Showing papers in "Annalen der Physik in 1974"

One‐Particle Distribution Functions and Thermodynamics of Crystals with Many‐Body Forces. General Consideration and Investigation of the Properties of the Inert Gas Solids

Abstract: A crystal is described by a probability density which is not symmetric regarding the interchange of phase-space coordinates between two molecules. The set of approximate equations for one-particle distribution functions with many-body forces is derived from the LIOUVILLE equation. The expression for the HELMHOLTZ free energy and the equation of state are obtained. The developed method is applied to the determination of the thermodynamic properties of crystalline argon, krypton, and xenon. The nearest-neighbor distances, internal energies, isothermal and adiabatic compressibilities, linear thermal expansion coefficients, specific heats Cv and Cp are calculated using the pair potentials of BARKER-POMPE, of BARKER-BOBETIC, and of LENNARD-JONES, together with the AXILROD-TELLER three-body potential. The obtained results are compared with the experimental data and discussed.

Approximation Methods for the Solution of Heat Conduction Problems Using Gyarmati's Principle

Abstract: After a brief description of GYARMATI's Governing Principle of Dissipative Processes, general approximation methods are developed for heat conduction phenomena on two scales. On the first scale the temperature and heat current density fields are approximated by two different sets of functions in such a way that the internal energy balance and the imposed boundary conditions be satisfied. On the second scale we introduce a new temperature field related to the heat current density through the constitutive equation. Since the dissipation potentials in GYARMATI's principle are connected with each other by LEGENDRE dual transformations we call “dual field methods” the approximation procedure based on the two temperature fields. It is shown that the equations of the GALERKIN method, the method of orthogonal projections, and the TREFFTZ method, when applied to the appropriate problems, are included in the approximation schemes. Due to their great importance a special paragraph is devoted to the treatment of eigenvalue problems. Finally, the approximation methods are illustrated by a simple example and the results are compared with the exact solution.

Generalization of the Governing Principle of Dissipative Processes to Complex Scalar Fields) Quantum Mechanics as “Abstract” Transport Theory

Abstract: The genuine variational principle of macroscopic dissipative continua is generalized to complex scalar fields in the universal form of GAUSSian type. The generalization makes it possible to extend the validity of the principle to the PS field of the non-relativistic SCHRODINGER equation, and to certain types of non-linear problems. Following MORSE's and FESHBACH's sequence of thoughtful ideas in reverse direction the fundamentals of an “abstract” transport theory, isomorphic with one-particle quantum theory, are developed and the possibility of interpreting the quantum theory by classical models is discussed. On the basis of new arguments, the impossibility of interpreting quantum mechanics in terms of classical transport theories (hydrodynamical model, diffusional and stochastic models) is established.

Degenerate Electron Gas at Finite Temperatures. II

Abstract: The degenerate high density electron gas is considered at finite temperatures using SOMMERFELD's expansion. In particular the energy and the life time of one-particle excitations are investigated. For this purpose the real part of the self energy function is calculated up to the order e4. Using results derived in [4] the spectral function A(poM) = 2 JmG(poM) can be given explicitely. Furthermore an equation of state and a correct expression for the specific heat are given, the latter containing additional terms to the result of GELL-MANN.

Die Dielektrizitätsfunktion für ein freies Elektronengas mit beliebigem Entartungsgrad

Abstract: The linear dielectric function for a free electron gas with arbitrary degree of degeneracy is derived using a density matrix method, thus generalizing the dielectric function of LINDHARD. The numerical values are given.

