Universal Properties of the Four-Boson System in Two Dimensions

We consider the nonrelativistic four-boson system in two dimensions interacting via a short-range attractive potential. For a weakly attractive potential with one shallow two-body bound state with binding energy B₂, the binding energies B_N of shallow N-body bound states are universal and thus do not depend on the details of the interaction potential. We compute the four-body binding energies in an effective quantum mechanics approach. There are exactly two bound states: the ground state with B₄⁽⁰⁾=197.3(1)B₂ and one excited state with B₄⁽¹⁾=25.5(1)B₂. We compare our results to recent predictions for N-body bound states with large N1.On leave from FZ Jülich, Institut für Kernphysik (Theorie), D-52425 Jülich and HISKP (Theorie), Universität Bonn, Nußallee 14–16, D-53115 Bonn, Germany     

Kondo-lattice: Kondo-effect?

The periodics-d-model is investigated by Green function methods. We find that the lnT-divergence appearing in third order perturbation theory for the electron selfenergy is smoothed out but still shows up in a characteristic decrease (exchange coupling<0) or increase (>0) of lifetime of electrons at the fermi level asT0 and a corresponding structure in the specific heat. However, in contrast to the single impurity case, the corresponding characteristic temperature does not vary like exp[–1/||] but always is of order ². From a mean field theory of the model, one finds a critical temperature for a transition into a magnetically ordered stateT _c0 which varies precisely like ². Thus an interesting competition between Kondo-effect and long-range magnetic order can be expected in this model.Work performed within the research program of the SFB 125 Aachen/Jülich/Köln     

Energy transfer to a copper surface by low energy noble gas ion bombardment

The energy transferred to a copper surface by bombardment with Xe⁺, Ar⁺, and He⁺ ions with kinetic energies in the range 100–4000 eV has been studied by our group in previous experiments. There were significant experimental uncertainties for that data at energies below about 200 eV. The present investigation overlaps the previous work, extends the energy range to 10 eV, and includes data for Ne⁺. Particular emphasis is placed on the energy range below 200eV. A specially designed ion source was employed in these experiments. A polycrystalline copper film deposited onto a highly sensitive calorimeter was used as the target material. The results show that the Xe⁺ ion deposits more than 97% of its energy over the entire range investigated whereas the lighter ions deposit a decreasing fraction of their energy below about 1 keV. The decrease is largest for the lightest ion (He⁺). In all cases the deposited energy is about or more than 70% of the incident energy. It will be shown that the present results are in agreement with previous measurements for copper and are qualitatively in good agreement with computer calculations using the TRIM.SP code.On leave from: Institut für Schicht- und Ionentechnik, Forschungszentrum Jülich GmbH, W-5170 Jülich, Fed. Rep. Germany     

Statistical theory of pinning on point defects

The statistical treatment of pinning on point defects is given including the correlations of the number of defects in neighbouring volumes (the interaction of these volumes with the fluxoid is taken as the elementary interaction causing the pinning). For higher defect densities, the agreement with the experiments on niobium is better than with the previous theory. This method of correlations seemed suitable for study the effect of cutting-off the small elementary interactions and for the replacement of the Gauss distribution function by the Poisson distribution function for the number of defects in the elementary volumes. Both these efforts give negative results with respect to the experiments; so far we are therefore not able to explain quantitatively the large increase of the pinning force at small defect densities and small magnetic fields, as well as its decrease to zero always for fields smaller thanH _c2 . The attractive interaction between the flux lines in type II superconductors with small Ginzburg-Landau parameter could give a qualitative explanation of the enhancement of the pinning at small defect densities.Part of this work was performed during the author's stay at the Institut für Festkörperforschung, KFA Jülich. The kind hospitality of this institute and many valuable discussions, especially with Dr. H.Ullmaier, are acknowledged.     

