A note on the Holst action, the time gauge, and the Barbero–Immirzi parameter

In this note, we review the canonical analysis of the Holst action in the time gauge, with a special emphasis on the Hamiltonian equations of motion and the fixation of the Lagrange multipliers. This enables us to identify at the Hamiltonian level the various components of the covariant torsion tensor, which have to be vanishing in order for the classical theory not to depend upon the Barbero–Immirzi parameter. We also introduce a formulation of three-dimensional gravity with an explicit phase space dependency on the Barbero–Immirzi parameter as a potential way to investigate its fate and relevance in the quantum theory.     

Cohesive energy, phonon spectra, and thermodynamic properties of elements with the structures A1, A2, A3, A4—Al, Cu, V, Ti, Mg, Si, and Sn

The dependences of the cohesive (atomization) energy on the interatomic distance for elements Al, Cu, Ti(A₂), V, Mg, Ti(A₃), Si, and Sn are calculated using methods based on the Thomas-Fermi-Dirac-Gambosh statistical atomic theory. The obtained dependences are approximated by the Mie-Grüneisen potential. The phonon spectra calculated on the basis of the Born-Kärmän model and the Born-Kärmän-Blackman-de Lunay approach are used to determine the temperature dependences of the specific heat, free energy, and internal energy of the elements under investigation. The calculated cohesive energy, equilibrium interatomic distances, and temperature dependences of the specific heat agree with the experimental data.     

A search for high energy neutrinos from SN 1987A,the Carb,Hercules X-1, and Cygnus X-3 with the Fréjus detector

With the Fréjus detector we studied four astrophysical point-like sources by using \(v_e (\bar v_e )\) and \(v_\mu (\bar v_\mu )\) interactions in the detector and \(v_\mu (\bar v_\mu )\) interactions in the surrounding rock. No excess of events was found. Therefore upper limits of neutrino fluxes and source luminositics are quoted. These limits confirm results from other experiments. In addition new limits are presented for spectral indices above 3.     

A modal analysis for the acoustic radiation problems, Ⅱ. Examples

The acoustic radiation modes and the field distribution modes describe the radiation patterns of a complex vibrating surface and the field distribution patterns respectively. The physical meanings of the acoustic radiation modes and the field distribution modes are revealed by numerical method. For a sphere body, a spinning body and a rectangular body, the geometrical patterns of the acoustic radiation modes and the field distribution modes are given. The radiation mode 1 represents the radiation behavior of a monopole radiator, the radiation modes 2 through 4 represent the radiation behavior of dipole radiators respectively, and the radiation modes 5 through 9 represent the radiation behavior of quadrapole radiators respectively. The acoustic radiation modes and the field distribution modes introduce the multi-pole decomposition method into discussion of the acoustic radiation problems.     

A modal analysis for the acoustic radiation problems, I. Theory

For the acoustic radiation problems from a complex vibrating body surface, a modal analysis approach is put forward. All the normal vibration velocities on a vibrating surface form the Hilbert space. In the Hilbert space, an operator is defined, which includes the radiation property of the vibrating surface and is linear, self-adjoint and positive. Using the operator, a set of basis functions in the Hilbert space are obtained, which describe the radiation patterns and are called the radiation modes. Based on the radiation modes, a set of basis functions of the radiation field are obtained by the Helmholtz simple layer potentials, which describe the distribution patterns of the radiation field and are called the field distribution modes. The radiation behavior can be expressed by expansions of the radiation modes and the field distribution modes. The modal analysis approach is introduced into the acoustic radiation problems.     

A 300 µA Upgrade for the ISIS Accelerator

The Rutherford Appleton Laboratory (RAL) is home to the world's leading spallation neutron source ISIS [1]. The ISIS neutron producing target is driven by a 50 Hz, 800 MeV, 200 _A proton beam from a rapid cycling synchrotron, which is fed by a 70 MeV H_ drift tube linac (DTL) which in turn accepts beam from an H_ 665 keV Cockcroft-Walton preinjector. The ever increasing international demand for neutrons has motivated a bid to build a second target station at ISIS, for which £100 million funding has recently been approved by the U.K. government [2]. The second target station, operating at 10 Hz, will provide new scientific opportunities in soft condensed matter, biology and advanced materials.     

Low temperature vibrational relaxation of OD in the A2Σ, state

The vibrational relaxation of the A ²Σ state of OD has been studied in the low translational temperature environment of an argon free-jet (T_trans near 5 K). Using laser induced fluorescence (LIF), the absolute vibrational relaxation rate coefficients were measured for OD A²Σ (ν′) to be 7.1 ± 2.6 × 10^?11, 5.9 ± 1.4 × 10^?11, and 2.7 ± 1.1 × 10^?11 cm³ s^?1 for the ν = 3, 2 and 1 states, respectively. State-to-state relaxation rate coefficients were also obtained for the ν= 1, ? = 1 level going to ν= 0, ? levels in the A²Σ manifold. The rotational relaxation rate coefficient for ν= 1, ?= 1 in the A state of OD was found to be 9.6 ± 1.0 × 10^?11cm³s^?1. These values are consistent with values measured for OH A²Σ, and the total loss rates are near the capture rate coefficient value. The vibrational relaxation rate coefficients k_ν appear to be governed by the vibrational energy of the molecule rather then by interaction with nearby dissociative states such as the a⁴Σ state. The relative Einstein A factors for the A²σ (ν = 3) state of OD were determined and compared with the available calculated value.     

