The Design of the Black Patch

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The physics of the τ lepton

A comprehensive review of the status of τ-lepton physics is presented. We include the knowledge on the properties of the tau, the decay branching fractions and tests of the standard model. Discussions of possible puzzles and an indication of the future possibilities in this field are a lso presented.     

The Structure of the Algebra of Observables in the Intermediate Situation of the ∈-Model

We look at the action of the spin-1/2 operatorsof quantum mechanics on the state of an entity in aphysical way, and use this as a guideline to define theoperators of the intermediate situations of a general spin-1/2 measurement model called the-model. Then we test the possible linearity ofthe operators so constructed.     

The Optimization of the PDA Optical System

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The triple-α process and the origin of the elements

The triple-α process is the nuclear fusion of helium to carbon. Two ⁴He nuclei collide and form an unstable state of ⁸Be. Before this can decay back a third α-particle collides with it to form a ¹²C nucleus. The reaction rate is probably the most temperature sensitive known to physics because there is a resonant state of the ¹²C nucleus at just the energy of the ⁸Be? and the ⁴He that have the greatest chance of penetrating the Coulomb barrier. The reaction takes place in stars that have exhausted their central hydrogen fuel. Most interesting are the asymptotic giants that can dredge the carbon produced to the surface and return it, perhaps first processing it to nitrogen, to the interstellar medium. The fortuitous energy of the resonant state of ¹²C and its consequences are crucial to the way stars evolve and the abundance of carbon on the Earth.     

The additivity of the η-invariant. The case of a singular tangential operator

We prove the decomposition formula for the -invariant of the compatible Dirac operator on a closed manifoldM which is a sum of two submanifolds with common boundary.Research partially supported by NSF     

The international Boltzmann project – the contribution of the PTB

To support new determinations of the Boltzmann constant, which have been requested by the International Committee for Weights and Measures (CIPM) and which are necessary for preparative steps towards new definitions of the kilogram, the ampere, the kelvin and the mole, an iMERAPlus joint research project is coordinating the European activities in this field in Spain (CEM), Denmark (DFM), France (LNE-INM/CNAM, University Paris North), Italy (INRiM, Universities of Naples and Milan), United Kingdom (NPL), Germany (PTB) and in the European Institute for Reference Materials and Measurements (IRMM). In this major European research project, the Boltzmann constant will be determined with various methods. The aims and the progress to date of the PTB contribution are reviewed in this article. To cite this article: B. Fellmuth et al., C. R. Physique 10 (2009).     

The local structure of the spectrum of the one-dimensional Schrödinger operator

Let \(H_V = - \frac{{d^{\text{2}} }}{{dt^{\text{2}} }} + q(t,\omega )\) be an one-dimensional random Schrödinger operator in ?²(?V,V) with the classical boundary conditions. The random potentialq(t, ω) has a formq(t, ω)=F(x _t ), wherex _t is a Brownian motion on the compact Riemannian manifoldK andF:K→R ¹ is a smooth Morse function, \(\mathop {\min }\limits_K F = 0\) . Let \(N_V (\Delta ) = \sum\limits_{Ei(V) \in \Delta } 1 \) , where Δ∈(0, ∞),E _i (V) are the eigenvalues ofH _V . The main result (Theorem 1) of this paper is the following. IfV→∞,E ₀>0,k∈Z ₊ anda>0 (a is a fixed constant) then $$P\left\{ {N_V \left( {E_0 - \frac{a}{{2V}},E_0 + \frac{a}{{2V}}} \right) = k} \right\}\xrightarrow[{V \to \infty }]{}e^{ - an(E_0 )} (an(E_0 ))^k |k!,$$ wheren(E ₀) is a limit state density ofH _V ,V→∞. This theorem mean that there is no repulsion between energy levels of the operatorH _V ,V→∞. The second result (Theorem 2) describes the phenomen of the repulsion of the corresponding wave functions.     

The Implications of the New Measurement of τ Lepton Mass

We discuss the physical implications for the new measurement of τ lepton mass.The Value of τ lifetime is predictcd.     

The Design of the Microwave Exciter for Klystron

To carry out lower hybrid wave heating and current drive plasma experiment on tokamak, we need mega-watt order of microwave power generated by the parallel-running klystrons. Those klystrons must be driven by the microwave exciter. Now our microwave exciter is used for many years and its performance is decreased very much. It can not satisfy any more the hybrid wave heating and current drive plasma experiment. So we set out to design a new microwave exciter that is consist of the microwave solid components, amplitudestabilization control, modularization design with multitude-outputs, microwave phase control in order to satisfy the demand of the different work in the hybrid wave heating and current drive plasma experiment.     

