Dynamical enhanced electron emission and discharges at contaminated surfaces

Broad-area electrodes show electron emission already at electric field strengthsF≈10⁷ V/m. This enhanced field emission (EFE) occurs only for contaminated surfaces. EFE is accompanied by photon emission and gas desorption yielding finally discharges. EFE is caused by dust and contaminants initiating the following effects:

an electron is stochastically emitted in a trigger zone

the electron gains energyΔE?eΔxF ^*

which excites electronic states

which relax by the emission of electrons, photons, and atoms

where the positive charges left behind enhanceF ^*=βF (β?1) initiating so an electron avalanche, i.e., a high conductivity channel. Because of charge migration and neutralization, this avalanche has a life time. This pulsating EFE is accompanied by light emission and gas desorption yielding finally a gas cloud and a discharge.

The pulsating, self-sustained EFE has the same root as:

the enhanced secondary emission found first by Malter

the conductivity switching exhibited by thin (≈ 1 μm) layers of semiconductors or insulators

the normal cathode fall and

the firing-wave instability in neurodynamics.

     

Absence of singular continuous spectrum for certain self-adjoint operators

We give a sufficient condition for a self-adjoint operator to have the following properties in a neighborhood of a pointE of its spectrum:

1. its point spectrum is finite;
2. its singular continuous spectrum is empty;
3. its resolvent satisfies a class of a priori estimates.

     

A phase cell cluster expansion for a hierarchical Ø 3 4 model

The formalism developed in a previous paper is applied to yield a phase cell cluster expansion for a hierarchical ø ₃ ⁴ model. The field is expanded into modes with specific renormalization group scaling properties. The present cluster expansion for a vacuum expectation value is formally the natural factorization of each term in the perturbation expansion into the contribution of modes connected to the variables in the expectation via interactions, and that of the complementary set. The expectation value is thus realized as a sum of contributions due tofinite subsets of the modes. We emphasize the following additional features:

1. Partitions of unity are not used.
2. There areessentially no cut-offs.
3. The expansion is developed directly, without an initial need to prove an ultraviolet stability bound, the most difficult part of the traditional approach.

Our main interest in the present phase cell cluster expansion is founded in the belief that it may be the right vehicle for proving the existence of a nontrivial four-dimensional field theory.     

Two-dimensional quantum field theories containing a massless scalar field

The following new findings are briefly reported:

1. A consistent quantum theory can be formulated for a free massless scalar field in two-dimensional spacetime.
2. Satisfactory operator solutions in terms of asymptotic fields can be constructed in the Thirring and Schwinger models.
3. Gauge invariance is spontaneously broken in the Thirring model as well as in the Schwinger model.

     

The moment of inertia at the saddle point of low energy fission of even-even nuclei

We use the molecular model of low energy fission, which describes the nucleus by two interacting fragments, to calculate the moment of inertia for U²³⁶ in the cranking approximation including BCS theory. We show that the moment of inertia at the saddle point:

1. depends almost linearly on the fragment distance.
2. is influenced only very weakly by the pairing constant and by the fragment deformations.
3. shows, as a function of the distribution of mass between the two fragments (A ₁ ,A ₂ ), a minimum near the magic configurationA ₁=132,Z ₁=50 and depends in this mass region strongly on the term structure near the Fermi energy.
4. is approximately that of a rigid body.

     

Production spectrum of gamma rays in high energy interactions and high energy gamma ray intensity at 2900 m

An extended array of emulsion and lead plates has been exposed at Zugspitze for 6 months. The results of the measurements carried out on individual high energy cascades, and families of cascades allow the following conclusions to be drawn:

1. The vertical intensity of electrons andγ-quanta with energy > 1000 GeV on Zugspitze (2900 m) is 4.5/8.8 × 10^?10 cm^?2sec^?1ster^?1.
2. The energy spectrum of these particles has the shape of a power law with exponent — 1.85.
3. The production spectrum of secondary particles in individual interactions is derived, and it steepens with increasing primary energy. Using other evidence one may then conclude that this is due to an increase of multiplicity with primary energy.

