Probing Correlated Ground States with Microscopic Optical Model for Nucleon Scattering off Doubly-Closed-Shell Nuclei

The RPA long range correlations are known to play a significant role in understanding the depletion of single particle-hole states observed in (e, e') and (e, e'p) measurements. Here the Random Phase Approximation (RPA) theory, implemented using the D1S force is considered for the specific purpose of building correlated ground states and related one-body density matrix elements. These may be implemented and tested in a fully microscopic optical model for NA scattering off doubly-closed-shell nuclei. A method is presented to correct for the correlations overcounting inherent to the RPA formalism. One-body density matrix elements in the uncorrelated (i.e. Hartree-Fock) and correlated (i.e. RPA) ground states are then challenged in proton scattering studies based on the Melbourne microscopic optical model to highlight the role played by the RPA correlations. Effects of such correlations which deplete the nuclear matter at small radial distance (r $<$ 2 fm) and enhance its surface region, are getting more and more sizeable as the incident energy increases. Illustrations are given for proton scattering observables measured up to 201 MeV for the $^{16}$O, $^{40}$Ca, $^{48}$Ca and $^{208}$Pb target nuclei. Handling the RPA correlations systematically improves the agreement between scattering predictions and data for energies higher than 150 MeV.Comment: 20 pages, 7 figure

PHARAO Laser Source Flight Model: Design and Performances

In this paper, we describe the design and the main performances of the PHARAO laser source flight model. PHARAO is a laser cooled cesium clock specially designed for operation in space and the laser source is one of the main sub-systems. The flight model presented in this work is the first remote-controlled laser system designed for spaceborne cold atom manipulation. The main challenges arise from mechanical compatibility with space constraints, which impose a high level of compactness, a low electric power consumption, a wide range of operating temperature and a vacuum environment. We describe the main functions of the laser source and give an overview of the main technologies developed for this instrument. We present some results of the qualification process. The characteristics of the laser source flight model, and their impact on the clock performances, have been verified in operational conditions.Comment: Accepted for publication in Review of Scientific Instrument

Radon--Nikodym representations of Cuntz--Krieger algebras and Lyapunov spectra for KMS states

We study relations between $(H,\beta)$--KMS states on Cuntz--Krieger algebras and the dual of the Perron--Frobenius operator $\mathcal{L}_{-\beta H}^{*}$. Generalising the well--studied purely hyperbolic situation, we obtain under mild conditions that for an expansive dynamical system there is a one--one correspondence between $(H,\beta)$--KMS states and eigenmeasures of $\mathcal{L}_{-\beta H}^{*}$ for the eigenvalue 1. We then consider representations of Cuntz--Krieger algebras which are induced by Markov fibred systems, and show that if the associated incidence matrix is irreducible then these are $\ast$--isomorphic to the given Cuntz--Krieger algebra. Finally, we apply these general results to study multifractal decompositions of limit sets of essentially free Kleinian groups $G$ which may have parabolic elements. We show that for the Cuntz--Krieger algebra arising from $G$ there exists an analytic family of KMS states induced by the Lyapunov spectrum of the analogue of the Bowen--Series map associated with $G$. Furthermore, we obtain a formula for the Hausdorff dimensions of the restrictions of these KMS states to the set of continuous functions on the limit set of $G$. If $G$ has no parabolic elements, then this formula can be interpreted as the singularity spectrum of the measure of maximal entropy associated with $G$.Comment: 30 pages, minor changes in the proofs of Theorem 3.9 and Fact

The Long Journey from Ab Initio Calculations to Density Functional Theory for Nuclear Large Amplitude Collective Motion

At present there are two vastly different ab initio approaches to the description of the the many-body dynamics: the Density Functional Theory (DFT) and the functional integral (path integral) approaches. On one hand, if implemented exactly, the DFT approach can allow in principle the exact evaluation of arbitrary one-body observable. However, when applied to Large Amplitude Collective Motion (LACM) this approach needs to be extended in order to accommodate the phenomenon of surface-hoping, when adiabaticity is strongly violated and the description of a system using a single (generalized) Slater determinant is not valid anymore. The functional integral approach on the other hand does not appear to have such restrictions, but its implementation does not appear to be straightforward endeavor. However, within a functional integral approach one seems to be able to evaluate in principle any kind of observables, such as the fragment mass and energy distributions in nuclear fission. These two radically approaches can likely be brought brought together by formulating a stochastic time-dependent DFT approach to many-body dynamics.Comment: 9 page

