Legendre Polynomials and Angular Momentum

An introduction to Legendre polynomials as precursor to studying angular momentum in quantum chemistry,

Advance P. Chem. Problems (I) Populations, Partition Functions, Particle in Box, Harmonic Oscillators, Angular Momentum and Rigid Rotor

This is a set of P. Chem. problems posed at slightly higher than the normal text book level, for students who are continuing in the study of this subject.

Alternative Formulations for Angular Momentum Operators, Cartesian and Spherical Polar Forms

The conversion between representations of angular momentum in spherical polar and cartesian form is discussed.

Unimolecular Rovibrational Bound and Resonance States for Large Angular Momentum: J=20 Calculations for HO2

We explore the calculation of unimolecular bound states and resonances for deep-well species at large angular momentum using a Chebychev filter diagonalization scheme incorporating doubling of the autocorrelation function as presented recently by Neumaier and Mandelshtam [Phys. Rev. Lett. 86, 5031 (2001)]. The method has been employed to compute the challenging J=20 bound and resonance states for the HO2 system. The methodology has firstly been tested for J=2 in comparison with previous calculations, and then extended to J=20 using a parallel computing strategy. The quantum J-specific unimolecular dissociation rates for HO2-> H+O-2 in the energy range from 2.114 to 2.596 eV have been reported for the first time, and comparisons with the results of Troe and co-workers [J. Chem. Phys. 113, 11019 (2000) Phys. Chem. Chem. Phys. 2, 631 (2000)] from statistical adiabatic channel method/classical trajectory calculations have been made. For most of the energies, the reported statistical adiabatic channel method/classical trajectory rate constants agree well with the average of the fluctuating quantum-mechanical rates. Near the dissociation threshold, quantum rates fluctuate more severely, but their average is still in agreement with the statistical adiabatic channel method/classical trajectory results.

Angular momentum of S0 galaxies

The aim of this thesis is to study the angular momentum of a sample of S0 galaxies. In the quest to understand whether the formation of S0 galaxies is more closely linked to that of ellipticals or that of spirals, our goal is to compare the amount of their specific angular momentum as a function of stellar mass with respect to spirals. Through kinematic comparison between these different classes of galaxies we aim to understand if a scenario of passive evolution, in which the galaxy’s gas is consumed and the star formation is quenched, can be considered as plausible mechanism to explain the transformation from spirals to S0s. In order to derive the structural and photometric parameters of galaxy sub-components we performed a bulge-disc decomposition of optical images using GALFIT. The stellar kinematic of the galaxies was measured using integral field spectroscopic data from CALIFA survey. The development of new original software, based on a Monte Carlo Markov Chain algorithm, allowed us to obtain the values of the line of sight velocity and velocity dispersion of disc and bulge components. The result that we obtained is that S0 discs have a distribution of stellar specific angular momentum that is in full agreement with that of spiral discs, so the mechanism of simple fading can be considered as one of the most important for transformation from spirals to S0s.

Design and modeling of optical fibers for spatial division multiplexing using the orbital angular momentum of light

