Recent developments and new trends in NMR on oriented nuclei

Recent developments in nuclear magnetic resonance on oriented nuclei (NMR-ON) are reviewed with the following main topics: (i) Measurement of magnetic moments. In this context the resonance shift of NMR-ON resonances with an external magnetic field is discussed critically. (ii) Resonance techniques for the measurement of electric quadrupole moments. It is shown that — with hcp-Co as host matrix — the techniques QI-NMR-ON (quadrupole-interaction-resolved NMR-ON) and MAPON (modulated adiabatic passage on oriented nuclei) have a tremendous potential for the measurement of quadrupole moments of radioactive nuclei. Data are presented for medium (Zr, Nb) and heavy elements (Ir, Pt, Au, Hg). With results on the 11/2^– isomers in Au it is shown that MAPON yields highly precise quadrupole moments of states with half-lives of the order of seconds, for which no other technique with comparable precision exists up to now. In the case of⁹⁰Nb it is demonstrated that MAPON allows also the measurement of very small quadrupole moments with high precision. (iii) Electric field gradients in cubic Fe, fcc-Co and Ni. MAPON experiments show a strong magnetic-field dependence of the effective quadrupole interaction; the implications are discussed. (iv)-decay-induced lattice site change identified by a double-resonance NMR-ON measurement. The resulting change of the hyperfme interaction has severe consequences for the interpretation of time-integral and even time-differential nuclear orientation measurements on nuclei far off stability. (v) Spin-lattice relaxation for nuclei on non-substitutional lattice sites. Recent experiments support the global character of the spin-lattice relaxation, in contrast to the local character of the static magnetic hyperfine interaction. (vi) Magnetic-field dependence of the spin-lattice relaxation. Recent experiments with hcp-Co as host lattice strongly support the so-called enhancement factor model and disfavour the one-, two- or three-magnon processes postulated in the literature.     

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.     

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.     

Lattice dynamics and transport equations for quantum crystals including singular interactions

The influence of frequency modulation of the rf field and modulation of the static magnetic field on NMR-response is investigated. The mathematical treatment using density operator formalism results in a different dynamical behaviour of the nuclei whether frequency—or field modulation is applied. Therefore a general equivalence of the two kinds of modulation does not exist. Explicite solutions for the nuclear magnetization with simultaneous frequency—and field modulation are evaluated for systems obeying Bloch equations. Resonance experiments have been performed using different detection methods:

1. rf spectrum analysis of the nuclear induction emf from a decoupled (zero leakage) crossed coil setup.
2. conventional lock-in detection of the signal information from an NMR-detector with single resonant circuit.

     

Detection of highly ionizing particles: Nonlinear near-surface phenomena in silicon radiation detectors

As far as the detection system is concerned, experimens on synthesis and study of the properties of superheavy nuclei is one of the most difficult tasks. In fact, these experiments can be considered extreme in many senses:

• —extremely low (fractions of a picobarn-picobarns) formation cross sections of the products under investigation
• —extremely high heavy ion beam intensities for example, ～1.1–1.5 pμA^{1 48}Ca
• —high radioactivity of actinide targets, which are used in the experiments aimed at the synthesis of super-heavy nuclei
• —very long duration of the experiment (as long as a year)
• —extremely low yield of the products under investigation (sometimes less than 1 per month)
• —very high sensitivity of the detection system
• —radical suppression of the background products (method of “active correlations”).

The two last points are the subject of the present paper, as well as the subject of two of my reviews published before. It is evident that without knowledge of the nature of the internal processes in semiconductor detectors it is virtually impossible to provide clear detection of ultra rare signals. In the present paper, the author reports on the investigation of near-surface phenomena in silicon radiation detectors, first of all bearing in mind the theoretical-methodological aspect of these phenomena. Non-equilibrium electron-hole recombination, pulse height defect formation, charge multiplication, and formation of “hot” electron system, are considered. With just these phenomena one can observe nonlinearity of energy-charge-amplitude conversion for heavy ion (recoil nucleus) registered by a silicon detector. Practical applications are also considered. One of them is a deeply modified method of “active correlations”. Projection of applying the method in the experiments with the modernized cyclotron (DC-280 FLNR project) is projected as well as possible applications in the heavy-ion-induced complete fusion nuclear reactions.     

Strong cluster properties for classical systems with finite range interaction

In a previous paper, “strong” decrease properties of the truncated correlation functions, taking into account the separation of all particles with respect to each other, have been presented and discussed. In this paper, we prove these properties for finite range interactions in various situations, in particular

1. at low activity for lattice and continuous systems,
2. at arbitrary activity and high temperature for lattice systems,
3. at ReH≠0, β arbitrary and atH=0 for appropriate temperatures in the case of ferromagnets.

