Homogenization of an ensemble of interacting resonant scatterers

We study theoretically the concept of homogenization in optics using an ensemble of randomly distributed resonant stationary atoms with density $\rho$. The ensemble is dense enough for the usual condition for homogenization, viz. $\rho\lambda^3 \gg 1$, to be reached. Introducing the coherent and incoherent scattered powers, we define two criteria to define the homogenization regime. We find that when the excitation field is tuned in a broad frequency range around the resonance, none of the criteria for homogenization is fulfilled, meaning that the condition $\rho\lambda^3\gg 1$ is not sufficient to characterize the homogenized regime around the atomic resonance. We interpret these results as a consequence of the light-induced dipole-dipole interactions between the atoms, which implies a description of scattering in terms of collective modes rather than as a sequence of individual scattering events. Finally, we show that, although homogenization can never be reached for a dense ensemble of randomly positioned laser-cooled atoms around resonance, it becomes possible if one introduces spatial correlations in the positions of the atoms or non-radiative losses, such as would be the case for organic molecules or quantum dots coupled to a phonon bath.Comment: 9 pages, 5 figures. Corrected mistakes in reference

Extended sudden approximation model for high-energy nucleon removal reactions

A model based on the sudden approximation has been developed to describe high energy single nucleon removal reactions. Within this approach, which takes as its starting point the formalism of Hansen \cite{Anne2}, the nucleon-removal cross section and the full 3-dimensional momentum distributions of the core fragments including absorption, diffraction, Coulomb and nuclear-Coulomb interference amplitudes, have been calculated. The Coulomb breakup has been treated to all orders for the dipole interaction. The model has been compared to experimental data for a range of light, neutron-rich psd-shell nuclei. Good agreement was found for both the inclusive cross sections and momentum distributions. In the case of $^{17}$C, comparison is also made with the results of calculations using the transfer-to-the-continuum model. The calculated 3-dimensional momentum distributions exhibit longitudinal and transverse momentum components that are strongly coupled by the reaction for s-wave states, whilst no such effect is apparent for d-waves. Incomplete detection of transverse momenta arising fromlimited experimental acceptances thus leads to a narrowing of the longitudinal distributions for nuclei with significant s-wave valence neutron configurations, as confirmed by the data. Asymmetries in the longitudinal momentum distributions attributed to diffractive dissociation are also explored.Comment: 16 figures, submitted to Phys. Rev.

Elastic and total reaction cross sections of oxygen isotopes in Glauber theory

We systematically calculate the total reaction cross sections of oxygen isotopes, $^{15-24}$O, on a $^{12}$C target at high energies using the Glauber theory. The oxygen isotopes are described with Slater determinants generated from a phenomenological mean-field potential. The agreement between theory and experiment is generally good, but a sharp increase of the reaction cross sections from ^{21}O to ^{23}O remains unresolved. To examine the sensitivity of the diffraction pattern of elastic scattering to the nuclear surface, we study the differential elastic-scattering cross sections of proton-^{20,21,23}O at the incident energy of 300 MeV by calculating the full Glauber amplitude.Comment: 9 pages, 8 figure

A global analysis of inclusive diffractive cross sections at HERA

We describe the most recent data on the diffractive structure functions from the H1 and ZEUS Collaborations at HERA using four models. First, a Pomeron Structure Function (PSF) model, in which the Pomeron is considered as an object with parton distribution functions. Then, the Bartels Ellis Kowalski Wusthoff (BEKW) approach is discussed, assuming the simplest perturbative description of the Pomeron using a two-gluon ladder. A third approach, the Bialas Peschanski (BP) model, based on the dipole formalism is then described. Finally, we discuss the Golec-Biernat-W\"usthoff (GBW) saturation model which takes into account saturation effects. The best description of all avaible measurements can be achieved with either the PSF based model or the BEKW approach. In particular, the BEKW prediction allows to include the highest $\beta$ measurements, which are dominated by higher twists effects and provide an efficient and compact parametrisation of the diffractive cross section. The two other models also give a good description of cross section measurements at small $x$ with a small number of parameters. The comparison of all predictions allows us to identify interesting differences in the behaviour of the effective pomeron intercept and in the shape of the longitudinal component of the diffractive structure functions. In this last part, we present some features that can be discriminated by new experimental measurements, completing the HERA program.Comment: 32 pages, 18 figure

Breakup of loosely bound nuclei as indirect method in nuclear astrophysics: 8B, 9C, 23Al

