Orbital Magnetic Dipole Mode in Deformed Clusters: A Fully Microscopic Analysis

The orbital M1 collective mode predicted for deformed clusters in a schematic model is studied in a self-consistent random-phase-approximation approach which fully exploits the shell structure of the clusters. The microscopic mechanism of the excitation is clarified and the close correlation with E2 mode established. The study shows that the M1 strength of the mode is fragmented over a large energy interval. In spite of that, the fraction remaining at low energy, well below the overwhelming dipole plasmon resonance, is comparable to the strength predicted in the schematic model. The importance of this result in view of future experiments is stressed.Comment: 10 pages, 3 Postscript figures, uses revte

Pinning control of hypergraphs

A standard assumption in control of network dynamical systems is that its nodes interact through pairwise interactions, which can be described by means of a directed graph. However, in several contexts, multibody, directed interactions may occur, thereby requiring the use of directed hypergraphs rather then digraphs. For the first time, we propose a strategy, inspired by the classic pinning control on graphs, that is tailored for controlling network systems coupled through a directed hypergraph. By drawing an analogy with signed graphs, we provide sufficient conditions for controlling the network onto the desired trajectory provided by the pinner, and a dedicated algorithm to design the control hyperedges

Orbital magnetism in axially deformed sodium clusters: From scissors mode to dia-para magnetic anisotropy

Low-energy orbital magnetic dipole excitations, known as scissors mode (SM), are studied in alkali metal clusters. Subsequent dynamic and static effects are explored. The treatment is based on a self-consistent microscopic approach using the jellium approximation for the ionic background and the Kohn-Sham mean field for the electrons. The microscopic origin of SM and its main features (structure of the mode in light and medium clusters, separation into low- and high-energy plasmons, coupling high-energy M1 scissors and E2 quadrupole plasmons, contributions of shape isomers, etc) are discussed. The scissors M1 strength acquires large values with increasing cluster size. The mode is responsible for the van Vleck paramagnetism of spin-saturated clusters. Quantum shell effects induce a fragile interplay between Langevin diamagnetism and van Vleck paramagnetism and lead to a remarkable dia-para anisotropy in magnetic susceptibility of particular light clusters. Finally, several routes for observing the SM experimentally are discussed.Comment: 21 pages, 7 figure

Pause-and-Go Self-Balancing Formation Control of Autonomous Vehicles Using Vision and Ultrasound Sensors

In this work, we implement a decentralized and noncooperative state estimation and control algorithm to autonomously balance a team of robots in a circular formation pattern. The group of robots includes a leader periodically moving at a constant steering angle and a set of followers that, by only leveraging intermittent and noisy proximity measurements, independently implement a fully decentralized state estimation control algorithm to determine and adjust their relative position with closest neighbors. The algorithm is conducted in a pause-and-go sequence, where, during the pause, each robot stops to gather and process the information coming from the measurements, estimate the relative phase with respect to the others, and identify its closest pursuant. During the go, each robot accelerates to space from its closest pursuant and then to move at a constant speed when the desired spacing is achieved. The algorithm is tested in an unprecedented experiment on a custom-made low-cost caster-wheeled robotic framework featuring sonar and vision sensors mounted on a rotating platform to estimate the proximity distance to closer neighbors. The control scheme, which does not necessitate cooperation and is capable of coping with uncertain and intermittent sensor feedback data, is shown to be effective in balancing the robot on the circle even when, at a steady state, no feedback sensor data are available

Removal of the center of mass in nuclei and its effects on 4He

Abstract The singular value decomposition of rectangular matrices is shown to provide the recipe for removing the center of mass spurious admixtures from the multiphonon basis generated by an equation of motion method for solving the nuclear eigenvalue problem. It works for any single particle basis without any energy restriction on the selection of the configurations. Its effects on 4He are illustrated

Temperature Dependence of Damping and Frequency Shifts of the Scissors Mode of a trapped Bose-Einstein Condensate

We have studied the properties of the scissors mode of a trapped Bose-Einstein condensate of $^{87}$Rb atoms at finite temperature. We measured a significant shift in the frequency of the mode below the hydrodynamic limit and a strong dependence of the damping rate as the temperature increased. We compared our damping rate results to recent theoretical calculations for other observed collective modes finding a fair agreement. From the frequency measurements we deduce the moment of inertia of the gas and show that it is quenched below the transition point, because of the superfluid nature of the condensed gas.Comment: 5 pages, 4 figure

Odd nuclei spectroscopy within a self-consistent multiphonon approach

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A self-consistent many-body approach to the electroproduction of hypernuclei

The electroproduction of selected $p$- and $sd$-shell hypernuclei was studied within a many-body approach using realistic interactions between the constituent baryons. The cross sections were computed in distorted-wave impulse approximation using two elementary amplitudes for the electroproduction of the $\Lambda$ hyperon. The structure of the hypernuclei was investigated within the framework of the self-consistent $\Lambda$-nucleon Tamm-Dancoff approach and its extension known as the $\Lambda$-nucleon equation of motion phonon method. Use was made of the NNLOsat chiral potential plus the effective Nijmegen-F YN interaction. The method was first implemented on light nuclei for studying the available experimental data and establishing a relation to other approaches. After this proof test, it was adopted for predicting the electroproduction cross section of the hypernuclei $^{40}_{~\Lambda}$K and $^{48}_{~\Lambda}$K in view of the E12-15-008 experiment in preparation at JLab. On the ground of these predictions, appreciable effects on the spectra are expected to be induced by the YN interaction.Comment: 11 pages, 9 figure

Self-consistent studies of the dipole response in neutron rich nuclei using realistic potentials

The dipole response in neutron rich nuclei is investigated within self-consistent approaches which make direct use of a nucleon-nucleon optimized chiral potential complemented with a density dependent term simulating a three-body force. Hartree-Fock-Bogoliubov plus Tamm-Dancoff and random-phase approximations show that such a potential improves the description of the dipole modes with respect to other realistic interactions. The inclusion of the two-phonon states within an equation of motion method induces a pronounced fragmentation of both giant and pygmy resonances in agreement with recent experiments

Competing electric and magnetic excitations in backward electron scattering from heavy deformed nuclei

Important $E2$ contributions to the $(e,e^{\prime})$ cross sections of low-lying orbital $M1$ excitations are found in heavy deformed nuclei, arising from the small energy separation between the two excitations with $I^{\pi}K = 2^+1$ and 1$^+1$, respectively. They are studied microscopically in QRPA using DWBA. The accompanying $E2$ response is negligible at small momentum transfer $q$ but contributes substantially to the cross sections measured at $\theta = 165 ^{\circ}$ for $0.6 < q_{\rm eff} < 0.9$ fm$^{-1}$ ($40 \le E_i \le 70$ MeV) and leads to a very good agreement with experiment. The electric response is of longitudinal $C2$ type for $\theta \le 175 ^{\circ}$ but becomes almost purely transverse $E2$ for larger backward angles. The transverse $E2$ response remains comparable with the $M1$ response for $q_{\rm eff} > 1.2$ fm$^{-1}$ ($E_i > 100$ MeV) and even dominant for $E_i > 200$ MeV. This happens even at large backward angles $\theta > 175 ^{\circ}$, where the $M1$ dominance is limited to the lower $q$ region.Comment: RevTeX, 19 pages, 8 figures included Accepted for publication in Phys Rev