Self-avoiding random walks on the hexagonal lattice

We use the algorithm recently introduce by A. Berretti and A. D. Sokal to compute numerically the critical exponents for the self-avoiding random walk on the hexagonal lattice. We find=1.3509±0.0057±0.0023v=0.7580±0.0049±0.0046=0.519±0.082±0.077 where the first error is the systematic one due to corrections to scaling and the second is the statistical error. For the effective coordination number we find=1.84779±0.00006±0.0017 The results support the Nienhuis conjecture=43/32 and provide a rough numerical check of the hyperscaling relationdv=2–. An additional analysis, taking the Nienhuis value of=(2+2^1/2)^1/2 for granted, gives=1.3459±0.0040±0.0008     

The PSI experiments on muon-catalyzed pt fusion

The experiments on pt fusion performed at Paul Scherrer Institut, Villigen, Switzerland, are described. Liquid triple mixtures of protium, deuterium and tritium with low concentrations on deuterium and tritium were used. Gamma rays, X-rays, neutrons and, for the first time, conversion muons, were measured. Preliminary results are: Rate for spin flip from the triplet to the singlet state of t(1s), ₁₀=(1.0±0.2) × 10³s^–1; rate for muon-catalyzed pt fusion from the (I=1) nuclear-spin state, _pt ^f (I=1)=0.07±0.01s^–1; and the molecular formation rate, _pt ^m =(7.5±1.3)s^–1 (all normalized to liquid hydrogen density).     

Positron mobility in polyethylene in the 60–400 K temperature range

We have determined the positron mobility (₊) in polyethylene samples (67.2% crystalline, glass transition temperatureT _g=151 K) in the 64–400 K temperature range by Doppler shift measurements. A method based on the simulataneous observation of two lines from¹³³Ba and¹³⁷Cs radioactive sources together with the positron annihilation line, was employed to measure the Doppler shift of the 511 keV line as a function of the electric field applied to the samples. With this method we were able to measure at the same time the drift velocity of positrons and theS parameter. This parameter is very important in the interpretation of the mobility trend in samples where the positron states change with temperature. The positron mobility was corrected for positronium formation. ₊ at 64 K is 31.7±0.8 cm² V^–1 s^–1 then decreases up to 123 K, increases at 148 K and decreases again up to 170 K (₊=26.9±0.8 cm² V^–s^–). This sharp change in mobility is centred around the glass transition temperature of our samples. Then the mobility remains almost constant up to 230 K. From 250 K to 377 K, ₊ increases and reaches the value of 38.4±1.0 cm² V^–1s^–1. The corrected experimental data were well fitted by a simple model taking into account scattering and a thermally activated process (hopping mechanism).     

Observation ofμ − spin precession in ferromagnetic Ni and giant hyperfine anomaly

A ^–SR signal in nickel was found representing the first observation of ^–SR in ferromagnetic materials, and the hyperfine anomaly was determined to be –2.82±0.08% in comparison with the hyperfine field at dilute Co in Ni known from NMR.     

Negative muon precession in nuclei with spin

Polarized negative muons were stopped in various materials containing nuclei with nonzero spin. The TF-SR precession signal of theF ⁺ hyperfine state (frequencyv ₊ > 0) was pronounced for ^–Li and ^–Be, faint for ^–Cl (in NiCl₂), and undetectable for ^–F (in CaF₂ or NiF₂) and ^–P. TheF ^– signal (frequencyv _– < 0) was observed clearly for ^–Be, ^–Al and ^–Na, marginally for ^–K, ^–V and ^–Nb, and not at all for ^–Ga (at 4 kOe) or ^–Co (ferrromagnetic, zero field). In the heavier elements theF ^– signal is fed by transitions from theF ⁺ to theF ^– state at a rateR, as long asR(v ₊ –v _–). [See separate paper on ^–Al in these Proceedings, p. 879.]I am grateful to Alex Schenck and Bruce Patterson for the loan of equipment and samples, to Fred Gygax for helping set up the apparatus, to Jun Imazato for help with the experiment, and to Toshi Yamazaki and Tak Suzuki for valuable comments. I am also indebted to SIN for several weeks of free ^– beam time and to SIN, BOOM, and the University of Tokyo for free time on their VAX computers, which were kept busy for several months in the analysis.     

