Mössbauer spectroscopy with the 93 keV-resonance in67Zn

The procedures and results of high resolution Mössbauer experiments performed with the 93.3 keV resonance in absorbers of⁶⁷ZnO,⁶⁷ZnS (both wurtzite and sphalerite structures),⁶⁷ZnSe,⁶⁷ZnTe and⁶⁷ZnF₂ are reported. An essentially linear dependence between the isomer shift and the Pauling electronegativity of the ligands was found. A value of r ²=+11×10^–3 fm² is estimated. The Mössbauer parameters for both ZnS structures are equal within present limits of error. In particular, no quadrupole interaction was observed in the wurtzite modification. This indicates a nearly identical local symmetry at the Zn site in the two ZnS structures.Work supported by the Bundesministerium für Forschung und Technologie, Federal Republic of Germany and the Kernfor-schungszentrum Karlsruhe     

Effect of elastic strain and stress on the superconducting transition temperature of quench-condensed films

The volume dependence of the superconducting transition temperatureT _c of amorphous and highly disordered films is investigated by bending the film substrate. The volume coefficientd InT _c /d InV of annealed Sn and Pb films agrees with the volume coefficient known from hydrostatic pressure experiments. This bending technique is applied to superconducting modifications which can be produced only by quench condensation onto a substrate at liquid helium temperature. Amorphous films such as Bi, Ga, Sn₉₀Cu₁₀ and Pb_xBi_1–x, as well as highly disordered Sn and Pb films, are investigated. The relations found between the volume coefficient, the electron-phonon coupling constant and the Grüneisen parameter _G are in reasonable agreement with the volume dependence ofT _c for non-transition metals, obtained on the basis of the McMillan equation. In particular, the results represent an expansion of this kind of investigation to very strong-coupling superconductors.Dedicated to Prof. Dr. W. Buckel on the occasion of his 60th birthdayPaper based in part on a Habilitationsschrift submitted to the Fakultät für Physik, Universität Karlsruhe (TH)     

On the short-range order of amorphous Al−Au films

Al_100–x Au _x films (20x71) are produced by quench condensation. The analysis of electron diffraction patterns as well as resistivity measurements reveal the liquid-like structure of these films. In contrast to amorphous Al–Cu films the amorphous Al–Au filsm exhibit prepeaks in their interference functions. Atomic distances as large as the smallest Au–Au separations existing in the compound Al₂Au are responsible for these prepeaks. The CaF₂-type structure of this particular compound is due to an ionic bonding contribution in Al₂Au. This bonding contribution, probably caused by the large electronegativity difference between Al and Au, seems to be responsible for the pronounced chemical short-range order in amorphous Al–Au films.     

The magnetic moment of103Ru

The nuclear magnetic moment of¹⁰³Ru has been determined using the technique of low-temperature nuclear orientation on¹⁰³Ru as a dilute impurity in Fe. The Fe lattice was cooled to 1.7 mK using a PrNi₅ enhanced nuclear demagnetisation stage precooled with a³He–⁴He dilution refrigerator. The¹⁰³RuFe system was observed to have a long nuclear spin-lattice relaxation time, but analysis of the relaxation indicates that the¹⁰³Ru nuclei are close to thermal equilibrium with the Fe lattice at times>200 min after demagnetising. From the near thermal equilibrium anisotropy of the 497 keV -ray in¹⁰³Rh we have deduced the nuclear magnetic moment as |(¹⁰³Ru)|=0.18(2)_N. This value is almost independent of the choice of spinI=3/2 or 5/2 for the nucleus, but is only consistent with systematics ifI(¹⁰³Ru)=3/2 and <0. UsingI=3/2 we obtain the E2/M1 mixing ratio of the 497 keV -ray as =–0.42(4). The sign of the anisotropy of the 610 keV -ray from the 650 keV level in¹⁰³Rh is only consistent with an allowed -decay to the state ifI(650 keV,¹⁰³Rh)=5/2. The E2/M1 mixing ratio of the 610 keV -ray is then =+0.15(3) or +60( _–40 ⁺ ), <–80. From the initial rise in -ray anisotropy following demagnetisation we determine the Korringa constant for¹⁰³RuFe to beC=5.7(5) K·s.     

Magnon spectrum and curie temperature of doped ferromagnetic semiconductors

The influence of a partially filled conduction band on the magnetic properties of ferromagnetic semiconductors is studied within the framework of thes-f model. Allowing for magnon scattering to arbitrary order in the form of virtual electron- holecreation the magnon spectral density is derived, from which one gets magnon energies which are substantially renormalized by the presence of conduction electrons. In particular it is shown how the quasiparticle structure of the electronic excitation energies [4, 5] leads to scattering corrections in the magnon spectrum. These corrections are always negative and reduce the positive mean field part, which is proportional to the electron densityn. The calculated magnon spectrum is then used to determine the strikingn-dependence of the Curie-temperatureT _c of Gd-doped EuO and EuS.     

The level structure of104Rh deduced from the103Rh(n, γ)104Rh reaction

A sensitive, high resolution study of the¹⁰³Rh(n, γ)¹⁰⁴Rh reaction has revealed the presence of 516 transitions in the energy range 3,700 to 7,000 keV. These results have been used to interpret the reaction in terms of a statistical model in which a constant temperature level density is assumed. Previous work which revealed a much simpler level structure is quantitatively explained in terms of resolution and sensitivity. The average reduced radiative width is significantly lower than that reported for nuclides in theA=100 mass region and the width shows an indication of an energy dependence somewhat greater thanE _γ ³ . The neutron separation energy of the reaction is found to be 6,999.0±0.1 keV.     

Nonlinear volterra equations with infinite delay

This paper is concerned with the existence and stability of nonlinear Volterra equations which have infinite delay and are of the form: $$x (\varphi ) (t) = W (t, \tau ) \varphi (0) + \int\limits_\tau ^t {W (t, s)} F(s,x_s (\varphi )) ds, x_\tau (\varphi ) = \varphi \in C_u .$$ Here,X denotes a Banach space;W(t, s) is a linear evolution operator mappingX toX; C _u is the space of uniformly continuous functions endowed with the supremum norm; andF(·,·) is a continuous mapping ofR×C _u toX. The autonomous version of the preceding equation is also considered. A nonlinear semigroup is associated with its solutions and the infinitesimal generator of the semigroup is characterized. The generator is then used to represent and approximate solutions to the autonomous equation.     

Why are spherical stellar systems relaxed?

Spherical stellar systems, from globular star dusters to compact galaxy clusters, appear to be dynamically relaxed. In galaxies and galaxy clusters, collisional relaxation acts too slowly to produce the observed result; and a new argument suggests that the same may be true of globular star clusters. Violent relaxation requires special initial conditions and seems unable to produce sufficiently extended halos. It is here proposed that dynamical relaxation may result from tidal perturbations by external systems. If this explanation is correct, it has important implications for the early history of galaxies and galaxy clusters.This essay was awarded the fourth prize for 1976 by the Gravity Research Foundation.     

Optimizing two types of discrete functions,subject to linear restrictions

This paper is a collection of four topics; they are: a discussion of two knapsack problems (see, for example, Gilmore and Gomory, 1966), some interesting heuristic remarks on computational experience, some remarks on the underlying algebraic structures directly related to the knapsack functions, and a new proof technique for optimizing the functions mentioned. All functions in sight are discrete and defined on the integers. Also, the proofs of the theorems do not use convexity and monotonicity of the more abstract optimization techniques.