124 research outputs found
Electron-Molecule Col1isions: Quantitative Approaches, and the Legacy of Aaron Temkin
This article, on electron-molecule collisions, is dedicated to the legacy of my good friend and sometime collaborator, Aaron Temkin on his retirement from the NASA-Goddard Space Flight Center after many years of work at the highest intellectual level in the theoretical treatment of electron-atom and electron-molecule scattering. Aaron's contributions to the manner in which we think about electron-molecule collisions is clear to all of us who have worked in this field. I doubt that the great progress that has occurred in the computational treatment of such complex collision problems could have happened without these contributions. For a brief historical account, see the discussion of Temkin's contribution to electron-molecule scattering in the first article of this volume by Dr. A. K. Bhatia. In this article, I will concentrate on the application of the so called, non-adiabatic R-matrix theory, to vibrational excitation and dissociative attachment, although I will also present some results applying the Linear Algebraic and Kohn-Variational methods to vibrational excitation. As a starting point for almost all computationally effective approaches to electron-molecule collisions, is the fixed nuclei approximation. That is, one recognizes, just as one does with molecular bound states, that there is a separation of electronic(fast) and nuclear(s1ow) degrees of freedom. This separation makes it possible to "freeze" the nuclei in space, calculate the collision parameters for the frozen molecule and then, somehow to add back the vibrations and rotations. The manner in which this is done, depends on the details of the collision problem. It is the work of Aaron and a number of other researchers that has provided the guidance necessary to resolve these issues
Complete collision data set for electrons scattering on molecular hydrogen and its isotopologues: IV. Vibrationally-resolved ionization of the ground and excited electronic states
We present a comprehensive set of vibrationally-resolved cross sections for electron-impact ionization of molecular hydrogen and its isotopologues (H2, D2, T2, HD, HT, and DT) in both the ground and excited electronic states. We apply the adiabatic-nuclei molecular convergent close-coupling (MCCC) method to calculate cross sections from threshold to 1000 eV for ionization of the ground and excited vibrational levels of the X1ÎŁg+, B1ÎŁu+, C1Î u, EF1ÎŁg+, a3ÎŁg+, and c3Î u electronic states, representing all states with united-atoms-limit principle quantum number n=1â2. The cross sections are presented in graphical form and provided as both numerical values and analytic fit functions in supplementary data files. The data can also be downloaded from the MCCC database at mccc-db.org
Collective excitations of trapped Bose condensates in the energy and time domains
A time-dependent method for calculating the collective excitation frequencies
and densities of a trapped, inhomogeneous Bose-Einstein condensate with
circulation is presented. The results are compared with time-independent
solutions of the Bogoliubov-deGennes equations. The method is based on
time-dependent linear-response theory combined with spectral analysis of
moments of the excitation modes of interest. The technique is straightforward
to apply, is extremely efficient in our implementation with parallel FFT
methods, and produces highly accurate results. The method is suitable for
general trap geometries, condensate flows and condensates permeated with vortex
structures.Comment: 6 pages, 3 figures small typos fixe
Critical-point scaling function for the specific heat of a Ginzburg-Landau superconductor
If the zero-field transition in high temperature superconductors such as
YBa_2Cu_3O_7-\delta is a critical point in the universality class of the
3-dimensional XY model, then the general theory of critical phenomena predicts
the existence of a critical region in which thermodynamic functions have a
characteristic scaling form. We report the first attempt to calculate the
universal scaling function associated with the specific heat, for which
experimental data have become available in recent years. Scaling behaviour is
extracted from a renormalization-group analysis, and the 1/N expansion is
adopted as a means of approximation. The estimated scaling function is
qualitatively similar to that observed experimentally, and also to the
lowest-Landau-level scaling function used by some authors to provide an
alternative interpretation of the same data. Unfortunately, the 1/N expansion
is not sufficiently reliable at small values of N for a quantitative fit to be
feasible.Comment: 20 pages; 4 figure
Dark soliton states of Bose-Einstein condensates in anisotropic traps
Dark soliton states of Bose-Einstein condensates in harmonic traps are
studied both analytically and computationally by the direct solution of the
Gross-Pitaevskii equation in three dimensions. The ground and self-consistent
excited states are found numerically by relaxation in imaginary time. The
energy of a stationary soliton in a harmonic trap is shown to be independent of
density and geometry for large numbers of atoms. Large amplitude field
modulation at a frequency resonant with the energy of a dark soliton is found
to give rise to a state with multiple vortices. The Bogoliubov excitation
spectrum of the soliton state contains complex frequencies, which disappear for
sufficiently small numbers of atoms or large transverse confinement. The
relationship between these complex modes and the snake instability is
investigated numerically by propagation in real time.Comment: 11 pages, 8 embedded figures (two in color
Observing many body effects on lepton pair production from low mass enhancement and flow at RHIC and LHC energies
The spectral function at finite temperature calculated using the
real-time formalism of thermal field theory is used to evaluate the low mass
dilepton spectra. The analytic structure of the propagator is studied
and contributions to the dilepton yield in the region below the bare
peak from the different cuts in the spectral function are discussed. The
space-time integrated yield shows significant enhancement in the region below
the bare peak in the invariant mass spectra. It is argued that the
variation of the inverse slope of the transverse mass () distribution can
be used as an efficient tool to predict the presence of two different phases of
the matter during the evolution of the system. Sensitivity of the effective
temperature obtained from the slopes of the spectra to the medium effects
are studied
Spectral method for the time-dependent Gross-Pitaevskii equation with a harmonic trap
We study the numerical resolution of the time-dependent Gross-Pitaevskii
equation, a non-linear Schroedinger equation used to simulate the dynamics of
Bose-Einstein condensates. Considering condensates trapped in harmonic
potentials, we present an efficient algorithm by making use of a spectral
Galerkin method, using a basis set of harmonic oscillator functions, and the
Gauss-Hermite quadrature. We apply this algorithm to the simulation of
condensate breathing and scissors modes.Comment: 23 pages, 5 figure
Numerical approximation of the Euler-Poisson-Boltzmann model in the quasineutral limit
This paper analyzes various schemes for the Euler-Poisson-Boltzmann (EPB)
model of plasma physics. This model consists of the pressureless gas dynamics
equations coupled with the Poisson equation and where the Boltzmann relation
relates the potential to the electron density. If the quasi-neutral assumption
is made, the Poisson equation is replaced by the constraint of zero local
charge and the model reduces to the Isothermal Compressible Euler (ICE) model.
We compare a numerical strategy based on the EPB model to a strategy using a
reformulation (called REPB formulation). The REPB scheme captures the
quasi-neutral limit more accurately
Highly anisotropic Bose-Einstein condensates: crossover to lower dimensionality
We develop a simple analytical model based on a variational method to explain
the properties of trapped cylindrically symmetric Bose-Einstein condensates
(BEC) of varying degrees of anisotropy well into regimes of effective one
dimension (1D) and effective two dimension (2D). Our results are accurate in
regimes where the Thomas-Fermi approximation breaks down and they are shown to
be in agreement with recent experimental data.Comment: 4 pages, 2 figures; significantly more new material added; title and
author-list changed due to changes in conten
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