Entanglement and four wave mixing effects in the dissipation free nonlinear interaction of two photons at a single atom

We investigate the nonlinear interaction between two photons in a single input pulse at an atomic two level nonlinearity. A one dimensional model for the propagation of light to and from the atom is used to describe the precise spatiotemporal coherence of the two photon state. It is shown that the interaction generates spatiotemporal entanglement in the output state similar to the entanglement observed in parametric downconversion. A method of generating photon pairs from coherent pump light using this quantum mechanical four wave mixing process is proposed.Comment: 10 pages, including 3 figures, correction in eq.(7), updated references, final version for publication in PR

Teacher interventions in small group work in secondary mathematics and science lessons

Collaborative problem solving, when students work in pairs or small groups on a curriculum-related task, has become an increasingly common feature of classroom education. This paper reports a study of a topic which has received relatively little attention: how teachers can most usefully intervene when students are working in a group, but have encountered some sort of problem. The data used comes from a large scale interventional study of mathematics and science teaching in secondary schools in south east England, in which interactions between teachers and students were recorded in their usual classrooms. We identify the typical problem situations which lead to teachers’ interventions, and describe the different ways teachers were observed to intervene. We examine the different types of intervention, and consider how effective they are in helping group work proceed in a productive manner. Finally, we offer some conclusions about the practical implications of these findings.This is the final version of the article. It was first available from Taylor & Francis via http://dx.doi.org/10.1080/09500782.2015.112536

Quest for a Nuclear Georeactor

Knowledge about the interior of our planet is mainly based on the interpretation of seismic data from earthquakes and nuclear explosions, and of composition of meteorites. Additional observations have led to a wide range of hypotheses on the heat flow from the interior to the crust, the abundance of certain noble gases in gasses vented from volcanoes and the possibility of a nuclear georeactor at the centre of the Earth. This paper focuses on a proposal for an underground laboratory to further develop antineutrinos as a tool to map the distribution of radiogenic heat sources, such as the natural radionuclides and the hypothetical nuclear georeactor.Comment: Invited talk presented at the International Symposium on Radiation Physics, Cape Town, 2003. Manuscript is submitted to Radiation Physics and Chemistr

Collective modes of asymmetric nuclear matter in Quantum HadroDynamics

We discuss a fully relativistic Landau Fermi liquid theory based on the Quantum Hadro-Dynamics ($QHD$) effective field picture of Nuclear Matter ({\it NM}). From the linearized kinetic equations we get the dispersion relations of the propagating collective modes. We focus our attention on the dynamical effects of the interplay between scalar and vector channel contributions. A beautiful ``mirror'' structure in the form of the dynamical response in the isoscalar/isovector degree of freedom is revealed, with a complete parallelism in the role respectively played by the compressibility and the symmetry energy. All that strongly supports the introduction of an explicit coupling to the scalar-isovector channel of the nucleon-nucleon interaction. In particular we study the influence of this coupling (to a $\delta$-meson-like effective field) on the collective response of asymmetric nuclear matter ($ANM$). Interesting contributions are found on the propagation of isovector-like modes at normal density and on an expected smooth transition to isoscalar-like oscillations at high baryon density. Important ``chemical'' effects on the neutron-proton structure of the mode are shown. For dilute $ANM$ we have the isospin distillation mechanism of the unstable isoscalar-like oscillations, while at high baryon density we predict an almost pure neutron wave structure of the propagating sounds.Comment: 18 pages (LATEX), 8 Postscript figures, uses "epsfig

A microscopic estimate of the nuclear matter compressibility and symmetry energy in relativistic mean-field models

The relativistic mean-field plus RPA calculations, based on effective Lagrangians with density-dependent meson-nucleon vertex functions, are employed in a microscopic analysis of the nuclear matter compressibility and symmetry energy. We compute the isoscalar monopole and the isovector dipole response of $^{208}$Pb, as well as the differences between the neutron and proton radii for $^{208}$Pb and several Sn isotopes. The comparison of the calculated excitation energies with the experimental data on the giant monopole resonance in $^{208}$Pb, restricts the nuclear matter compression modulus of structure models based on the relativistic mean-field approximation to $K_{\rm nm}\approx 250 - 270$ MeV. The isovector giant dipole resonance in $^{208}$Pb, and the available data on differences between neutron and proton radii, limit the range of the nuclear matter symmetry energy at saturation (volume asymmetry) to 32 MeV $\leq a_4 \leq$ 36 MeV.Comment: 16 pages, 6 figure

Relativistic Random-Phase Approximation with density-dependent meson-nucleon couplings

The matrix equations of the relativistic random-phase approximation (RRPA) are derived for an effective Lagrangian characterized by density-dependent meson-nucleon vertex functions. The explicit density dependence of the meson-nucleon couplings introduces rearrangement terms in the residual two-body interaction, that are essential for a quantitative description of excited states. Illustrative calculations of the isoscalar monopole, isovector dipole and isoscalar quadrupole response of $^{208}$Pb, are performed in the fully self-consistent RRPA framework, based on effective interactions with a phenomenological density dependence adjusted to nuclear matter and ground-state properties of spherical nuclei. The comparison of the RRPA results on multipole giant resonances with experimental data constrains the parameters that characterize the isoscalar and isovector channel of the density-dependent effective interactions.Comment: RevTeX, 8 eps figures, submitted to Phys. Rev.

Density Functional Theory for a Confined Fermi System with Short-Range Interaction

Effective field theory (EFT) methods are applied to density functional theory (DFT) as part of a program to systematically go beyond mean-field approaches to medium and heavy nuclei. A system of fermions with short-range, natural interactions and an external confining potential (e.g., fermionic atoms in an optical trap) serves as a laboratory for studying DFT/EFT. An effective action formalism leads to a Kohn-Sham DFT by applying an inversion method order-by-order in the EFT expansion parameter. Representative results showing the convergence of Kohn-Sham calculations at zero temperature in the local density approximation (LDA) are compared to Thomas-Fermi calculations and to power-counting estimates.Comment: 36 pages, 20 figures, RevTeX

Relativistic Mean Field Model with Generalized Derivative Nucleon-Meson Couplings

The quantum hadrodynamics (QHD) model with minimal nucleon-meson couplings is generalized by introducing couplings of mesons to derivatives of the nucleon field in the Lagrangian density. This approach allows an effective description of a state-dependent in-medium interaction in the mean-field approximation. Various parametrizations for the generalized couplings are developed and applied to infinite nuclear matter. In this approach, scalar and vector self-energies depend on both density and momentum similarly as in the Dirac-Brueckner theory. The Schr\"{o}diger-equivalent optical potential is much less repulsive at high nucleon energies as compared to standard relativistic mean field models and thus agrees better with experimental findings. The derivative couplings in the extended model have significant effects on properties of symmetric nuclear matter and neutron matter.Comment: 35 pages, 1 table, 10 figure