Vertex form factors of the rho-meson nucleon interaction at low momentum transfer

We calculated the one pion loop contributions to the form factors of the rho-nucleon interaction within a field theoretical model using effective Lagrangians. The results show that the tensor interaction is likely to be described well within such an approach. We obtain a magnetic coupling in the range of 3.5–7.1 atQ ²=0, depending on the choice of pion-nucleon form factor and a dipole form for theQ ² dependence tensor form factor with a scale of roughly 900 MeV for space-like momentum transfer. The results agree with the findings of the recent analysis of thep-N interaction and support a small scale parameter (0.5 GeV) for the pion-nucleon form factor.This work is supported by BMFT (06BO7027) and COSY-KFA Jülich (41140512)     

Preequilibrium emission in (p,x n) reactions on palladium isotopes

Energy spectra of neutrons from the^{104, 105, 106, 108, 110}pd(p, xn) reactions atE _p=26.1 MeV have been measured using the time-of-flight technique with good overall energy resolution (< 250=" kev).=" the=" hard=" part=" of=" angle-integrated=" spectra=" corresponding=" to=" low=" residual=" excitations=">U6MeV) exhibits pronounced structure varying from isotope to isotope. The observed structure can be reasonably well described by preequilibrium-model calculations with two-quasiparticle state densities for proton-particle neutron-hole configurations based on Nilsson-model single-particle levels instead of equidistant ones. The influence of nuclear deformation and pairing on preequilibrium particle emission is explored.Supported in part by the exchange program of the Universities of Hamburg and Zagreb, Internationales Büro — KFA Jülich, and by the BMFT (Contract 06 HH 142)     

Integrable non-linear σ models with fermions

The two-dimensional non-linear model on a Riemannian symmetric spaceM=G/H is coupled to fermions with quartic self-interactions. The resulting hybrid model is presented in a gauge-dependent formulation, with a bosonic field taking values inG and a fermionic field transforming under a given representation of the gauge groupH. General criteria for classical integrability are presented: they essentially fix the Lagrangian of the model but leave the fermion representation completely arbitrary. It is shown that by a special choice for the fermion representation (derived from the adjoint representation ofG by an appropriate reduction) one arrives naturally at the supersymmetric non-linear model onM=G/H. The issue of quantum integrability is also discussed, though with less stringent results.Work partially supported by CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico), Brazil, and KFA Jülich, Federal Republic of GermanyOn leave of absence from Fakultät für Physik der Universität Freiburg, Federal Republic of Germany     

The mean jump number of a vacancy in annealing experiments

In this paper we shall calculate the mean jump number ¯n which a vacancy makes during its life in a nearly perfect lattice, before it is absorbed in a sink. We suppose that the sinks are unfillable and that there is no interaction between the vacancies. The dependence of ¯n on the shape and size of the sink in the f.c.c. lattice will be discussed.The author is indebted to Dr. K. Míek and L. Smrka for stimulating discussions and Dr. J. Polák for critical remarks.This paper was read at the International Conference on Vacancies and Interstitials in Metals in KFA Jülich, September 1968.     

The thermal conductivity of disordered and amorphous metal films

The thermal conductivity of quenched condensed polycrystalline and amorphous Pb and Pb_0.9Cu_0.1 films has been measured between 0.5 and 11 K, i.e. in the superconducting (T7 K) and in the normal state (T7 K). Whereas, in agreement with previous results, phonon heat transport is very small for crystalline films, a considerable portion of heat is carried by phonons in amorphous films, owing to the absence of extended lattice defects. Phonon scattering in these latter films is analyzed in terms of scattering from conduction electrons aboveT _c, whereas well belowT _c it is very likely due to low energy excitations inherent in the amorphous structure.Work performed within the research program of the Sonderforschungsbereich 125 — Aachen/Jülich/Köln     

Algebraic derivation of symmetry relations for disordered electronic systems

By means of superfields two time-reversal invariant disordered electronicn-orbital models one without, the other with a spin-dependent random potential can be described by the same Lagrangian except for the sign of an overall prefactor. Similarly two different treatments of a system which breaks time-reversal invariance yields the same Lagrangian but with opposite sign of the prefactor. Since this prefactor is proportional ton, identical saddle point expansions in powers of ±n ^–1 for the averaged Green's functions are obtained, relations first found diagrammatically by Oppermann and Jüngling. The invariance of the Lagrangian under unitary graded and unitary orthosymplectic transformations of the fields for systems without and with time-reversal invariance, respectively, is pointed out.Work supported in part through the Sonderforschungsbereich 123 Stochastic Mathematical Models by the Deutsche Forschungsgemeinschaft     