Les besoins toujours croissants en terme de transfert de données numériques poussent au développement de nouvelles technologies pour accroître la capacité des réseaux, notamment en ce qui concerne les réseaux de fibre optique. Parmi ces nouvelles technologies, le multiplexage spatial permet de multiplier la capacité des liens optiques actuels. Nous nous intéressons particulièrement à une forme de multiplexage spatial utilisant le moment cinétique orbital de la lumière comme base orthogonale pour séparer un certain nombre de canaux. Nous présentons d’abord les notions d’électromagnétisme et de physique nécessaires à la compréhension des développements ultérieurs. Les équations de Maxwell sont dérivées afin d’expliquer les modes scalaires et vectoriels de la fibre optique. Nous présentons également d’autres propriétés modales, soit la coupure des modes, et les indices de groupe et de dispersion. La notion de moment cinétique orbital est ensuite introduite, avec plus particulièrement ses applications dans le domaine des télécommunications. Dans une seconde partie, nous proposons la carte modale comme un outil pour aider au design des fibres optiques à quelques modes. Nous développons la solution vectorielle des équations de coupure des modes pour les fibres en anneau, puis nous généralisons ces équations pour tous les profils de fibres à trois couches. Enfin, nous donnons quelques exemples d’application de la carte modale. Dans la troisième partie, nous présentons des designs de fibres pour la transmission des modes avec un moment cinétique orbital. Les outils développés dans la seconde partie sont utilisés pour effectuer ces designs. Un premier design de fibre, caractérisé par un centre creux, est étudié et démontré. Puis un second design, une famille de fibres avec un profil en anneau, est étudié. Des mesures d’indice effectif et d’indice de groupe sont effectuées sur ces fibres. Les outils et les fibres développés auront permis une meilleure compréhension de la transmission dans la fibre optique des modes ayant un moment cinétique orbital. Nous espérons que ces avancements aideront à développer prochainement des systèmes de communications performants utilisant le multiplexage spatial.

Shaken not stirred: creating exotic angular momentum states by shaking an optical lattice

We propose a method to create higher orbital states of ultracold atoms in the Mott regime of an optical lattice. This is done by periodically modulating the position of the trap minima (known as shaking) and controlling the interference term of the lasers creating the lattice. These methods are combined with techniques of shortcuts to adiabaticity. As an example of this, we show specifically how to create an anti-ferromagnetic type ordering of angular momentum states of atoms. The specific pulse sequences are designed using Lewis-Riesenfeld invariants and a fourlevel model for each well. The results are compared with numerical simulations of the full Schrodinger equation.

Electronic structure and exciton states in the freestanding ZnO nanorods

The electronic structure and exciton states of cylindrical ZnO nanorods with radius from 2 to 6 nm are investigated based on the framework of the effective-mass theory. Using the adiabatic approximation, the exciton binding energies taking account of the dielectric mismatch are solved exactly when the total angular momentum of the exciton states L = 0 and L = +/- 1. We find that the exciton binding energies can be enhanced greatly by the dielectric mismatch and the calculated results are almost consistent with the experimental data. Meanwhile, we obtain the optical transition rule when the small spin-obit splitting Delta(so) of ZnO is neglected. Furthermore, the radiative lifetime and linear optical susceptibilities chi(w) of the exciton states are calculated theoretically. The theoretical results are consistent with the experimental data very well. (C) 2009 American Institute of Physics. [DOI 10.1063/1.3125456]

Energy-level shifts of a stationary hydrogen atom in a static external gravitational field with Schwarzschild geometry

he first order perturbations of the energy levels of a stationary hydrogen atom in a static external gravitational field, with Schwarzschild metric, are investigated. The energy shifts are calculated for the relativistic 1S, 2S, 2P, 3S, 3P, 3D, 4S, 4P, 4D, and 4F levels. The results show that the energy-level shifts of the states with total angular momentum quantum number 1/2 are all zero, and the ratio of absolute energy shifts with total angular momentum quantum number 5/2 is 145. This feature can be used to help us to distinguish the gravitational effect from other effects.

Gravitational corrections to energy-levels of a hydrogen atom

The first-order perturbations of the energy levels of a hydrogen atom in central internal gravitational field are investigated. The internal gravitational field is produced by the mass of the atomic nucleus. The energy shifts are calculated for the relativistic 1S, 2S, 2P, 3S, 3P, 3D, 4S, and 4P levels with Schwarzschild metric. The calculated results show that the gravitational corrections are sensitive to the total angular momentum quantum number.