The σK coupling in the chiral unitary approach and the isoscalar ¯N , ¯A interaction

We evaluate the “σ " exchange contribution to the ˉN → ˉN scattering within a chiral unitary approach. We show that the chiral transition potentials for ππ → Kˉ in the t -channel lead to a “σ " contribution that vanishes in the ˉ forward direction and, hence, would produce a null “σ " exchange contribution to the K^- optical potential in nuclear matter in a simple impulse approximation. This is a consequence of the fact that the leading-order chiral Lagrangian gives an I = 0 ππ → Kˉ amplitude proportional to the squared momentum transfer, q². This finding poses questions on the meaning or the origin of “σ " exchange potentials used in relativistic mean-field approaches to the K^- nuclear self-energy. This elementary “σ ” exchange potential in ˉN → ˉN is compared to the Weinberg-Tomozawa term and is found to be smaller than the present theoretical uncertainties but will be relevant in the future when aiming at fitting increasingly more accurate data.     

A variational principle giving gravitational “superpotentials,” the affine connection,Riemann tensor,and Einstein field equations

A first-order Lagrangian is given, from which follow the definitions of the fully covariant form of the Riemann tensorR _k in terms of the affine connection and metric; the definition of the affine connection in terms of the metric; the Einstein field equations; and the definition of a set of gravitational superpotentials closely connected with the Komar conservation laws [7]. Substitution of the definition of the affine connection into this Lagrangian results in a second-order Lagrangian, from which follow the definition of the fully covariant Riemann tensor in terms of the metric, the Einstein equations, and the definition of the gravitational superpotentials.Dedicated to Achille Papapetrou on the occasion of his retirement.     

A Search on the Klein-Gordon Equation

The s-wave Klein-Gordon equation for the bound states is separated in two parts to see clearly the relativistic contributions to the solution in the non-relativistic limit. The reliability of the model is discussed with two examples chosen specifically.     

Measurement of the spin-correlation coefficients A x,x and A y,y in the quasi-free np → {pp} s π− reaction near threshold at ANKE-COSY

A kinematically complete double-polarization measurement of the quasi-free np → {pp} _s π^? reaction near threshold has been performed using the ANKE spectrometer at COSY-Jülich. Here {pp} _s represents a two-proton system with an excitation energy less than 3 MeV. The transversely vector polarized deuteron beam and the internal polarized ANKE hydrogen target were used to determine the spin-correlation coefficients A _x,x and A _y,y . Events from the quasi-free np → dπ⁰ reaction were recorded simultaneously and used for both beam and target polarimetry. In addition, the product of the beam and target polarizations could be estimated from the A _y,y coefficient. The storage cell within the polarized target was the main source of background events. Dedicated runs, with no gas in the cell and with the cell filled with N ₂ gas, were taken to study the backgrounds. The data analysis procedure and the initial results of the experiment are presented.     

A Lower Bound on the Entanglement in the Jaynes-Cummings Model

The entanglement between an atom and field is investigated by using the 3aynes-Cummings model. The initial atomic state is supposed in a mixed state and the field is in a squeezed state. The lower bound on the entanglement quantified by concurrence is calculated. It is found that the entanglement with the atom being initially in a mixed state can be larger than that with the atom being initially in a pure state. The entanglement is not a monotone function of the squeezing parameter r of the field and it achieves the maximum for certain r and then decreases with further increase of r.     

Analysis of the Effects of Three-nucleon Forces in A = 3, 4 Systems

It is not possible to reproduce both the three- and four-nucleon binding energies using the available two-nucleon potentials. This is one manifestation of the need to include a three-nucleon force in the corresponding Hamiltonian. In this paper we will analyze the capability of a three-nucleon force model to describe not only the aforementioned binding energies but also some N ? d low energy scattering observables.     

A New Loop Algebra and the Corresponding Computing Formula of Constant γ in the Quadratic-Form Identity, as Well as the Generalized Burgers Hierarchy

A new loop algebra containing four arbitrary constants is presented, and the corresponding computing formula of constant γ in the quadratic-form identity is obtained in this paper, which can be reduced to computing formula of constant γ in the trace identity. As application, a new Liouville integrable hierarchy which possess bi-Hamiltonian structure and generalized Burgers hierarchy are derived.     

A search for the lepton-flavour violating decays τ → eα, τ → μα

Lepton spectra in decays have been studied with the ARGUS detector at thee ⁺ e ^– storage ring DORIS II at DESY using the pseudo-rest-frame technique. We have improved upper limits for two-body -decays into a lepton and an unobservable particle.Supported by the German Bundesministerium für Forschung und Technologie, under contract number 054DO51P     

Precise Measurements of the Masses of Cs, Rb and Na – A New Route to the Fine Structure Constant

We report new values for the atomic masses of the alkali ¹³³Cs, ⁸⁷Rb, ⁸⁵Rb, and ²³Na with uncertainties ≤ 0.2 ppb. These results, obtained using Penning trap single ion mass spectrometry, are typically two orders of magnitude more accurate than previously measured values. Combined with values of h/m _atom from atom interferometry measurements and accurate wavelength measurements for different atoms, these values will lead to new ppb-level determinations of the molar Planck constant N _A h and the fine structure constant α. This route to α is based on simple physics. It can potentially achieve the several ppb level of accuracy needed to test the QED determination of α extracted from measurements of the electron g factor. We also demonstrate an electronic cooling technique that cools our detector and ion below the 4 K ambient temperature. This technique improves by about a factor of three our ability to measure the ion's axial motion. This revised version was published online in July 2006 with corrections to the Cover Date.