     

Photoemission on the highT c superconductors Y−Ba−Cu−O

XPS and UPS photoemission experiments on the highT _c superconductors (T _c ≈90 K) with nominal composition YBa₂Cu₃O_9-y (y≈2) show the following:

1. The density of electronic states at the Fermi energy is very small, much smaller than in pure Cu.
2. The Cu 2p spectra show only a Cu²⁺ contribution.
3. The Ba core levels show a structure with two components of nearly equal magnitude, which leads to the suggestion that these compounds have large O^2? vacancies coordinated to Ba²⁺ sites.
4. Annealing at 400°C under UHV conditions leads possibly to a partial reduction of Cu²⁺ to lower Cu valence states and to a small increase of the O^2? vacancy component of the Ba²⁺ line.

     

Three applications toSO(4) invariant systems of a theorem of L. Michel relating extremal points to invariance properties

We consider a theorem due to Michel [1] which relates the invariance properties in peculiar directions in a linear space on which we represent a Lie groupG to the extremal points of an arbitrary smoothG-invariant function. The group we are interested in isSO(4) and we apply the mathematical results to the following problems:

1. mixed linear Stark Zeeman effect in a hydrogen atom,
2. perturbation of a finite Robertson-Walker metric,
3. gas evolutions preserving angular momentum and vorticity.

     

Interactions of neutrons with gallium and its isotopes

Coherent neutron scattering lengths and total cross sections were measured on elemental Ga, Ga-compounds and on isotopically enriched samples at neutron energies from 0.5 meV up to 143 keV using different techniques. From the experimental data the following quantities could be obtained:

the coherent scattering length of Ga and the spin state scattering lengths of the isotopes.

the potential scattering radii (R′)

the absorption cross sections of Ga,⁶⁹Ga,⁷¹Ga and⁷⁵As.

As derived quantities are given the coherent and incoherent cross sections and the resonance spin scattering lengths for theJ=1 andJ=2 states of⁷⁰Ga and⁷²Ga. The physical meaning of these data and ofR′ and the comparison with the resonance parameters are considered.     

The process e + e − → bb̅W + W − at the next linear collider in the Minimal Supersymmetric Standard Model

The complete matrix element for e ⁺ e^? → bb?W⁺ W^? is computed at tree-level within the Minimal Supersymmetric Standard Model. Rates of interest to phenomenological analyses at the Next Linear Collider are given. In particular, we study:

• ? tt? production and decay tt? →(bW ⁺)(b?W ^?)
• ? ZH production followed by Z → bb? and H → W ⁺ W^?
• ? AH production followed by A→ bb? and H → W ⁺ W^?
• ? hW ⁺ W^? production followed by h→ bb?.

Top and Higgs finite width effects are included, as well as all those of the irreducible backgrounds.     

A proof of the unitarity ofS-matrix in a nonlocal quantum field theory

Using the formfactors which are entire analytic functions in a momentum space, nonlocality is introduced for a wide class of interaction Lagrangians in the quantum theory of one-component scalar field φ(x). We point out a regularization procedure which possesses the following features:

1. The regularizedS ^δ matrix is defined and there exists the limit $$\mathop {\lim }\limits_{\delta \to 0} S^\delta = S.$$
2. The Green positive-frequency functions which determine the operation of multiplication in \(S \cdot S^ + \mathop = \limits_{Df} S \circledast S^ + \) can be also regularized ?^δ and there exists the limit $$\mathop {\lim }\limits_{\delta \to 0} \circledast ^\delta = \circledast \equiv .$$
3. The operator \(J(\delta _1 ,\delta _2 ,\delta _3 ) = S^{\delta _1 } \circledast ^{\delta _2 } S^{\delta _3 + } \) is continuous at the point δ₁=δ₂=δ₃=0.
4. $$S^\delta \circledast ^\delta S^{\delta + } \equiv 1at\delta > 0.$$ Consequently, theS-matrix is unitary, i.e. $$S \circledast S^ + = S \cdot S^ + = 1.$$

     

Correlation inequalities and uniqueness of the equilibrium state for the plane rotator ferromagnetic model

We derive new inequalities for the plane rotator ferromagnetic model and use them to obtain the following results:

1. If the model is isotropic, the derivability of the free energy as function of the magnetic fieldh implies the existence of a unique translation invariant Gibbs state and if furthermoreh=0 all Gibbs states are invariant by rotation of the spins.
2. If the model is anisotropic the above assertion holds forh non-zero.
3. If the model is anisotropic then there are at most two extremal translation invariant Gibbs states for almost all values of the anisotropy parameter.