Elektronen-Spin-Gitter- und Spin-Spin-Relaxation von Cu(II) in Ni(II)-bis(1,1-dicyanoäthylen-2,2-dithiolat)-Einkristallen

Abstract: Es wird uber die Temperaturabhangigkeit der Elektronen-Spin-Gitter- und -Spin-Spin-Relaxationszeiten T1 und T2 von Cu(II) in (Tetrabutylammonium)-Ni(II)bis(1,1-dicyanoathylen-2,2-dithiolat)-Einkristallen berichtet. Im Bereich der direkten Relaxationsprozesse (2…7°K) wird eine Abhangigkeit der Spin-Gitter-Relaxationsgeschwindigkeit von der Projektion des Cu-Kernspins beobachtet. Uber die Temperaturabhangigkeit des RAMAN-Prozesses wird die DEBYE-Temperatur des Molekulkristalles zu θ = (100 ± 10)°K sowie die mittlere Schallgeschwindigkeit 〈v〉 ≈ 0,7. 105 cm/sec abgeleitet. Zur Aufklarung der im gesamten untersuchten Temperaturbereich von 2,0…300°K ungewohnlich geringen Linienbreite der 63,65Cu-Hyperfeinstrukturlinien des EPR-Spektrums werden die Beitrage der zur Linienbreite beitragenden Mechanismen analysiert. Es werden Betrachtungen zum moglichen Einflus der starken Kovalenz der Cu-Ligand-Bindungen auf T1 durchgefuhrt. The temperature-dependence of the electron-spin-lattice- and -spin-spin-relaxation times T1 and T2 of Cu(II) in (Tetrabutyl-ammonium)-Ni(II)bis(1,1-dicyanoethylene-2,2-dithiolate) single crystals are reported. In the range of the direct processes (T = 2…7°K) a dependence of the spin-lattice relaxation rate on the orientation of the Cu-nuclear spin was observed. From the temperature-dependence of the RAMAN-process the DEBYE-temperature and the averaged soundvelocity of the molecular crystal have been derived being θ = (100 ± 10)°K and 〈v〉 ≈ 0.7. 105 cm/sec. In order to explain the unusual small line-width of the 63,65Cu-hyperfine structure lines of the EP R-spectrum in the investigated large temperature-range of T = 2.0…300°K the mechanisms contributing to the line width were analyzed. The possible influence of the strong covalency of the Cu-ligand bonds to T1 is considered.

Gravitationskollaps und Lichtgeschwindigkeit im Gravitationsfeld

Abstract: An elementary criterion of the stability of a matter sphere against gravitational collapse is given by the circular velocity condition of POINCARE: In a space with a spherically symmetric gravitation potential ϕ (r) and with a spherically symmetric metric gik (e.g., a SCHWARZSCHILD space time) the circular velocity V* of a particle on the surface r = R of the matter-sphere must be (This condition is a consequence of the virial theorem and of the POINCARE theorem.) - However, EINSTEIN's axiom of causality implies that this velocity V* must be smaller than the local velocity of light v: V*2 < v2. And this local velocity v is a function of the gravitation potential ϕ, too: v = v [ϕ]. In the case of NEWTON's or EINSTEIN's theory the spherically symmetric gravitation potential is given by the NEWTONian function ϕ = fM/r. In the special theory of relativity, we would have v = c (c = EINSTEIN's fundamental velocity) and grr = 1. Therefore, the specialrelativistic stability condition is R > fMc−2. - But in the NEWTONian theory v is depending of the gravitation potential and depends of the boundary condition for the light propagation, also. According to the ansatz of LAPLACE (1799) we have: (emanation-theory of light). But, according to SOLDNER (1801), we have Therefore, we are finding in the case of LAPLACE the same condition R > fMc−2 as in the SRT. But, in the case of SOLDER's ansatz non condition for stability is resulting. - In the general relativistic theories the local velocity of light is given by EINSTEIN 's expression According to EINSTEIN's theory of “static gravitation” (1911/12) we have grr = 1 and therefore the formula and according to the GRT (with - gω = grr−1) we have the formula Therefore, the Hilbert-Laue condition r= R > 3fMc−2 results as stability condition. From the gravo-optical point of view, in GRT and for the classical ansatz of LAPLACE “black-holes” with bounding states of light result for R ≤ 2fM−2. But, no “black-holes” are existing according to SOLDNER's ansatz. However, in GRT each black-hole must be a “collapsar”. But according to the classical theory of LAPLACE we have uncollapsed “black- holes” for the domain .