Full-Folding Optical Potentials for Elastic Nucleon-Nucleus Scattering based on Realistic Densities

Optical model potentials for elastic nucleon nucleus scattering are calculated for a number of target nuclides from a full-folding integral of two different realistic target density matrices together with full off-shell nucleon-nucleon t-matrices derived from two different Bonn meson exchange models. Elastic proton and neutron scattering observables calculated from these full-folding optical potentials are compared to those obtained from `optimum factorized' approximations in the energy regime between 65 and 400 MeV projectile energy. The optimum factorized form is found to provide a good approximation to elastic scattering observables obtained from the full-folding optical potentials, although the potentials differ somewhat in the structure of their nonlocality.Comment: 21 pages, LaTeX, 17 postscript figure

Relativistic Nuclear Energy Density Functionals: Mean-Field and Beyond

Relativistic energy density functionals (EDF) have become a standard tool for nuclear structure calculations, providing a complete and accurate, global description of nuclear ground states and collective excitations. Guided by the medium dependence of the microscopic nucleon self-energies in nuclear matter, semi-empirical functionals have been adjusted to the nuclear matter equation of state and to bulk properties of finite nuclei, and applied to studies of arbitrarily heavy nuclei, exotic nuclei far from stability, and even systems at the nucleon drip-lines. REDF-based structure models have also been developed that go beyond the static mean-field approximation, and include collective correlations related to the restoration of broken symmetries and to fluctuations of collective variables. These models are employed in analyses of structure phenomena related to shell evolution, including detailed predictions of excitation spectra and electromagnetic transition rates.Comment: To be published in Progress in Particle and Nuclear Physic

Measuring processes and the Heisenberg picture

In this paper, we attempt to establish quantum measurement theory in the Heisenberg picture. First, we review foundations of quantum measurement theory, that is usually based on the Schr\"{o}dinger picture. The concept of instrument is introduced there. Next, we define the concept of system of measurement correlations and that of measuring process. The former is the exact counterpart of instrument in the (generalized) Heisenberg picture. In quantum mechanical systems, we then show a one-to-one correspondence between systems of measurement correlations and measuring processes up to complete equivalence. This is nothing but a unitary dilation theorem of systems of measurement correlations. Furthermore, from the viewpoint of the statistical approach to quantum measurement theory, we focus on the extendability of instruments to systems of measurement correlations. It is shown that all completely positive (CP) instruments are extended into systems of measurement correlations. Lastly, we study the approximate realizability of CP instruments by measuring processes within arbitrarily given error limits.Comment: v

Progress in noncommutative function theory

In this expository paper we describe the study of certain non-self-adjoint operator algebras, the Hardy algebras, and their representation theory. We view these algebras as algebras of (operator valued) functions on their spaces of representations. We will show that these spaces of representations can be parameterized as unit balls of certain $W^{*}$-correspondences and the functions can be viewed as Schur class operator functions on these balls. We will provide evidence to show that the elements in these (non commutative) Hardy algebras behave very much like bounded analytic functions and the study of these algebras should be viewed as noncommutative function theory

First spectroscopy of 66^{66}Se and 65^{65}As: Investigating shape coexistence beyond the N = Z line

The experiment was performed at the National Superconducting Cyclotron Laboratory (NSCL), at Michigan State University (USA).We report on the first γ spectroscopy of 66Se and 65As from two-neutron removal at intermediate beam energies. The deduced excitation energies for the first-excited states in 66Se and 65As are compared to mean-field-based predictions within a collective Hamiltonian formalism using the Gogny D1S effective interaction and to state-of-the-art shell-model calculations restricted to the pf5/2 g9/2 valence space. The obtained Coulomb-energy differences for the first excited states in 66Se and 65As are discussed within the shell-model formalism to assess the shape-coexistence picture for both nuclei. Our results support a favored oblate ground-state deformation in 66Se and 65As. A shape transition for the ground state of even-odd As isotopes from oblate in 65As to prolate in 67,69,71As is suggested