Search results for "Approx"
showing 10 items of 922 documents
Quasi-wavelength-independent broadband optical Fourier transformer
1999
The chromatic behaviour associated with diffractive optical elements is exploited herein to design a hybrid (diffractive-refractive) lens triplet showing very great wavelength-compensation capabilities for the Fraunhofer diffraction pattern of any diffracting screen under broadband point-source illumination. Within the paraxial Fresnel diffraction theory, we show that perfect compensation for the axial position of the Fourier transform of the input can be accomplished if we neglect the secondary spectrum of the refractive objective. Simultaneously, an achromatic correction for the scale of the Fraunhofer pattern is achieved. In this way, even for white light, only a low residual transversal…
Space-time analogy for partially coherent plane-wave-type pulses.
2005
In this Letter we extend the well-known space-time duality to partially coherent wave fields and, as a limit case, to incoherent sources. We show that there is a general analogy between the paraxial diffraction of quasi-monochromatic beams of limited spatial coherence and the temporal distortion of partially coherent plane-wave pulses in parabolic dispersive media. Next, coherence-dependent effects in the propagation of Gaussian Schell-model pulses are retrieved from that of their spatial counterpart, the Gaussian Schell-model beam. Finally, the last result allows us to present a source linewidth analysis in an optical fiber communication system operating around the 1.55 microm wavelength w…
Debye representation of dispersive focused waves
2006
We report on a matrix-based diffraction integral that evaluates the focal field of any diffraction-limited axisymmetric complex system. This diffraction formula is a generalization of the Debye integral applied to apertured focused beams, which may be accommodated to broadband problems. Longitudinal chromatic aberration may limit the convenience of the Debye formulation and, additionally, spatial boundaries of validity around the focal point are provided. Fresnel number is reformulated in order to guarantee that the focal region is entirely into the region of validity of the Debye approximation when the Fresnel number of the focusing geometry largely exceeds unity. We have applied the matri…
Finite Nc corrections in the Balitsky-Kovchegov equation at next-to-leading order
2021
Publisher Copyright: © owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). We study the finite-Nc corrections to the next-to-leading order (NLO) Balitsky-Kovchegov (BK) equation. This contains correlators of six Wilson lines, which we express in terms of the two-point function using the Gaussian approximation. Numerically, the effects of these finite-Nc corrections on the NLO BK equation are found to be smaller than the expected 1/Nc2 ∼ 10%. Corrections may be large for individual correlators, but have less of an influence on the shape of the amplitude as a function of the dipole size. There is a…
Effective axial-vector strength and β -decay systematics
2014
We use the weak axial-vector coupling strength as a key parameter to reproduce simultaneously the available data for both the Gamow-Teller and decay rates in nine triplets of isobars with mass numbers . We use the proton-neutron quasiparticle random-phase approximation (pnQRPA) with schematic dipole interaction containing particle-particle and particle-hole parts with mass-dependent strengths. Our analysis points to a strongly quenched effective value , with a relative error of 28%. We then perform a systematic computation of 218 experimentally known and decays with quite a remarkable success. The presently extracted value of should be taken as an effective one, specific for a given nuclear…
Measurement of the Dipole Polarizability of the Unstable Neutron-Rich NucleusNi68
2013
The E1 strength distribution in Ni68 has been investigated using Coulomb excitation in inverse kinematics at the RB3-LAND setup and by measuring the invariant mass in the one- and two-neutron decay channels. The giant dipole resonance and a low-lying peak (pygmy dipole resonance) have been observed at 17.1(2) and 9.55(17) MeV, respectively. The measured dipole polarizability is compared to relativistic random phase approximation calculations yielding a neutron-skin thickness of 0.17(2) fm. A method and analysis applicable to neutron-rich nuclei has been developed, allowing for a precise determination of neutron skins in nuclei as a function of neutron excess.
The effect of dynamical screening on helium (e, 3e) differential cross-sections
2005
A simplified derivation of dynamic screening in the case of three Coulomb-interacting particles in the continuum is given and applied to describe the shapes of multi-differential cross-sections for the (e, 3e) process on the helium atom in which the incident fast electron is treated in first-order Born approximation. A very good agreement with experimental multi-differential cross-sections is obtained for two slow ejected electrons (specifically both electrons have 5 eV) but the strategy appears to be breaking down at intermediate emission energies.
Isospin Character of Low-Lying Pygmy Dipole States inPb208via Inelastic Scattering ofO17Ions
2014
The properties of pygmy dipole states in Pb-208 were investigated using the Pb-208(O-17, O-17'gamma) reaction at 340 MeV and measuring the gamma decay with high resolution with the AGATA demonstrator array. Cross sections and angular distributions of the emitted gamma rays and of the scattered particles were measured. The results are compared with (gamma, gamma') and (p, p') data. The data analysis with the distorted wave Born approximation approach gives a good description of the elastic scattering and of the inelastic excitation of the 2(+) and 3(-) states. For the dipole transitions a form factor obtained by folding a microscopically calculated transition density was used for the first t…
Low-energy corrections to the eikonal description of elastic scattering and breakup of one-neutron halo nuclei in nuclear-dominated reactions
2018
Background: The eikonal approximation is a high-energy reaction model, which is very computationally efficient and provides a simple interpretation of the collision. Unfortunately, it is not valid at energies around 10 MeV/nucleon, the range of energy of HIE-ISOLDE at CERN and the future ReA12 at MSU. Fukui et al. [Phys. Rev. C 90, 034617 (2014)10.1103/PhysRevC.90.034617] have shown that a simple semiclassical correction of the projectile-target deflection could improve the description of breakup of halo nuclei on heavy targets down to 20 MeV/nucleon. Purpose: We study two similar corrections, which aim at improving the projectile-target relative motion within the eikonal approximation, wit…
Extension of the ratio method to proton-rich nuclei
2019
The ratio method has been developed to improve the study of one-neutron halo nuclei through reactions. By taking the ratio of angular distributions for two processes, viz. breakup and elastic scattering, this new observable is nearly independent of the reaction mechanism and hence much more sensitive to the projectile structure than the cross sections for each single process. We study the extension of the ratio method to proton-rich nuclei and also explore the optimum experimental conditions for measuring this new observable. We compare accurate dynamical calculations of reactions for proton-rich projectiles to the prediction of the ratio method. We use the dynamical eikonal approximation t…