix. For applications in the high temperature limit, formulae within the infinite order sudden approximation (IOS) are given for 1Σ electronic state molecules and 2S+1Σ electronic state molecules in the Hund's case (b) limit. Application to collisions of CS by He atoms shows that a good agreement is found between close coupling and IOS results at moderate energies and that multipolar depolarizing rates within a j-level are of the same order of magnitude whatever the considered multipole order k whereas multipolar transfer rates are lower by an order of magnitude. Propensity rules in relation to the CS–He potential energy surface are given.

Intermolecular Raman spectroscopy of long-range interactions: TheCO2−Arcollision-inducedν3CO2band

We report an exhaustive joint theoretical/experimental collision-induced Raman scattering (CIRS) study of the Raman-forbidden ${\ensuremath{\nu}}_{3}$ band of $\mathrm{C}{\mathrm{O}}_{2}$. Original zeroth and second anisotropic spectral moment formulas for $\mathrm{C}{\mathrm{O}}_{2}\text{\ensuremath{-}}\mathrm{Ar}$ are derived, in which complete expressions of Raman amplitudes (derived by the authors with a recently reported universal method [Phys. Rev. A 74, 012723 (2006)]) are input. The method, applicable to any kind of spectroscopy and whatever the number of photons, molecules, or interaction involved, uses the irreducible spherical tensor formalism in conjunction with a Feynman-like diagrammatic technique to describe any long-range induced property mechanism. Experimentally, spectral moments are deduced from careful, absolute-scale, frequency-resolved $\mathrm{C}{\mathrm{O}}_{2}\text{\ensuremath{-}}\mathrm{Ar}$ depolarized CIRS measurements of unprecedented accuracy. From comparison between theory and experiment, we provide quantitative evidence of a substantial contribution of a nonlinear dipole polarization mechanism, predicted theoretically in the preceding paper. In this mechanism, both photons are shown to interact with Ar (which then couples to $\mathrm{C}{\mathrm{O}}_{2}$ via intermolecular interactions), rather than with both colliders that is the case in the standard dipole-induced quadrupole (DIQ) interaction. The effect had thus far escaped notice possibly because of the reduced accuracy of the earlier self-consistent field dipole-quadrupole polarizablity computations along with a lack of CIRS measurements. In light of recent extensive computations by Haskopoulos and Maroulis [Chem. Phys. Lett. 417, 235 (2006)], the improved ab initio data of these properties are found to corroborate our predictions, and confirm that the Raman amplitude owing to the dipole-dipole-quadrupole hyperpolarizability of the atomic perturber strongly and destructively interferes with the (otherwise dominant) DIQ Raman amplitude.

Photodisintegration of polarized deuterons at astrophysical energies

A model independent irreducible tensor formalism, developed earlier for np fusion, is extended to discuss photodisintegration of the deuteron at astrophysical energies. It is shown that target analysing powers at θ = π/2 provide a sensitive test to the presence of isoscalar M1 and E2 amplitudes. It is also suggested that a measurement of the coefficient of cos θ in the differential cross section for photodisintegration at photon energies below 2.5 MeV could be very useful to assess the contribution of the isoscalar amplitudes at the astrophysically relevant range of energies to sharpen the predictions of big bang nucleosynthesis (BBN).

ω production inppcollisions

A model-independent irreducible tensor formalism that was developed earlier to analyze measurements of $\stackrel{\ensuremath{\rightarrow}}{p}\stackrel{\ensuremath{\rightarrow}}{p}\ensuremath{\rightarrow}\mathit{pp}{\ensuremath{\pi}}^{\ifmmode^\circ\else\textdegree\fi{}}$ is extended to present a theoretical discussion of $\stackrel{\ensuremath{\rightarrow}}{p}\stackrel{\ensuremath{\rightarrow}}{p}\ensuremath{\rightarrow}pp\ensuremath{\omega}$ and of \ensuremath{\omega} polarization in $\mathit{pp}\ensuremath{\rightarrow}\mathit{pp}\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\omega}}$ and in $p\stackrel{\ensuremath{\rightarrow}}{p}\ensuremath{\rightarrow}pp\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\omega}}$. The recent measurement of an unpolarized differential cross section for $pp\ensuremath{\rightarrow}pp\ensuremath{\omega}$ is analyzed by use of this theoretical formalism.

The MIRS computer package for modeling the rovibrational spectra of polyatomic molecules

The MIRS spectroscopic software for the modeling of ro-vibrational spectra of polyatomic molecules is presented. It is designed for the global treatment of complex band systems of molecules to take full account of symmetry properties. It includes efficient algorithms based on the irreducible tensor formalism. Predictions and simultaneous data fitting (positions and intensities) are implemented as well as advanced options related to group theory algebra. Illustrative examples on CH 3D, CH 4, CH 3Cl and PH 3 are reported and the present status of data available is given. It is written in C ++ for standard PC computer operating under Windows. The full package including on-line documentation and recent data is freely available at the URL: http://www.u-bourgogne.fr/LPUB/MIRS.html.