We discuss the use of one-nucleon breakup reactions of loosely bound nuclei at intermediate energies as an indirect method in nuclear astrophysics. These are peripheral processes, therefore we can extract asymptotic normalization coefficients (ANC) from which reaction rates of astrophysical interest can be inferred. To show the usefulness of the method, three different cases are discussed. In the first, existing experimental data for the breakup of 8B at energies from 30 to 1000 MeV/u and of 9C at 285 MeV/u on light through heavy targets are analyzed. Glauber model calculations in the eikonal approximation and in the optical limit using different effective interactions give consistent, though slightly different results, showing the limits of the precision of the method. The results lead to the astrophysical factor S_17(0)=18.7+/-1.9 eVb for the key reaction for solar neutrino production 7Be(p,\gamma)8B. It is consistent with the values from other indirect methods and most direct measurements, but one. Breakup reactions can be measured with radioactive beams as weak as a few particles per second, and therefore can be used for cases where no direct measurements or other indirect methods for nuclear astrophysics can be applied. We discuss a proposed use of the breakup of the proton drip line nucleus 23Al to obtain spectroscopic information and the stellar reaction rate for 22Mg(p,\gamma)23Al.Comment: 6 pages, 4 figures. Presented at the conference "Nuclear Physics for Astrophysics 2", Debrecen, Hungary, May 2005. Prepared for the Proceeding

Modelling of photonic wire Bragg Gratings

Some important properties of photonic wire Bragg grating structures have been investigate. The design, obtained as a generalisation of the full-width gap grating, has been modelled using 3D finite-difference time-domain simulations. Different types of stop-band have been observed. The impact of the grating geometry on the lowest order (longest wavelength) stop-band has been investigated - and has identified deeply indented configurations where reduction of the stop-bandwidth and of the reflectivity occurred. Our computational results have been substantially validated by an experimental demonstration of the fundamental stop-band of photonic wire Bragg gratings fabricated on silicon-on-insulator material. The accuracy of two distinct 2D computational models based on the effective index method has also been studied - because of their inherently much greater rapidity and consequent utility for approximate initial designs. A 2D plan-view model has been found to reproduce a large part of the essential features of the spectral response of full 3D models

Asymptotic normalization coefficient of ^{8}B from breakup reactions and the S_{17} astrophysical factor

We show that asymptotic normalization coefficients (ANC) can be extracted from one nucleon breakup reactions of loosely bound nuclei at 30-300 MeV/u. In particular, the breakup of ^{8}B is described in terms of an extended Glauber model. The 8B ANC extracted for the ground state of this nucleus from breakup data at several energies and on different targets, C^2 = 0.450+/-0.039} fm^-1, leads to the astrophysical factor S_{17}(0)= 17.4+/-1.5 eVb for the key reaction for solar neutrino production 7Be(p,gamma)8B. The procedure described here is more general, providing an indirect method to determine reaction rates of astrophysical interest with beams of loosely bound radioactive nuclei.Comment: 4 pages, RevTex, 3 figures revised version to appear in Phys Rev Let

Structure and Coulomb dissociation of 23O within the quark-meson coupling model

We study the ground-state structure of nuclei in the vicinity of the one-neutron dripline within the latest version of the quark-meson coupling (QMC) model with a particular emphasis on 23O. For this nucleus the model predicts a [22O(0+) + n (2s_{1/2})] configuration for its ground state, with a one neutron separation energy in close agreement with the corresponding experimental value. The wave function describing the valence neutron-core relative motion was then used to calculate the Coulomb dissociation of 23O on a lead target at a beam energy of 422 MeV/nucleon. The experimental neutron-core relative energy spectrum and the total one-neutron removal cross sections are well described by the calculations. The widths of the longitudinal momentum distributions of the 22O fragment are found to be broad, which do not support the formation of a neutron halo in this nucleus.Comment: Revised and extended version, accepted for publication in Nucl. Phys.

One-neutron removal reactions on light neutron-rich nuclei

A study of high energy (43--68 MeV/nucleon) one-neutron removal reactions on a range of neutron-rich psd-shell nuclei (Z = 5--9, A = 12--25) has been undertaken. The inclusive longitudinal and transverse momentum distributions for the core fragments, together with the cross sections have been measured for breakup on a carbon target. Momentum distributions for reactions on tantalum were also measured for a subset of nuclei. An extended version of the Glauber model incorporating second order noneikonal corrections to the JLM parametrisation of the optical potential has been used to describe the nuclear breakup, whilst the Coulomb dissociation is treated within first order perturbation theory. The projectile structure has been taken into account via shell model calculations employing the psd-interaction of Warburton and Brown. Both the longitudinal and transverse momentum distributions, together with the integrated cross sections were well reproduced by these calculations and spin-parity assignments are thus proposed for $^{15}$B, $^{17}$C, $^{19-21}$N, $^{21,23}$O, $^{23-25}$F. In addition to the large spectroscopic amplitudes for the $\nu2$s$_{1/2}$ intruder configuration in the N=9 isotones,$^{14}$B and $^{15}$C, significant $\nu2$s$_{1/2}^2$ admixtures appear to occur in the ground state of the neighbouring N=10 nuclei $^{15}$B and $^{16}$C. Similarly, crossing the N=14 subshell, the occupation of the $\nu2$s$_{1/2}$ orbital is observed for $^{23}$O, $^{24,25}$F. Analysis of the longitudinal and transverse momentum distributions reveals that both carry spectroscopic information, often of a complementary nature. The general utility of high energy nucleon removal reactions as a spectroscopic tool is also examined.Comment: 50 pages, 19 figures, submitted to Phys. Rev.