Über die mögliche lineare Form von Lorentz-kovarianten Gravitationstheorien.

Abstract: LORENTZ-covariant theories of gravitation which fulfil EINSTEIN's weak principle of equivalence and which contain a pure Newtonian theory as an approximation are tensortheories with the linear approximative form for the field equations. In the case of EINSTEIN's strong principle of equivalence the exact field equations must be the general relativistic EINSTEIN-equations (or the bimetrical EINSTEIN-ROSEN-equations). This follows from the dynamical equations and the BIANCHI identity according to JANOSSY and TREDER. However, from NEWTON's axiom of reaction together with the weak principle of equivalence results that the strong principle of equivalence must be valid for the linear approximation of the field equations with sources. Therefore, the linear approximation of all physically meaningful Lorentz-covariant theories of gravitation is given by the linearized EINSTEIN-equations (with HILBERT-conditions): , that is by the ansatz α = 2. The main point of our arguments is LAUE's postulate of the self-consistency of perfect static systems of isolated gravitational masses. In the lowest order of approximation this self-consistency is only possible if the gravitational matter-tensor is identical with the special-relativistic energy-momentum-tensor Tμv. LAUE's postulate is fulfilled exactly for the general relativistic field equations according to the theorems of BIRKHOFF, TOLMAN and EINSTEIN and PAULI.

Elastic Scattering of α‐Particles on Be9

Abstract: The differential cross-section for the elastic scattering of He4 particles on Be9 has been studied in the bombarding energy range 1.4-2.5 MeV. The excitation functions for the elastically scattered α-particles from Be9 were measured at six angles 90°, 125°, 132°, 140°, 150° and 160° in the centre of mass system. A clear and pronounced resonance is observed in the measured cross-section at incident α-particle energy 1.93 MeV. Analysis of the data in terms of the single level approximation theory leads to the assignment Jπ = 5+/2 for the observed resonance. Reduced and partial widths for elastic scattering were determined.

Zur Anregung und Emission im N2‐Impulsgaslaser

Abstract: A theoretical treatment of pulsed nitrogen laser operation is presented. The properties of laser pulses were investigated as functions of various parameters (electric circuit parameters, laser length, gas pressure). Based on this model some conditions are obtained which are necessary for effective laser pulse emission, and the known nitrogen laser devices are discussed.

Zur Theorie der stimulierten Resonanz-RAMAN-Streuung

Abstract: The gain of the stimulated resonance RAMAN scattering (SRRS) and stimulated fluorescence is obtained by means of an analytical solution of the density matrix equation and MAXWELL's equations for laser- und STOKES-radiation. The transient effects, which are caused by the population change of the molecule levels, and the influence of the resonance absorption on the pumping and the STOKES radiation are studied. The strong laser absorption yields a maximal gain, which shows, why the stimulated resonance RAMAN scattering could not be observed in many substances. As a result of our paper we give a possible interpretation of the experimentally observed relation between the stimulated fluorescence and the resonant RAMAN scattering.

Theorie der parametrischen Vier-Photonen-Wechselwirkung. III. Verstärkung und Oszillation bei Berücksichtigung der Rückwirkung auf die Pumpwelle

Abstract: The processes of parametric amplification and oscillation in a medium with cubic polarization are investigated theoretically taking into consideration the depletion of the pump wave. We suppose that phase-matching is realized exactly (a possible nonlinear detuning of the exact phase-matching should be compensated by a suitable subsequent adjustment of the frequencies). A consequence of linear losses is the appearance of a threshold for the parametric amplification. There exist a maximum length, a minimum length and an optimum length of the nonlinear medium for the process of parametric amplification. The threshold intensity, the optimum length of the nonlinear medium and the optimum reflection coefficient for outcoupling are determined for two arrangements of the double resonant parametric four-photon oscillator (ring resonator, FABRY-PEROT resonator). It is shown that for the above mentioned arrangements of the single resonant and the double resonant four-photon oscillator the efficiency is a monotonous function of the threshold excess. On the contrary in case of the three-photon oscillator there exists an optimum value of the threshold excess.

