Spin polarized neutron matter within the Dirac-Brueckner-Hartree-Fock approach

The relation between energy and density (known as the nuclear equation of state) plays a major role in a variety of nuclear and astrophysical systems. Spin and isospin asymmetries can have a dramatic impact on the equation of state and possibly alter its stability conditions. An example is the possible manifestation of ferromagnetic instabilities, which would indicate the existence, at a certain density, of a spin-polarized state with lower energy than the unpolarized one. This issue is being discussed extensively in the literature and the conclusions are presently very model dependent. We will report and discuss our recent progress in the study of spin-polarized neutron matter. The approach we take is microscopic and relativistic. The calculated neutron matter properties are derived from realistic nucleon-nucleon interactions. This makes it possible to understand the nature of the EOS properties in terms of specific features of the nuclear force model.Comment: 6 pages, 11 figures, revised/extended calculation

Thermal and dissipative effects in Casimir physics

We report on current efforts to detect the thermal and dissipative contributions to the Casimir force. For the thermal component, two experiments are in progress at Dartmouth and at the Institute Laue Langevin in Grenoble. The first experiment will seek to detect the Casimir force at the largest explorable distance using a cylinder-plane geometry which offers various advantages with respect to both sphere-plane and parallel-plane geometries. In the second experiment, the Casimir force in the parallel-plane configuration is measured with a dedicated torsional balance, up to 10 micrometers. Parallelism of large surfaces, critical in this configuration, is maintained through the use of inclinometer technology already implemented at Grenoble for the study of gravitationally bound states of ultracold neutrons, For the dissipative component of the Casimir force, we discuss detection techniques based upon the use of hyperfine spectroscopy of ultracold atoms and Rydberg atoms. Although quite challenging, this triad of experimental efforts, if successful, will give us a better knowledge of the interplay between quantum and thermal fluctuations of the electromagnetic field and of the nature of dissipation induced by the motion of objects in a quantum vacuum.Comment: Contribution to QFEXT'06, appeared in special issue of Journal of Physics

Universal behavior of quantum Green's functions

We consider a general one-particle Hamiltonian H = - \Delta_r + u(r) defined in a d-dimensional domain. The object of interest is the time-independent Green function G_z(r,r') = . Recently, in one dimension (1D), the Green's function problem was solved explicitly in inverse form, with diagonal elements of Green's function as prescribed variables. The first aim of this paper is to extract from the 1D inverse solution such information about Green's function which cannot be deduced directly from its definition. Among others, this information involves universal, i.e. u(r)-independent, behavior of Green's function close to the domain boundary. The second aim is to extend the inverse formalism to higher dimensions, especially to 3D, and to derive the universal form of Green's function for various shapes of the confining domain boundary.Comment: 46 pages, the shortened version submitted to J. Math. Phy

A zeta function approach to the relation between the numbers of symmetry planes and axes of a polytope

A derivation of the Ces\`aro-Fedorov relation from the Selberg trace formula on an orbifolded 2-sphere is elaborated and extended to higher dimensions using the known heat-kernel coefficients for manifolds with piecewise-linear boundaries. Several results are obtained that relate the coefficients, $b_i$, in the Shephard-Todd polynomial to the geometry of the fundamental domain. For the 3-sphere we show that $b_4$ is given by the ratio of the volume of the fundamental tetrahedron to its Schl\"afli reciprocal.Comment: Plain TeX, 26 pages (eqn. (86) corrected

Determination of longitudinal bunch shape by means of coherent Smith-Purcell radiation

Coherent enhancement of the Smith-Purcell radiation produced from the interaction of a 1.8 MeV electron beam with a grating has been observed. The emitted radiation has been measured at angles in the 40° to 120° range, which correspond to wavelengths from 0.65 to 4 mm, approximately. The radiated power was 320 mW at 90°. Its angular distribution agrees well with the description of the process in terms of induced surface currents and has been used to infer the longitudinal profile of the electron bunch. It is concluded that the bunch has an approximately triangular profile, with 85% of the bunch particles contained within 14 ps. The possibilities of the technique as a bunch-shape diagnostic tool are also discussed. © 2002 The American Physical Society

Determination of longitudinal bunch shape by means of coherent Smith-Purcell radiation

