Search results for "Formalism"
showing 10 items of 357 documents
Tensorial Development of the Rovibronic Hamiltonian and Dipole Moment Operators for XY3Z Molecules with a Degenerate Electronic State. Preliminary Ap…
2009
Abstract We present a development of the Hamiltonian and transition moment operators of XY3Z ( C 3 v ) symmetric tops molecules in a degenerate electronic state with the aid of a tensorial formalism developed in a recent paper [A. El Hilali, V. Boudon, M. Loete, J. Mol. Spectrosc. 239 (2006) 41–50]. Electronic operators are defined from group theory properties. They provide a new approach to build an effective rovibronic Hamiltonian as well as an effective dipole moment operator for rovibronic transition of XY3Z molecules. This model is studied qualitatively thanks to the tensorial algebra properties. Expressions of the matrix elements are derived for these operators. A first simple applica…
Computing the position-spread tensor in the CAS-SCF formalism II: Spin partition
2016
Abstract The Spin-Partitioned (SP) Total Position-Spread (TPS) tensor provides finer insights that supplement the information conveyed in the Spin-Summed (SS) TPS. The calculation of the SP-TPS has been implemented in the MOLPRO code for CAS-SCF wavefunctions allowing the study of electron (de) localization in relatively large molecular systems where the FCI treatment is rather unfeasible. An illustrative example considering one-dimensional Be wires is given as an application of the formalism.
Spectroscopy of XY3Z (C3v) radicals with an odd number of electrons: A tensorial formalism adapted to the group chain
2006
Abstract A tensorial formalism adapted to the case of XY 3 Z symmetric tops with half integer angular momenta is proposed as an extension of the formalism for the group chain O (3) ⊃ C ∞ v ⊃ C 3 v developed in a recent paper [A. El Hilali, V. Boudon, M. Loete, J. Mol. Spectrosc. 234 (2005) 113–121]. We use the chain SU ( 2 ) ⊗ C I ⊃ C ∞ v S ⊃ C 3 v S , where G S ( G being C ∞ v or C 3 v ) is the G point group with its spinorial representations. Coupling coefficients and formulas for the computation of matrix elements of the tensor operators are derived for this chain. A deduction of coupling coefficients (Clebsch-Gordan, 6 C , 9 C , …) and similar formulas is proposed for the group C 3 …
Unitary Approach to Vibrational Spectra of Tetrahedral Molecules: Generalized Infrared Intensity Model.
1997
International audience; In this paper we further extend a previous formalism, the construction of a dipole function adapted to tetrahedral molecules. The extension is based on an algebraic construction of symmetrized tensor operators through unitary algebra and point group symmetry. We prove that this generalization allows us to find the particular formalism that has been established and satisfactorily tested in a previous paper (C. Leroy et al., J. Mol. Spectrosc. 175, 289–295 (1996)).
Rovibrational Interactions in the Local-Mode Limit: The (n000) Stretching Overtone Bands of Spherical Tops
1995
Abstract We present a tensorial formalism adapted to the study of the ( n 000) rovibrational stretching states of spherical tops in the local mode limit. A local symmetrized rovibrational basis is built to take explicitly into account the fact that, in these states, the local symmetry is C 3ν rather than T d . Likewise, we introduce local rovibrational operators to build an effective Hamiltonian for these states. We then test our model by fitting the energy levels of 28 SiH 4 for 3 ≤ n ≤ 5.
Stellar Wakes from Dark Matter Subhalos
2017
We propose a novel method utilizing stellar kinematic data to detect low-mass substructure in the Milky Way's dark matter halo. By probing characteristic wakes that a passing dark matter subhalo leaves in the phase space distribution of ambient halo stars, we estimate sensitivities down to subhalo masses $\sim 10^7\,M_\odot$ or below. The detection of such subhalos would have implications for dark-matter and cosmological models that predict modifications to the halo-mass function at low halo masses. We develop an analytic formalism for describing the perturbed stellar phase-space distributions, and we demonstrate through simulations the ability to detect subhalos using the phase-space model…
Progress in three-particle scattering from LQCD
2017
We present the status of our formalism for extracting three-particle scattering observables from lattice QCD (LQCD). The method relies on relating the discrete finite-volume spectrum of a quantum field theory with its scattering amplitudes. As the finite-volume spectrum can be directly determined in LQCD, this provides a method for determining scattering observables, and associated resonance properties, from the underlying theory. In a pair of papers published over the last two years, two of us have extended this approach to apply to relativistic three-particle scattering states. In this talk we summarize recent progress in checking and further extending this result. We describe an extensio…
Beam normal spin asymmetry for the ep→eΔ(1232) process
2017
We calculate the single spin asymmetry for the $e p \to e \Delta(1232)$ process, for an electron beam polarized normal to the scattering plane. Such single spin asymmetries vanish in the one-photon exchange approximation, and are directly proportional to the absorptive part of a two-photon exchange amplitude. As the intermediate state in such two-photon exchange process is on its mass shell, the asymmetry allows one to access for the first time the on-shell $\Delta \to \Delta$ as well as $N^\ast \to \Delta$ electromagnetic transitions. We present the general formalism to describe the $e p \to e \Delta$ beam normal spin asymmetry, and provide a numerical estimate of its value using the nucle…
Highly deformed bands in Nd nuclei: New results and consistent interpretation within the cranked Nilsson-Strutinsky formalism
2019
International audience; Three new highly-deformed (HD) bands are identified in Nd136 and the highly deformed band of Nd137 is extended at higher spin by four transitions, revealing a band crossing associated with the occupation of the second νi13/2 intruder orbital. Extended cranked Nilsson-Strutinsky calculations are performed for all HD bands observed in Nd134, Nd136, and Nd137, achieving for the first time a consistent interpretation of all HD bands in the Nd nuclei. The new interpretation has significant consequences, like the change of parity of the yrast HD bands of Nd134 and Nd136, and the involvement of two negative-parity neutron intruder orbitals in the configurations of most HD b…
Chapter 1 The Resolution Challenge in 3D Optical Microscopy
2009
Publisher Summary This chapter discusses the theoretical principles of 3D microscopy with the widespread realizations of 3D microscopy.Based on the paraxial diffraction equations, it has been shown that conventional microscopes, when dealing with 3D fluorescent samples, provide sets of 2D images. These images of the different transverse sections of the 3D object contain, in addition to the sharp image of the in focus section, the blurred images of the rest of the specimen. The paraxial formalism has been generalized in a very simple way to a non-paraxial context, showing that the equations that govern non-paraxial imaging are similar to those that govern paraxial imaging. The only differenc…