Self-consistent theory of pairbreaking in kondo superconductors

A theory is presented for the calculation of equilibrium properties of superconductors containing magnetic impuritiesof finite concentration. The theory is based on the Nagaoka-Suhl approach to thes — d model and treats finite impurity concentrations within a self-consistentT-matrix-approximation. An integral equation is derived for the pairbreaking parameter which describes de-pairing of Cooper pairs by spin flip scattering. Numerical solutions of this equation are used to compute the phase diagram in the temperature-concentration-plane and the transition-temperature-dependence of the upper critical field. These calculations are in good agreement with experimental data on LaCeAl₂-samples. In addition, the recent discovery of three normal superconducting transitions in LaCeY is discussed quantitatively.Work performed within the research program of the Sonderforschungsbereich 125 Aachen/Jülich/Köln     

Another look at meson-exchange interactions

We calculate the nucleon structure in a two-phase model, assuming forlow Q ²: meson dynamics, and forhigh Q ²: quark-gluon dynamics, and find a low meson scale in accordance with electron-nucleon scattering. Using these form factors we show that with the increased importance of nucleon structure in the nucleon-nucleon interaction, higher-mass meson exchange (m>1 GeV) becomes important. We argue that these contributions can be taken into account by a sort of closure relation, leading to contact interactions of the physical nucleons. A one-boson-exchange potential is constructed including these direct nucleon structure interactions. Implications concerning the corresponding three-nucleon interaction are also discussed. A partial-wave calculation of neutron-proton scattering is performed showing satisfactory agreement with experiment. The model has several advantages over conventional bosonexchange models.Work is supported by Deutsche Forschungsgemeinschaft (Ga 153/11-2 and Ga 153/11-3) and partially by NATO (0581/87) and COSY-KFA Jülich (41092744 and 41116381)     

On Suhl's dispersion equations for dilute magnetic alloys in a finite magnetic field

A one dimensional, nonlinear, singular integral equation was recently shown to be equivalent to Suhl's dispersion equations for the Kondo-problem of a half-spin magnetic impurity in a finite magnetic field. We investigate this integral equation further analytically and numerically and obtain numerical solutions which we use for a calculation of transport coefficients. The normal part of the scattering potential of the magnetic impurity is included via ans-wave phase shift. The transport coefficients are universal functions of the ratiosT/T _K andB/B _K of the temperatureT and the zero magnetic field Kondo-temperatureT _K and of the magnetic inductionB and the Kondo magnetic inductionB _K. We find maxima in the electrical and thermal resistivities as functions ofT/T _K forBB _K. These are typical Kondo phenomena, and can be influenced by. Interference of and the phases of Kondo-scattering amplitudes leads to dramatic effects in the thermopower and the Hall coefficient.SFB 125The numerical part of this work was performed at the Institut für Festkörperforschung, Kernforschungsanlage Jülich, F.R. Germany     

Trapping by vacancies and mobility of positive muons in neutron-irradiated aluminium

By means of the muon spin rotation (µSR) technique the trapping at vacancies and the mobility of positive muons are investigated in the temperature range 2.5 K to 297 K in polycrystalline aluminium irradiated with fast neutrons at 4.6 K. The observed damping of the µSR signal at temperatures below 50 K is in good agreement with saturation trapping at monovacancies. The temperature dependence of the damping above 50 K indicates that the muon diffusivity exhibits a minimumD _min ^µ+ 110^–13 m² s^–1 near 125 K, which is explained by a transition from coherent to incoherent tunneling. With the help of an estimated trapping cross section a monovacancy concentration of ~3 × 10^–4 after 125 K annealing is deduced, in good agreement with measurements of the residual electrical resistivity. As expected, the vacancy recovery shows up in an irreversible decrease of the damping above ~ 175 K.Work supported by the Bundesminister für Forschung und Technologie and by Schweizerisches Institut für Nuklearforschung (SIN). Requests for reprints and correspondence should be addressed to A. Seeger, MPI für Metallforschung, Heisenbergstraße 1, D 7000 Stuttgart-80, Germany     

Anisotropy effects in superconductors with magnetic impurities

The influence of Fermi surface anisotropy on the specific heat jumps,C, at the phase transition for superconductors containing magnetic and nonmagnetic impurities is discussed. In the framework of a simple two-band or two-zone model we find for small interband electron-phonon coupling constants characteristic maxima in theC(T _c )-curve.These departures from the correspondingC-curve of a single-band isotropic superconductor are mostly pronounced forweak andstrong interband Coulomb scattering of conduction electrons on nonmagnetic ions. There is only a small range of intermediate scattering rates for which the maxima are smeared out.Work performed within the research program of the Sonderforschungsbereich 125 — Aachen/Jülich/Köln     