Die Relaxation der Elektronengeschwindigkeitsverteilungsfunktion im homogenen feldfreien LORENTZ-Plasma

Abstract: Fur ein homogenes feldfreies LORENTZ-Plasma wird die zeitliche Anderung der Elektronengeschwindigkeitsverteilungsfunktion (EGV) ausgehend von einem beliebig wahlbaren homogenen Anfangswert fur die EGV vollstandig aus der Elektronen-BOLTZMANN-Gleichung berechnet. Als unkorrelierte Zweierstoswechselwirkungsprozesse werden hierbei elastische Stose und eine beliebige Anzahl anregender Stosprozesse zwischen den Elektronen und einer vor dem Stos als ruhend betrachteten Neutralgasart berucksichtigt. Die die Stoswechselwirkung beschreibenden differentiellen Streuquerschnitte fur elastische und anregende Stose werden hierbei praktisch keinen Einschrankungen bezuglich ihrer Geschwindigkeits- und Streuwinkelabhangigkeit unterworfen. Die Untersuchungen basieren auf der vollstandigen Kugelflachenfunktionsentwicklung der Elektronen-BOLTZMANN-Gleichung. An Hand der abgeleiteten Losungen fur den Isotropteil und alle Anisotropiekomponenten der EGV wird die Relaxation aller Verteilungsfunktionsanteile diskutiert, wobei insbesondere die Auswirkung unterschiedlicher Streuwinkelabhangigkeiten der differentiellen Querschnitte auf den Relaxationsmechanismus der EGV im LORENTZ-Plasma aufgezeigt wird.

Zur Elektronenstreuung an ionisierten Störstellen in Halbleitern mit isotroper effektiver Masse

Abstract: A selfconsistent scattering-potential for a ionized impurity in a semiconductor with a isotropic effective mass and arbitrary degree of degeneracy is derived. For this scattering-potential the mobility formula for electrons is deduced, the corrections to the Brooks-Herring-formula are evaluated for the case of n-type GaAs.

Zur kernmagnetischen Relaxation in Mehrbereichsystemen mit endlicher räumlicher Ausdehnung

Abstract: General equations, describing the nuclear spin relaxation behaviour in heterogeneous systems, consisting of regions with different relaxation times and diffusion coefficients, are presented. For a special two region system, by means of analogue computing technique the influence of both diffusivity and height of the barriers between the regions on total relaxation is studied. It is shown, that using appropriate expressions for the mean lifetimes of the nuclei in the regions, the relaxation function of total magnetisation may be approximated by the formulae of ZIMMERMAN and BRITTIN. These relations may be used for a rough estimation of diffusivity in the systems under consideration.

Zur Grenzschichtdämpfung von Verbundwerkstoffen mit kurzfasrigen Einlagerungen

Abstract: Es werden Verbundwerkstoffe mit Fasern endlicher Lange im Falle einer Wechselzugbelastung theoretisch untersucht. Mit Hilfe einfacher Modelle last sich das Verhalten eines Verbundes mit elastischer Matrix, elastischen Fasern und plastifizierbarer Grenzschicht beschreiben. Fur eine ideal-plastische, eine viskose und eine viskoplastische Grenzschicht wird die durch das Abgleiten der Grenzschicht hervorgerufene mechanische Dampfung berechnet. In Abhangigkeit von der Spannung bzw. der Frequenz treten Dampfungsmaxima auf. Aus deren Lage lassen sich die Grenzschichtparameter, insbesondere die Grenzschichtscherfestigkeit, ablesen. Damit besteht die Moglichkeit, mit Hilfe von Dampfungsmessungen die Eigenschaften der Grenzschicht im Verbund selbst zu bestimmen. Composite materials with discontinuous fibres are theoretically examined under alternating tension. By the aid of simple models for a composite with elastic matrix, elastic fibres, and plastificable interface the behaviour of the composite material can be described. The mechanical damping, caused by slipping of the interface, is computed for the cases of a perfect-plastic, a viscous and a visco-plastic boundary layer. Damping peaks occur in dependence of the stress amplitude and the frequency, respectively. From the position of these peaks we can conclude to the parameters of the interface, in particular, to its shear strength. Thus damping measurements render it possible to determine the properties of the interface within the composite.

