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.     

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.

     

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.

     

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.

     

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.     

The possibility of using a semiconductor thermal probe to investigate the power flow distribution in waveguides

Conclusions

1. The temperature profile of an absorbing film for a given microwave power flux distribution has been considered.
2. The conditions under which agreement is found between the temperature relief and the flux distribution has been clarified.
3. An experimental investigation has been carried out of the temperature profile in a matched film for the TE₁₀ mode.
4. The possibility of using a semiconductor thermal probe to investigate the microwave power flux distribution has been demonstrated.

     

Voltage/current characteristics of high-current vacuum arc at a small gap length

Measurements of arc voltage for semiwave currents of the amplitude up to 13 kA and frequencies 0.9 kHz and 6.0 kHz were done for CuCr electrodes whose separtion was 2 mm. The obtained data were used to determine voltage/current and voltage-time characteristics of high-current vacuum arc. They enabled to state as:

1. The shape and values of arc voltage during a sinusoidal current semiwave flow depend on the current amplitude and frequency. As the current amplitude increases the arc voltage rises, and its shape changes from relatively low and quiet to high with considerable fluctuations of high frequency and amplitude (HAF).
2. Arc voltage at a given current instantaneous valuei _a1 depends on the current waveform before reachingi _a1 . The arc voltage beyond the range of HAF occurrence, at the same instantaneous value of the sinusoidal current, is higher during the current increase than during its decrease and higher for higher current frequency.
3. Mean arc voltage and current value at the moment of HAF onset, rise with the increase of current peak and frequency.

This article presents qualitative correlations between the measured arc voltage and an expected discharge mode in the intercontact gap.     

An investigation of the axial mode behaviour of a helical TEA-CO2 laser

The frequency behaviour of axial modes was investigated during the initial phase of mode competition in case of a helical TEA-CO₂ laser. With the help of a homodyne technique single-shot and multi-shot beat spectra were measured. Analysing these under various aspects and combining the results of an earlier investigation it was found that

1. inferior modes exist only for 100–200 ns.
2. their spectral width is less than 1 MHz and is determined by lifetime broadening, with the dominant mode narrower than 0.77 MHz,
3. in the average over many shots the spectral envelope of modes does not follow a Lorentzian shape as expected for the Lorentzian gain curve,
4. the beat powers change widely from shot to shot, whereas the total laser power remains constant,
5. no specific phase structures are likely to govern the laser emission, although the maximum emission principle appears to be obeyed with every individual shot. In an appendix relations are derived and summarized which are required for the evaluation of beat mode spectra and for the determination of line width as they apply to the actual time dependence of the laser emission.

     

Bounds on the number of eigenvalues of the Schrödinger operator

Inequalities on eigenvalues of the Schrödinger operator are re-examined in the case of spherically symmetric potentials. In particular, we obtain:

1. A connection between the moments of order (n ? 1)/2 of the eigenvalues of a one-dimensional problem and the total number of bound statesN _n, inn space dimensions;
2. optimal bounds on the total number of bound states below a given energy in one dimension;
3. alower bound onN ₂;
4. a self-contained proof of the inequality for α ≧ 0,n ≧ 3, leading to the optimalC ₀₄,C ₃;
5. solutions of non-linear variation equations which lead, forn ≧ 7, to counter examples to the conjecture thatC _0n is given either by the one-bound state case or by the classic limit; at the same time a conjecture on the nodal structure of the wave functions is disproved.

     

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.

     

Spin-order and magnetic properties of BaZn2Fe16O27 (Zn2-W) hexagonal ferrite

We have observed large peaks in the ultrasonic attenuation of a pure and two doped LaAl₂ crystals in the temperature region of about 45 K which are possibly of the Bordoni type. Their most interesting characteristics are:

1. There is only one peak in each sample.
2. The peaks are so narrow that they can be described by the original Seeger model with only one actication energy and one attempt frequency.

     

Neutron star magnetism

It is shown that

1. an appreciable change of magnetic moment of a neutron star cannot occur via ohmic dissipation
2. pulsars provide evidence for large internal magnetic fields in main sequence stars. If pulsars are born from stars with masses exceeding 3 ?_⊙ the internal field must be of the order of 10³-10⁴ Gauss while if they derived from less massive urstars 10² Gauss are sufficient to give rise to a magnetic moment ofM～10³⁰ Gauss cm³.

     

Jump discontinuities of semilinear,strictly hyperbolic systems in two variables: Creation and propagation

The creation and propagation of jump discontinuities in the solutions of semilinear strictly hyperbolic systems is studied in the case where the initial data has a discrete set, {x _i } _i ⁼¹ⁿ , of jump discontinuities. LetS be the smallest closed set which satisfies:

1. S is a union of forward characteristics.
2. S contains all the forward characteristics from the points {x _i } _i ⁼¹ⁿ .
3. if two forward characteristics inS intersect, then all forward characteristics from the point of intersection lie inS.

We prove that the singular support of the solution lies inS. We derive a sum law which gives a lower bound on the smoothness of the solution across forward characteristics from an intersection point. We prove a sufficient condition which guarantees that in many cases the lower bound is also an upper bound.     

Probing of the Higgs-fermion coupling atγγ-colliders

Three possibilities to observe the Higgs-top interation at future γγ-colliders are discussed:

1. associated Higgs production via the \(\gamma \gamma \to t\bar tH\) reaction,
2. Higgs obliged radiative correction to the \(\gamma \gamma \to t\bar t\) channel,
3. Higgs resonance production via γγ→H→ZZ.

The results obtained show windows of the Higgs mass where the Yukawa interaction of the Higgs with the top quark can be studied at γγ-colliders.     

Existence of phase transitions for quantum lattice systems

We prove that the following lattice systems:

1. anisotropic Heisenberg model,
2. Ising model with transverse magnetic field,
3. quantum lattice gas with hard cores extending over nearest neighbours,

exhibit phase transitions if the temperature is sufficiently low and the transverse (or kinetic) part of the interaction sufficiently small.     

Ambiguities in theη-nucleon scattering length determination

The positive sign of theη-nucleon scattering lengthb _ηN was predicted in [1] assuming the resonance mechanism for theπ ^?p → ηn reaction. We demonstrate that

1. the assumption about thet-channel mechanism of the reaction leads tob _ηN < 0 and
2. the experimental data on theη production cross section are equally compatible with both resonance andt-channel mechanisms.

     

Quasi-particles at finite temperatures

We study the consequences of the KMS-condition on the properties of quasi-particles, assuming their existence. We establish

1. If the correlation functions decay sufficiently, we can create them by quasi-free field operators.
2. The outgoing and incoming quasi-free fields coincide, there is no scattering.
3. There are may age-operatorsT conjugate toH. For special forms of the dispersion law ε(k) of the quasi-particles there is aT commuting with the number of quasi-particles and its time-monotonicity describes how the quasi-particles travel to infinity.

     

New interferometric method for determining the refractive index of thin dielectric film,its thickness,the phase shift,and the order of interference

A new interferometric method is proposed, using white light fringes of equal chromatic order to determine simultaneously the following paramcters:

1. The refractive index of a thin dielectric film, and hence its dispersion.
2. The film thickness.
3. The correct value of the order of interference.
4. The phase shift occuring due to reflection at the dielectric/metal interface. In the present work, doubly silvered zinc sulphide (ZnS) thin dielectric film was used as an example in applying the proposed method.

     

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. $$S \circledast S^ + = S \cdot S^ + = 1.$$

     

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.