Diffusion in three-dimensional random systems at their percolation thresholds

Extensive Monte Carlo simulations of theant-in-the-labyrinth problem on randomL* L* L simple cubic lattices are performed, forL up to 960 on a CRAY-YMP supercomputer. The exponentk for the rms displacementr witht inrt ^k is found to bek=0.190±0.003. As a second approach, large percolation clusters with chemical shells up to 300 are generated on a simple cubic lattice at criticality. The diffusion equation is then solved by using the exact enumeration technique. The corresponding critical exponentd ^w is found to be 1/d ^w =0.250±0.003.On leave from I. Institut für Theoretische für Physik, Universität Hamburg, D-2000 Hamburg, Federal Republic of Germany.     

Lifetime of the two-phonon vibrational state in232Th

We report on a measurement of the lifetime of the 1414 keV state in²³²Th by the Doppler-shift recoil-distance method. This 4⁺ state shows all characteristics of a nearly-harmonic two-phonon-vibrational excitation. The result for the B(E2) value obtained from the lifetime,=3.2 ± 0.7 ps, is in agreement with an earlier estimate of the collectivity from Coulomb-excitation yields and supports the interpretation of the 1414 keV state as a two-phonon-vibrational excitation.We would like to thank the accelerator crew of the Max-Planck-Institut für Kernphysik for the excellent running conditions they maintain. We are also indebted to Dr. H.J. Maier, University Munich for supplying us with the²³²Th targets. This work was supported by the Bundesminister für Forschung und Technologie under contract numbers 06BN601 and 06HD5251.     

The electronic thermal conductivity of superconductors with paramagnetic impurities

We have measured the thermal conductivitiesK _s in the superconducting state andK _n in the normal state of (La_1–x RE_x) Al₂ single crystals (RE: Gd, Ce;x0.005) between 0.4 and 8 K. The lattice conductivity is small in the superconducting state above 0.5T _c and in the normal state and is independent of annealing. Annealing does, however, strongly depress the ratioK _s ^e /K _n ^e of the electronic thermal conductivities. We also report on a theory of the electronic thermal conductivity which describes the experimental results quantitatively. Interaction effects between impurities show up for the samples with the highest RE-concentration.Work performed within the research program of the Sonderforschungsbereich 125 Aachen/Jülich/Köln     

Spin-polarized photoemission study on the temperature dependence of the exchange splitting of Ni

Using spin-polarized photoemission with high energy- and angle resolution (E=100 meV, =±3°) we have investigated the temperature dependence of the exchange splitting of Ni in the temperature range 0.5T/T _c0.94. At room temperature we find _ex=0.18 eV for the exchange splitting of theS ₄ band at theX point of the Brillouin zone. With increasing temperature the total (spin-averaged) energy distribution shows a narrowing and merges into one peak. The spin-resolved energy distribution curves approach each other and are strongly broadened. A discussion of the data within current theories of itinerant electron magnetism is given. The spectra indicate that neither the pure Stoner model nor the prediction of local band theory, assuming a temperature independent exchange splitting are justified for Ni. We conclude that the exchange splitting decreases with increasing temperature and that transverse as well as longitudinal spin fluctuations are responsible for the broadening of the spin-resoived energy distribution curves.Experimental part of the work performed at Institut für Festkörperforschung of the KFA Jülich and supported by the Deutsche Forschungsgemeinschaft through SFB 125     

Transfer Matrix Spectrum and Bound States for Lattice Classical Ferromagnetic Spin Systems at High Temperature

We obtain new properties of general d-dimensional lattice ferromagnetic spin systems with nearest neighbor interactions in the high-temperature region (1). Each model is characterized by a single-site a priori spin distribution, taken to be even. We state our results in terms of the parameter =s ⁴–3s ²², where s ^k denotes the kth moment of the a priori distribution. Associated with the model is a lattice quantum field theory which is known to contain particles. We show that for >0, small, there exists a bound state with mass below the two-particle threshold. The existence of the bound state has implications for the decay of correlations, i.e., the 4-point functions decay at a slower rate than twice that of the 2-point function. These results are obtained using a lattice version of the Bethe–Salpeter equation. The existence results generalize to N-component models with rotationally invariant a priori spin distributions.