Kovariante Dichten. Probleme der Makrokausalität und Teilchendichte in der relativistischen Wellenmechanik. I

Abstract: We consider signals represented by skalar particle densities ϱ. It is then proven that the assumptions (i) ϱ ≥ s° (ii) ϱ = s0 is the fourth component of a four-vector sμ (iii) the scalar particles form a repesentation of the POINCARE group in HILBERT space, are incompatible with experimental data (formfactors of pions).

Die Struktur von NMR‐Signalen in nematischen Phasen

Abstract: Die Linienaufspaltung der Protonen-Resonanz wird in nematischen Phasen von Zwei-Spin-Systemen berechnet, deren Verbindungsvektor mit der Molekullangsachse einen festen Winkel bildet. Bei Berucksichtigung der Verteilung der Achsen in lokalen Bereichen ergibt sich ein Mas fur den Orientierungsgrad, das von der klassischen Definition etwas abweicht. Die mit einer verbesserten experimentellen Technik aufgenommenen Spektren zeigen Strukturen, die sich mit den gewonnenen Beziehungen erklaren lassen. Man mus hierzu unterschiedliche Orientierungen der Benzolringe und verschiedene Beweglichkeiten der aliphatischen „Schwanze” annehmen. Aus den Spektren homologer Verbindungen werden einige Gesetzmasigkeiten uber das Verhalten der Molekule in nematischen Phasen abgeleitet. The line-splitting of the proton-nmr of two-spin-systems in nematic phases is calculated in the case, if the angle between the spin-spin-vector and the molecular axis is constant. Taking into consideration the distribution of the axes in local spheres, we receive a measure for the degree of orientation, that is slightly different from the classical definitions. These results are used, to explain the structure of spectra, which we received with an improved experimental technic. This leads to the assumption, that in one molecule the benzene-rings have different orientations and the aliphatic tails different mobilities. From spectra of a series of homologous compounds some rules concerning the behaviour of molecules in nematic phases are stated.

On the SU(3) Mass Formulae

Abstract: It is found that in the SU(3) broken quark model the SU(3) generators and their time derivatives belong to the SU(3) x SU(3) algebra. Using this algebra and the infinite momentum method the SU(3) mass Bum rules are obtained. The possibility is discussed that normal spin-parity nonets and anomalous ones differ in the structure of the mass spectrum. 1. Introduction In the paper by OQIEVETSKY [l] an exhaustive analysis of SU(3) mass formulae obtained in the algebraic realization of the SU(3) symmetry has been given. It has been proved that nonets are necessary if states with Y = 0, T = 1 and Y =.T = 0 are not degenerate. Two general restrictions on masses have been found. The SCHWINGER formula for nonets adthe GELL-MANN-OKUBO formula for decuplets can be obtained from those restrictions. Similar results have been obtained by ONEDA and MATSUDA [Z] in the asymptotic SU(3) symmetry. In this paper a simple proof of the OOIEVETSKY restrictions is given. The algebra of time dependent SU(3) generators and their time derivatives is used. It is shown that in the quark model these operators belong to the SU(3) x SU(3) algebra. The mass sum rules are obtained using the infinite momentum method.

