Search results for "approximation"
showing 10 items of 818 documents
Density gradients for the exchange energy of electrons in two dimensions
2009
We derive a generalized gradient approximation to the exchange energy to be used in density functional theory calculations of two-dimensional systems. This class of approximations has a long and successful history, but it has not yet been fully investigated for electrons in two dimensions. We follow the approach originally proposed by Becke for three-dimensional systems [Int. J. Quantum Chem. 23, 1915 (1983), J. Chem. Phys. 85, 7184 (1986)]. The resulting functional depends on two parameters that are adjusted to a test set of parabolically confined quantum dots. Our exchange functional is then tested on a variety of systems with promising results, reducing the error in the exchange energy b…
The average over a sphere
1980
Abstract The N points ri and the N segments ΔΩi of the unit sphere used in the numerical approximation of the average over the sphere are optimized to approximate the average of the set of spherical harmonics {;Yl,m;l = 0, 1, 2, …, L}; up to L = 18. The symmetry of f( r ) can be taken into acount by using only a distinct subquantity of the N point {; r i , ΔΩ i }; . Sets for N = 48n (n = 1, 2, …, 6) are tabulated. The advantage of the method is shown by the calculation of a powder Mossbauer spectrum including electric and magnetic hyperfine interactions.
Spiral conical approximations to double reflection Wolter optics
2008
The design of a grazing incidence focusing optic obtained from a spiral approximation to multiple nested cones produces an annular image of a point source. The angular size of the annulus depends mainly on the pitch of the winding and the focal length. For a spiral conical approximation to Wolter optics, the effect is magnified by the double reflection. However, if the two conical spirals are wound one clock-wise and the other counter-clock-wise, then the aberration is partially compensated. We use a ray tracing code to evaluate advantages and disadvantages of this optical design for potential applications of a light weight optics technology based on plastic foils that we are currently inve…
Remarks on quadratic Hamiltonians in spaceflight mechanics
2006
A particular family of Hamiltonian functions is considered. Such functions are quadratic in the moment variables and arise in spaceflight mechanics when the averaged system of energy minimizing trajectories of the Kepler equation is computed. An important issue of perturbation theory and averaging is to provide integrable approximations of nonlinear systems. It turns out that such integrability properties hold here.
Linear response of homogeneous nuclear matter with energy density functionals
2014
Response functions of infinite nuclear matter with arbitrary isospin asymmetry are studied in the framework of the random phase approximation. The residual interaction is derived from a general nuclear Skyrme energy density functional. Besides the usual central, spin-orbit and tensor terms it could also include other components as new density-dependent terms or three-body terms. Algebraic expressions for the response functions are obtained from the Bethe-Salpeter equation for the particle-hole propagator. Applications to symmetric nuclear matter, pure neutron matter and asymmetric nuclear matter are presented and discussed. Spin-isospin strength functions are analyzed for varying conditions…
Scaling the abruptly autofocusing beams in the direct-space
2017
International audience; We propose a simple technique to scale the abruptly autofocusing beams in the direct space by introducing a scaling factor in the phase. Analytical formulas are deduced based on optical caustics, explicitly revealing how the scaling factor controls location, peak intensity, and size of the focal spot. We demonstrate that the multiplication of a scaling factor on the phase is equivalent to the axial-scaling transformation under the paraxial approximation. Further numerical and experimental results confirm theoretical predictions. In addition, amplitude modulation using phase-only holograms is used to maintain the peak intensity level of the focal spots.
Cluster-transfer reactions with radioactive beams: A spectroscopic tool for neutron-rich nuclei
2015
An exploratory experiment performed at REX-ISOLDE to investigate cluster-transfer reactions with radioactive beams in inverse kinematics is presented. The aim of the experiment was to test the potential of cluster-transfer reactions at the Coulomb barrier as a mechanism to explore the structure of exotic neutron-rich nuclei. The reactions Li7(Rb98,αxn) and Li7(Rb98,txn) were studied through particle-γ coincidence measurements, and the results are presented in terms of the observed excitation energies and spins. Moreover, the reaction mechanism is qualitatively discussed as a transfer of a clusterlike particle within a distorted-wave Born approximation framework. The results indicate that cl…
Exact Solutions of the Two Dimensional Boussinesq and Dispersive Water Waves Equations
2010
In this paper two-dimensional Boussinesq and dispersive water waves equations are investigated in exact solutions. The Exp-function method is used for seeking exact solutions of the equations through symbolic computation.
Twisted-Light-Ion Interaction: The Role of Longitudinal Fields.
2017
The propagation of light beams is well described using the paraxial approximation, where field components along the propagation direction are usually neglected. For strongly inhomogeneous or shaped light fields, however, this approximation may fail, leading to intriguing variations of the light-matter interaction. This is the case of twisted light having opposite orbital and spin angular momenta. We compare experimental data for the excitation of a quadrupole transition in a single trapped $^{40}$Ca$^+$ ion by Schmiegelow et al, Nat.\ Comm.\ 7, 12998 (2016), with a complete model where longitudinal components of the electric field are taken into account. Our model matches the experimental d…
Laser Pulse Effects in Two-level Systems Driven by Coherent and Fluctuating Radiation Fields
1988
Abstract We reconsider the problem of a two-level system interacting with a radiation field in order to study some new features suggested by the actual experimental conditions. Pulse shape and duration effects are included in the formalism and the counter-rotating terms are retained. The criterion of validity of the rotating wave approximation (RWA) for pulsed fields is investigated; generalizing results well known in RWA, we establish some new formal results, including non-RWA contributions to all orders and for any pulse shape. The analysis is then carried out for fluctuating fields, by developing a method based on the theory of multiplicative stochastic differential equations. For short …