     

Magnetic field and doppler velocity correlation in quiescent solar prominences

Analyzing statistically the magnetic and Doppler velocity data for 85 quiescent prominences observed in 1983–1987 by Nikolsky's magnetograph, we came to the following preliminary conclusions:

The average longitudinal magnetic field of the prominence determines the dynamic velocity of the latter: the stronger magnetic fields correspond to the higher Doppler velocities.

A longitudinal magnetic field less than 25 G allows the material to move with arbitrary velocity within the limits of several kilometers per second. A magnetic field higher than 25 G suppresses such movements.

The horizontal length of the flux tube exceeds its vertical part by 1.5 orders of magnitude (the upper limit).

There is an angle of 10°between the horizontal component of the velocity vector in quiescent prominences and the long axis of the filament.

The maximum velocity in quiescent prominences is about 7 km/s.

     

Unbounded derivations ofC*-algebras II

It is demonstrated that a closed symmetric derivation δ of aC?-algebra \(\mathfrak{A}\) generates a strongly continuous one-parameter group of automorphisms of aC?-algebra \(\mathfrak{A}\) if and only if, it satisfies one of the following three conditions

1. (αδ+1)(D(δ))= \(\mathfrak{A}\) , α∈?\{0}.
2. δ possesses a dense set of analytic elements.
3. δ possesses a dense set of geometric elements.

Together with one of the following two conditions

1. ∥(αδ+1)(A)∥≧∥A∥, α∈IR,A∈D(δ).
2. If α∈IR andA∈D(δ) then (αδ+1)(A)≧0 impliesA≧0.

Other characterizations are given in terms of invariant states and the invariance ofD(δ) under the square root operation of positive elements.     

Small-angle X-ray scattering on spinodal,nucleotic or coarsening processes in two-phase systems containing spherical,fibrillar or lamellar inhomogeneities

We study the effects of some of the most important and typical structural changes in two-phase systems on selected structural parameters obtained from small-angle x-ray scattering (SAXS) measurements. To limit the present study, it was assumed that the Phase, 1, embedded in the matrix

1. is monodispersed and homogeneous,
2. possesses one of the three most extreme shapes (spherical, fibrillar or lamellar) and
3. changes its behaviour

1. through type change (spinodal or nucleotic or coarsening), without changing the shape,
2. through a change of the shape only, or
3. through a) (type change) and b) (shape change) simultaneously.

To find the type of change for three basically different shapes of Phase 1 and to calculate its intensity (amount of the change) the following three SAXS parameters must be compared before and after the treatment of the system:

1. chord lengthl ₁ (and/or radius of gyrationR),
2. volume partw ₁ of the Phase 1, and
3. relative inner surfaceS _v of the system.

It is shown by this comparison that by the pure type change in the case of

1. spinodal change, all three SAXRS parameters are increasing or decreasing simultaneously and proportional to a power of the intensity of the change,
2. nucleotic change,l ₁ (and/orR) is unchanged, the other two (w ₁ andS _v ) are increasing or decreasing simultaneously and directly proportional to the intensity,
3. coarsening change,w ₁ is unchanged and anincreasing ofl ₁ is always accompanied by adecreasing ofS _v and vice versa.

In addition to this type change, the cases of mere changes of the shape (“shape change”) and finally of simultaneous type and/or shape change are studied. For the case of pure shape change the alteration of the dimensions (chord lengthl ₁ and/or radius of gyrationR) must be followed. The limitations of the analyses of the simultaneous type and/or shape change are discussed in detail.     