Zur Theorie der kantenfernen Feinstruktur von Röntgenabsorptionsspektren

Abstract: Die kantenferne Feinstruktur des Rontgenabsorptionsspektrums eines Atoms in einem chemischen Verband ist abhangig von dessen Orientierung zu einem polarisierten und unpolarisierten Rontgenstrahl. Fur diese Abhangigkeiten werden allgemeine Gleichungen ohne Berucksichtigung der Spin-Bahn-Wechselwirkungen angegeben. Die Gultigkeit der KOSLENKOWschen Gleichung fur polykristalline Festkorper, Flussigkeiten und Gase wird allgemein bewiesen. Fur die K-Absorption werden die von ISRAILEWA hergeleiteten Gleichungen erhalten. Auserdem werden die expliziten Gleichungen fur die LII- und LIII-Absorption angegeben. The extended fine structure of the X-ray absorption spectra of an atom in a chemical system depends on its orientation with respect to a polarized and nonpolarized X-ray beam. General equationes are developed to describe these dependences without consideration of spin-orbital interactions. Evidence is given for the validity of KOZLENKOV's equation for the fine structure of polycrystalline solids, liquids, and gases. For the case of K absorption we obtain the equations formerly published by IZRAILEVA. Further, the explicite formulae for the LIII and LIII absorption fine structures are presented.

Distribution of Shower Particles as Obtained in the Analysis of a 10 + 13p Shower Event

Abstract: We present here the analysis of an accelerator produced 10 + 13p shower event observed in nuclear emulsion. The DULLER-~ALKF.R method is applied to obtain the distribution of secondary shower particles, and the particles having the closest log,, tan Ot values are taken to form a cluster. This cluster formation is also confirmed by the target diagram method. If this cluster is conceived to be a high spin resonance and the secondary pions to be the decay products of this resonance, then the azimuthal integral distribution curve fits fairly well with our experimental data.

Semiphenomenological Model Approach to Continuous Spectrum States. II

Abstract: The Semiphenomenological Model of the Nucleus (SPM) is applied to description of inelastic nucleon scattering with excitation of rotational states. Cross sections of inelastic scattering of protons with E = 6 Mev by 6BFe with excitation of the states 11°K) = 12+0> and 11°K) = 12+2) are calculated for illustration. The total deformation and non-axiality parameters are derived and compared with predictions of SPM, the agreement being satisfactory. In paper [l] (to be referred to in what follows as I) the Semiphenomenological Model of the Nucleus (SPM), developed in papers [2-41, is applied to description of the continuous spectrum states. In paper I “direct” mechanism (onestep and two-step processes) and resonance mechanism of inelastic nucleon scattering are considered, the imaginary part of the optical potential is calculated, etc. However, in I the theory is carried out with accounting only for quasi-particle states of the target nucleus and those of the intermediate nucleus. In the present paper the application of SPM to description of the continuous spectrum states is extended to the inelastic nucleon scattering with excitation of rotational states. However, besides the problem of describing nucleon-nucleus scattering in the framework of SPM, we pursue here additional purposes connected with the description of the nuclear structure. The point is that the parameters of nonaxiality of the nuclear matter obtained from the same experimental spectra in the SPM.and the DAVYDOV-FILLIPPOV-CHABAN model [5] (DFC in what follows) differ essentially. Actually, according to SPM [2] the parameter of non-axiality (for even-even nucleus) is given by:

A Model Independent Method of the X° (960) Meson Spin Parity Determination

Abstract: To establish the X (960) meson spin parity it is suggested to study the correlation between the production process K−He4 X0 ΔH4 and the decay process X0 η2π

J-Plane Analysis of the Veneziano Amplitude with Nonlinear Trajectories

Abstract: The structure of singularities of the Veneziano amplitude in the complex angular momentum plane is studied. The introduction of a nonlinear term in the trajectory essentially changes the properties of the partial amplitude as compared to the case of linear trajectories. In the J-plane, besides simple poles lying on the leading and on the conventional daughter trajectories, additional poles lying on mirage trajectories (situated below the leading trajectory) emerge. In the partial amplitude also non-reggeised poles in the s-plane emerge whose position is independent of the angular momentum. Such are, for example, the ancestors.