We also give some general results, in particular an equivalence, on the links between analyticity and strong cluster properties of the truncated correlation functions.     

The unitary irreducible representations of\overline {SO} _0 (4,2)

An exhaustive classification of all irreducible Harish-Chandra \(\mathfrak{s}\mathfrak{o}\) (4,2)-modules, integrable to unitarizable projective representations of the conformal group, is established by infinitesimal methods: the classification is based

1. on the reduction upon the maximal compact subalgebra, associated with a lattice of points in ?³, and
2. on a set of additional parameters upon which the eigenvalues of central elements of the enveloping algebra depend polynomially.

     

Astroparticle physics with high energy neutrinos: from AMANDA to IceCube

Kilometer-scale neutrino detectors such as IceCube are discovery instruments covering nuclear and particle physics, cosmology and astronomy. Examples of their multidisciplinary missions include the search for the particle nature of dark matter and for additional small dimensions of space. In the end, their conceptual design is very much anchored to the observational fact that Nature produces protons and photons with energies in excess of 10²⁰ eV and 10¹³ eV, respectively. The puzzle of where and how Nature accelerates the highest energy cosmic particles is unresolved almost a century after their discovery. The cosmic ray connection sets the scale of cosmic neutrino fluxes. In this context, we discuss the first results of the completed AMANDA detector and the science reach of its extension, IceCube. Similar experiments are under construction in the Mediterranean. Neutrino astronomy is also expanding in new directions with efforts to detect air showers, acoustic and radio signals initiated by super-EeV neutrinos. The outline of this review is as follows:

Introduction

Why kilometer-scale detectors?

Cosmic neutrinos associated with the highest energy cosmic rays

High energy neutrino telescopes: methodologies of neutrino detection

High energy neutrino telescopes: status

     

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.

     

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.

     

Quadrupole and magnetic moment measurements on spin-aligned projectile fragments

The Level Mixing Resonance (LMR) technique allows to determine ground-state nuclear moments by measuring the spin-polarization of the betaddecay, and starting from an initially aligned ensemble of nuclei. Using this new technique, the ratio of the quadrupole frequency to the magnetic moment of the neutron rich¹⁸N ground state has been measured: $\nu _Q /\mu (^{18} N\underline {Mg} ) = 1328(33)$ kHz/n.m. In order to measure the nuclear moments independently, the Nuclear Magnetic Resonance (NMR) and LMR techniques will be combined.     

Hyperfine fields and neutron scattering in ferromagnetic metals

The origin of ferromagnetism in the transition metal ferromagnets, iron, cobalt, and nickel is discussed, from an ab initio band structure point of view, with proper attention to the explicit roles of exchange, correlation and hybridization effects. The influence of these effects and all the mechanisms such as direct, exchange core polarization and many-body effects that have been found important for the hyperfine properties of atomic systems are included in attempting to understand the experimentally observed hyperfine fields at the nuclei in these metals. Spin-density distributions using calculated spin polarized band wave-functions are used to make comparisons with experimental neutron scattering data. The impact of the results of analyses of hyperfine fields at the nuclei and spin density distributions on the origin of hyperfine fields at muon sites is discussed. This talk, and the corresponding article for the proceedings of this conference, will deal with the theoretical understanding of the hyperfine fields at the nuclei and neutron scattering form factors in the three ferromagnetic metals, iron, cobalt and nickel and the impact of this understanding on that of the origin of the hyperfine fields at positive muon sites in these metals. With these aims in mind, the plan of my talk will be the following.

1. Discussion of a first-principle principle procedure to obtain the energy bands and electronic wave-functions in these metals and the understanding of the origin of their ferromagnetism from a band point of view.
2. Mechanisms contributing to hyperfine fields in atomic systems and their relevance for ferromagnetic metals.
3. The mechanisms for the origin of hyperfine fields in these metals, corresponding theoretical results and comparison with experiment.
4. Comparison between calculated spin-density distributions and experimental results from neutron scattering data.
5. Remarks on the origin of hyperfine fields at muon sites in these metals.

     

Phases coexistence and surface tensions for the potts model

Theq states Potts model exhibits a first order phase transition at some inverse temperature β _t between “ordered” and “disordered” phases forq large as proved in [1]. In space dimension 2 we use theduality transformation as aninternal symmetry of the partition function at β _t to derive an estimate on the probability of a contour. This enables us to prove the preceding result and the following new results:

1. The discontinuity of the mass gap at β _t .
2. The existence of astrictly positive surface tension between two ordered phases up to β _t .
3. The existence of a non-zero surface tension between an “ordered” and the “disordered” phase at β _t .

     

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.

     

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.

     

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.

     

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.     

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.

     

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.