Coherent enhancement of the Smith-Purcell radiation produced from the interaction of a 1.8 MeV electron beam with a grating has been observed. The emitted radiation has been measured at angles in the 40° to 120° range, which correspond to wavelengths from 0.65 to 4 mm, approximately. The radiated power was 320 mW at 90°. Its angular distribution agrees well with the description of the process in terms of induced surface currents and has been used to infer the longitudinal profile of the electron bunch. It is concluded that the bunch has an approximately triangular profile, with 85% of the bunch particles contained within 14 ps. The possibilities of the technique as a bunch-shape diagnostic tool are also discussed

Development of competency models for assessors and simulators in high-stakes selection processes

Background: Selection for entry into UK medical specialty training is a high-stakes, high-volume process. For selection into General Practice, a large number of assessors and simulators are involved in the delivery of the selection centre, which represents the final stage of selection. Aim: In order to standardize and quality-assure assessor and simulator involvement in the process, we developed two competency models outlining the knowledge, skills and attributes associated with each role using a previously validated job analysis methodology. Results: The final qualitative analysis resulted in two competency models, each encompassing eight competency domains. In general, results from a validation questionnaire demonstrated positive feedback from various regional recruitment leads in the UK (n = 14). Conclusion: Both models are currently being used in practice for quality assurance and training purposes. We conclude that the competency models can be used in three ways: (1) recruiting assessors/simulators; (2) in measuring performance of assessors/simulators and highlighting areas for potential development; and (3) they can be used for training assessors/simulators

Bose-Einstein condensation in arbitrarily shaped cavities

We discuss the phenomenon of Bose-Einstein condensation of an ideal non-relativistic Bose gas in an arbitrarily shaped cavity. The influence of the finite extension of the cavity on all thermodynamical quantities, especially on the critical temperature of the system, is considered. We use two main methods which are shown to be equivalent. The first deals with the partition function as a sum over energy levels and uses a Mellin-Barnes integral representation to extract an asymptotic formula. The second method converts the sum over the energy levels to an integral with a suitable density of states factor obtained from spectral analysis. The application to some simple cavities is discussed.Comment: 10 pages, LaTeX, to appear in Physical Review

Casimir effect due to a single boundary as a manifestation of the Weyl problem

The Casimir self-energy of a boundary is ultraviolet-divergent. In many cases the divergences can be eliminated by methods such as zeta-function regularization or through physical arguments (ultraviolet transparency of the boundary would provide a cutoff). Using the example of a massless scalar field theory with a single Dirichlet boundary we explore the relationship between such approaches, with the goal of better understanding the origin of the divergences. We are guided by the insight due to Dowker and Kennedy (1978) and Deutsch and Candelas (1979), that the divergences represent measurable effects that can be interpreted with the aid of the theory of the asymptotic distribution of eigenvalues of the Laplacian discussed by Weyl. In many cases the Casimir self-energy is the sum of cutoff-dependent (Weyl) terms having geometrical origin, and an "intrinsic" term that is independent of the cutoff. The Weyl terms make a measurable contribution to the physical situation even when regularization methods succeed in isolating the intrinsic part. Regularization methods fail when the Weyl terms and intrinsic parts of the Casimir effect cannot be clearly separated. Specifically, we demonstrate that the Casimir self-energy of a smooth boundary in two dimensions is a sum of two Weyl terms (exhibiting quadratic and logarithmic cutoff dependence), a geometrical term that is independent of cutoff, and a non-geometrical intrinsic term. As by-products we resolve the puzzle of the divergent Casimir force on a ring and correct the sign of the coefficient of linear tension of the Dirichlet line predicted in earlier treatments.Comment: 13 pages, 1 figure, minor changes to the text, extra references added, version to be published in J. Phys.

Equation of state and magnetic susceptibility of spin polarized isospin asymmetric nuclear matter

Properties of spin polarized isospin asymmetric nuclear matter are studied within the framework of the Brueckner--Hartree--Fock formalism. The single-particle potentials of neutrons and protons with spin up and down are determined for several values of the neutron and proton spin polarizations and the asymmetry parameter. It is found an almost linear and symmetric variation of the single-particle potentials as increasing these parameters. An analytic parametrization of the total energy per particle as a function of the asymmetry and spin polarizations is constructed. This parametrization is employed to compute the magnetic susceptibility of nuclear matter for several values of the asymmetry from neutron to symmetric matter. The results show no indication of a ferromagnetic transition at any density for any asymmetry of nuclear matter.Comment: 23 pages, 8 figures, 2 tables (submitted to Phys. Rev. C