Berechnung der Aufbauzeit eines doppeltresonanten optischen parametrischen Oszillators

Abstract: The rise time for the output power of a doubly resonant optical parametric oscillator with ring resonator configuration is calculated for the special case of subharmonic generation. It is shown that the rise time decreases by increasing the pumping level (for a constant threshold power) and, for a constant pumping level, by increasing the resonator loss.

Pion PT Distribution and a Test of Scaling Hypothesis at an Incident Proton Energy of 24 GeV

Abstract: The transverse momentum distribution of 900 secondary pions produced in interactions of 24 CeV protons with emulsion nuclei is seen to agree fairly well with the HAGEDORN distribution for ‘u’ = 312 and ‘Y adjusted to 133 MeV. A satisfactory fit of FEYNMANS scaling idea is also observed at this incident energy.

On the Theory of the Optical Potential for Even‐Even Deformed Nuclei

Abstract: Optical-model potentials are constructed for nucleon-nucleus scattering. The contribution of collective states to the imaginary part of the optical potential is investigated; the interaction between the incident nucleon and an even-even deformed target nucleus is considered in the weak coupling scheme of the Semiphenomenological Model of the Nucleus. The potentials constructed are in good agreement with the phenomenological ones. Numerical estimates are given for the target nucleus 156Gd at the incident energy 16 Mev.

Bootstrap und Feuerballverteilungen

Abstract: Es wird angenommen, das sich im inelastischen Stos zweier hochenergetischer Elementarteilchen Feuerballe bilden, deren Zerfall die erzeugten Teilchen ergibt. Die Feuerballverteilung entsteht durch den Zerfall des angeregten Hydronensystems in einen leading Feuerball und ein Restsystem. Es wird verlangt, das der Zerfall einer Bootstrapbedingung genugt, derzufolge die Feuerballverteilung vom Restsystem in seinem Ruhsystem die gleiche Form hat wie die Feuerballverteilung vom gesamten Stos im Schwerpunktsystem. Die Bootstrapbedingung fuhrt auf eine Integralgleichung. Naherungslosungen der Integralgleichung werden in der Scalinggrenze diskutiert. It is assumed that in an inelastic collision of two particles at high energy fireballs are created, the decay of which produces the observed particles. The fireball distribution results from the decay of the primary hadron system into a leading fireball and a rest system, which can decay further. The decay is assumed to behave according to a bootstrap condition, making the fireball distribution, that results from the rest system in its rest frame, equal to the fireball distribution in the total collision in the c.m. frame. This bootstrap condition leads to an integral equation. Approximate solutions of this integral equation in the scaling limit are discussed.

Temperature- and Concentration-Dependence of the Spin- lattice Relaxation Time of Chromium Ions in GASH

Abstract: Investigations of the temperature- and concentration dependence of the spin-lattice relaxation time T1 in ferroelectric GASH (= Guanidinium aluminium sulfate hexahydrate) single crystals doped with Cr3+-ions are reported. The concentration-dependence found on the higher concentrated crystals C 0.1% Cr3+) as well as the observed cross-relaxation are explained in terms of spin-lattice relaxation via exchange pairs. Using the VAN VLECK formalism T1 has been estimated for Cr3+: GASH by comparision of the present system and K-Cr-alum. Es wird uber Untersuchungen der Temperatur- und Konzentrationsabhangigkeit der Spin-Gitter-Relaxationszeit T1 in mit Cr3-Ionen dotierten ferroelektrischen GASH (= Guanidinium-Aluminiumsulfat Hexahydrat) Einkristallen berichtet. Die bei hoherkonzentrierten Kristallen (C > 0,1% Cr3+) gefundene Konzentrationsabhangigkeit sowie auch die beobachtete Cross-Relaxation werden mittels eines Relaxationsmechanismus uber austauschgekoppelte Cr-Paare erklart. Unter Benutzung des VAN VLECK-Formalismus wird anhand eines Vergleiches mit dem System K-Cr-Alaun T1 fur Cr3+: GASH abgeschatzt.