Magnetostriction measurement by means of strain modulated ferromagnetic resonance (SMFMR)

A novel method for measuring magnetostriction constants is presented. A strain, periodic in time, applied to the sample, causes a modulation of the ferromagnetic resonance line position. The height of the signal obtained after phase-sensitive detection is proportional to the strain modulation depth. The appropriate magnetostriction constant λ is obtained by comparing the height of the SMFMR signal with that of the FMR line, as recorded by means of magnetic field modulation. Features of the new technique are:

1. high sensitivity: λ_min? 10_?9 forM=100 Oe and linewidth ΔH _d=1 Oe;
2. λ's belonging to distinct precession modes are separately determined;
3. applicable to thin layers for which strain gauge techniques cannot be used;
4. wide temperature range: 1.2 K<T<300 K;
5. uniform stress.

An illustrative example (YIG layer on GGG substrate) is given.     

On the existence of crossing symmetric and unitary scattering amplitudes with Regge poles

We give a complete proof of the existence of scattering amplitudesA(s,t,u) with the following properties

1. the amplitudes are total symmetric ins,t, andu.
2. they satisfy elastic unitarity for 4≦s≦16, and
3. they develop resonances forl≧2 on a bounded Regge trajectory which dominates the asymptotics for large energies.

     

Berechnung der Signalform bei Doppelresonanzexperimenten an2 P 3/2-Zuständen im starken Magnetfeld

A computer program has been set up, which permits to calculate the signal shape for optical double resonance experiments in² P _3/2-states of alkali atoms in a strong magnetic field. The application to the 5² P _3/2-state of³⁹K, where recently large discrepancies have been reported between early double resonance measurements and new level crossing experiments, has the following results:

1. The measured strong field spectra can be reproduced satisfactorily, if the level crossing data for the hyperfine structure coupling constants are used.
2. The computed line shifts are in good agreement with a formula recently deduced by means of a new approximation methode.

     

Testing general relativity: Progress,problems, and prospects

Recent results from radar and radio gravity experiments are:

1. Retardation of radar signals: 1.02 +?0.05 (planetary radar), 1.00 +? 0.04 (spacecraft);
2. Deflection of radio waves: 0.99 +? 0.12 (short baseline interferometry), +0.15 1.04 (short baseline interferometry), ?0.10. 0.90 +? 0.05 (short baseline interferometry);
3. Relativistic perihelion advance of Mercury: 0.99 +? 0.03 (planetary radar), 1.00 +? 0.01 (radar plus optical);
4. Time variation of the gravitational constant: (G/G) < 4 ×10^?10/yr (planetary radar). The first three results are expressed as fractions of the corresponding effects predicted by general relativity. In terms of the Eddington-Robertson parameters, the first two are approximately equal to (1+γ)/2 and the third to (2 + 2γ-β)/3. The third result depends on the assumption that the solar gravitational quadrupole moment vanishes; its effects cannot be separated usefully from those of general relativity with the present data set. The uncertainties are as given by the individual experimenters; in some cases they represent formal standard errors, in others an allowance for possible systematic errors is included.

     

Nachwirkungsmechanismen in Ferriten

In ferrites a large number of after-effects are found, with time constants between nano-seconds and years. In this review the after-effects due to ion-and electron motion will be treated. One finds:

1. single-ion effects in combination with lattice deformations, e.g. Mn³⁺;
2. ion effects caused by mobile vacancies, e.g. Co²⁺;
3. effects due to electron transfer:
4. Co²⁺?Co³⁺
5. Me²⁺?Fe³⁺, in combination with Me⁴⁺ and vacancies.
6. Me⁴⁺?Fe²⁺, with Me=Si, Ti (photomagnetic effect).

The electron transfer is found to be related to electrical effects. In analogy to the photoelectric effect, one has found that illumination produces changes in magnetic properties. Generally speaking, one has in ferrites as many problems with donors and acceptors as in other semiconductors. Information from magnetic measurements helps to elucidate their nature.