The π-electron spectra of the benzene N-heterocyclics

The π-electron spectra of the nitrogen heterocyclics are discussed on the basis of a perturbation applied to the spectra of the corresponding aromatic hydrocarbons. The frequency of the first π→π band in pyridine is the same as that of the corresponding band in benzene, because of the accidental cancellation of a first-order blue shift by a second-order red shift. The first-and second-order shifts are related to two perturbation parameters, and these are obtained from experiment by examining the spectra of the benzene heterocyclics. These parameters can then be satisfactorily related to one another by assuming a perturbation field of the form exp (?2ηr)/r and by allowing for the C-N bond being shorter than the C-C bond in benzene.     

The effect of the irradiation of germanium with α-particles on the recombination of current carriers

A study was made of the effect of irradiation with -particles on surface recombination on germanium. An approximative evaluation of the results showed that the position of the energy level of the recombination centre produced by irradiation lies near to the upper edge of the valence band or the lower edge of the conduction band. A value of roughly 3. 10^–12 cm² was obtained for the effective recombination surface produced by the absorption of one -particle.     

The Precise Measurement of the μ+ Lifetime

The lifetime of the positive muon (τ_μ ⁺) can be directly associated with the Fermi Coupling Constant (G _F ), which is one of the most basic parameters of the Standard Model. However, the current experimental accuracy of the τ_μ ⁺ is ∼30 ppm and it has not been improved for more than 15 years. We propose a new experiment for a pulsed muon facility such as RIKEN-RAL to measure the muon lifetime with multi-decay per one time window method. The advantage of our setup, no time window limitation, enables us to test the exponential decay law (EDL) in the long decay time region at the same time. The preliminary analysis set a new upperlimit for the EDL deviation in the muon decay. We accumulated ∼10¹⁰ muon decays and analysis is in progress. This revised version was published online in August 2006 with corrections to the Cover Date.     

The generation of the ϱ-resonance by QCD

By showing that the imaginary part of a suitable QCD amplitude, after extrapolation up to the cut, exhibits indeed a prominent bump structure where the -resonance is expected to be, a rather direct indication for the generation of the -resonance by QCD is given. This is achieved by using a mathematically rigorous method of stable analytic extrapolation, based on the theory of maximally converging sequences of polynomials and the application of conformal mappings.Supported in part by BMFT contract 06 MZ 758 and by the PROCOPE program     

The origin of the pseudogap in α-Ga

Density functional theory, the free-electron empty lattice approximation and the nearly free-electron approximation are employed to investigate the electronic properties of partially covalent α-Ga. Whereas free-electron-like properties are revealed over a large energy range, a deep pseudogap at the Fermi level is characteristic of α-Ga. We explain the origin of the pseudogap in terms of a delicate interplay between the electronic states and the specific Brillouin zone geometry.     

The generalization of the Boltzmann–Matano method

The phenomenological Boltzmann–Matano (B–M) analysis allows approximating the concentration dependent interdiffusion coefficients related to infinite binary diffusion couple experiments. However, the complete understanding of the phenomenological process related to the Kirkendall plane position coupled with the B–M method is still lacking. A purpose of the present study is to generalize the Boltzmann–Matano analysis and propose a method of estimating the unique intrinsic diffusion coefficients of components from the experimental concentration profile and the positions of Matano and Kirkendall planes in multicomponent systems. The proposed physico-chemical approach is used to approximate the intrinsic diffusivities in a single phase of Ni–Pd binary and Cu–Fe–Ni ternary diffusion couples.     

The Hamiltonian dynamics of the soliton of the discrete nonlinear Schrödinger equation

Hamiltonian equations are formulated in terms of collective variables describing the dynamics of the soliton of an integrable nonlinear Schrödinger equation on a 1D lattice. Earlier, similar equations of motion were suggested for the soliton of the nonlinear Schrödinger equation in partial derivatives. The operator of soliton momentum in a discrete chain is defined; this operator is unambiguously related to the velocity of the center of gravity of the soliton. The resulting Hamiltonian equations are similar to those for the continuous nonlinear Schrödinger equation, but the role of the field momentum is played by the summed quasi-momentum of virtual elementary system excitations related to the soliton.     

The Effect of the Relative Motion of Atoms on the Frequency of the Emitted Light and the Reinterpretation of the Ives-Stilwell Experiment

We examine the process of the emission of light from an atom that is in a relative translational motion with respect to the medium at rest in which the electromagnetic excitations propagate. The effect of Lorentz contraction of the of electron orbits on the emitted frequency is incorporated in the Rydberg formula, as well as the emitter’s Doppler effect is acknowledged. The result is that the frequency of the emitted light is modified by a factor that is identical with what is called the ‘relativistic Doppler effect’. The new emission formula is applied for reinterpretation of the Ives-Stilwell experiment and shown that within the second order of approximation with respect to the speeds of the atom and the ‘absolute speed’ (Earth’s speed relative to the medium), the absolute motion does not affect the interference. The expression for the modification of the frequency involves both a first and a second-order term with respect to the speed of the atoms in the cathode tube. The latter turns out to be quantitatively the same as if the time would have changed its rate in the frame moving with the atoms. Thus, a new interpretation of the results of this famous experiment is provided without stipulating time dilation.