Close-coupling time-dependent quantum dynamics study of the H+HCl reaction

The paper presents a theoretical study of the dynamics of the H + HCl system on the potential energy surface (PES) of Bian and Werner (Bian, W.; Werner, H. -J., J. Chem. Phys. 2000, 112, 220). A time-dependent wave packet approach was employed to calculate state-to-state reaction probabilities for the exchanged and abstraction channels. The most recent PES for the system has been used in the calculations. Reaction probabilities have also been calculated for several values of the total angular momentum J > 0. Those have then been used to estimate cross sections and rate constants for both channels. The calculated cross sections can be compared with the results of previous quasiclassical trajectory calculations and reaction dynamics experimental on the abstraction channel. In addition, the calculated rate constants are in the reasonably good agreement with experimental measurement.

Electron-impact excitation of Ni II: Effective collision strengths for optically allowed fine-structure transitions

In this paper, we present collision strengths and Maxwellian averaged effective collision strengths for the electron-impact excitation of Ni II. Attention is expressly concentrated on the optically allowed fine-structure transitions between the 3d 9, 3d 84s, and 3d 74s 2 even parity levels and the 3d 84p and 3d 74s 4p odd parity levels. The parallel RMATRXII R-matrix package has been recently extended to allow for the inclusion of relativistic fine-structure effects. This suite of codes has been utilized in conjunction with the parallel PSTGF and PSTGICF programs in order to compute converged total collision strengths for the allowed transitions with which this study is concerned. All 113 LS terms identified with the 3d 9, 3d 84s, 3d 74s 2, 3d 84p, and 3d 74s 4p basis configurations were included in the target wavefunction representation, giving rise to a sophisticated 295 jj-level, 1930 coupled channel scattering complex. Maxwellian averaged effective collision strengths have been computed at 30 individual electron temperatures ranging from 30 to 1,000,000 K. This range comfortably encompasses all temperatures significant to astrophysical and plasma applications. The convergence of the collision strengths is exhaustively investigated and comparisons are made with previous theoretical works, where significant discrepancies exist for the majority of transitions. We conclude that intrinsic in achieving converged collision strengths and thus effective collision strengths for the allowed transitions is the combined inclusion of contributions from the (N + 1) partial waves extending to a total angular momentum value of L = 50 and further contributions from even higher partial waves accomplished by employing a "top-up" procedure.

Electron scattering by atoms and ions using the Breit-Pauli Hamiltonian:An R-matrix approach

The R-matrix method describing the scattering of low-energy electrons by complex atoms and ions is extended to include terms of the Breit-Pauli Hamiltonian. An application is made to the astrophysically important 1s 2s S-1s 2s2p P transition in Fe XXIII, where in the most accurate calculations carried out all terms of the 1s 2s, 1s2s2p and 1s2p configurations are included in the expansion describing the collision. This gives up to 28 coupled channels for each total angular momentum and parity which are solved on a CRAY-1. The collision strengths are increased by more than a factor of two from their non-relativistic values at all energies considered.

Characterization of Bose-Hubbard models with quantum nondemolition measurements

We propose a scheme for the detection of quantum phase transitions in the one-dimensional (1D) Bose-Hubbard (BH) and 1D Extended Bose-Hubbard (EBH) models, using the nondemolition measurement technique of quantum polarization spectroscopy. We use collective measurements of the effective total angular momentum of a particular spatial mode to characterize the Mott insulator to superfluid phase transition in the BH model and the transition to a density wave state in the EBH model. We extend the application of collective measurements to the ground states at various deformations of a superlattice potential.

Tests of MULTIMODE calculations of rovibrational energies of CH4

We report variational calculations of rovibrational energies of CH4 using the code MULTIMODE and an ab initio force field of Schwenke and Partridge. The systematic convergence of the energies with respect to the level of mode coupling is presented. Converged vibrational energies calculated using the five-mode representation of the potential for zero total angular momentum are compared with previous, benchmark calculations based on Radau coordinates using this force field for zero total angular momentum and for J = 1. Very good agreement with the previous benchmark calculations is found. (c) 2006 Elsevier B.V. All rights reserved.