A μSR study of spin density wave condensation in Cr85Mo15

Zero field SR spectra from Cr₈₅Mo₁₅ are well described by the sum of a lightly damped (0.02s^–1<₁<0.2s^–1) and a heavily damped (2s^–1<₂<15s^–1) exponential. The temperature dependence of these components is discussed in relation to the condensation of the incommensurate spin density wave and the onset of the antiferromagnetic state in this Cr-like alloy below T_N=120K. Evidence is presented for the nucleation of the spin density wave at temperatures greater than 1.5T_N.     

Experimental determination of the rates of the excited muonic hydrogen charge exchange on helium

The data of the experiment with the H₂+⁴He mixture are analyzed in order to estimate muon transfer rates from the excited states of p atoms to helium. Experimental data turned out to be insensible to the transfer rates from the metastable 2s state. The rates forn=3, 4, 5 were found to be: ⁽³⁾=(2±7)×10¹⁰ s^–1, ⁽⁴⁾=(16±13)×10¹¹ s^–1, ⁽⁵⁾=(75±60) ×10¹¹ s^–1, respectively.     

μ+SR in magnetically ordered BCC metals: Local fields, μ+ sites,quantum diffusion,and strain effects

The paper gives a critical discussion of the procedures for extracting from the ⁺SR signals obtainable on magnetically ordered metals information on ⁺ sites, on local lattice distortions induced by the ⁺, on the local magnetic fields felt by the ⁺, and on quantum diffusion. Results for-Fe are: ⁺ occupy O sites, the tetragonality of the elastic double-force tensor isA–B 2eV, the dipolar magnetic field acting on the ⁺ isB _dip=(0.66±0.02)T. Using this information ⁺ hopping rates and diffusivities in Fe are deduced and compared with diffusivities obtained for hydrogen and deuterium. From this it is concluded that hydrogen in Fe diffuses via the adiabatic mechanism. In addition, the paper contains a brief summary of the theoretical background required for taking advantage of the rather large ¦A– B¦ values expected for ⁺ at O sites in bcc metals in order to gain information on the effects of energy asymmetries between neighbouring ⁺ sites on the ⁺ hopping rates.     

Towards slow μ− production via muon catalyzed fusion

Slow ^– production via dd-CF using a two-layer arrangement is investigated. To determine its feasibility, experimental measurements are now in progress using the muonic X-ray detection method. The following experimental steps are being considered: (1) measurement of the number of ^– stopped inside a solid H₂/D₂ layer by detecting p K X-rays, (2) hot d emission detection by placing a secondary target at a distance of 10–30 mm from the layer and by detecting specific delayed X-rays, (3) measurement of the disappearance of d emission as the added D₂ layer is increased, (4) dd-CF measurement by detecting fusion protons, and (5) slow ^– emission detection. Results of the initial test experiment are presented.     

Radiation effects in lepton decays of neutral vector mesons and μ-e universality

A study has been made of the effects of radiation corrections of order as regards the probability of lepton decay of a moving neutral vector meson V e⁺e^– and V ^+– (V = ⁰, , ); -e universality has been checked by examining the effects of radiation corrections due to exchange of virtual photons between lepton and antilepton, and also to vacuum polarization by e⁺e^– electron and ^+–muon closed loops; in addition, a study has been made of the emission of soft photons as regards the partial width for the electron and muon modes of V-meson decay. Closed expressions (1), (4), and (5) for the corrections imply that the ratio ¦R_v¦ for the probabilities of decay of a V meson to e⁺e^– and ^+–, which are given by (11), agree well with the available evidence on ⁰ e⁺e^{– +–} decays and indicates a possible deviation from -e universality in e⁺e^–+– decays.Read at the meeting on high-energy physics, Nuclear Physics Section Academy of Sciences of the USSR (Moscow, February 11–15, 1974).Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 84–89, July 1975.We are indebted to Professor A. A. Sokolov for a discussion.     

Conductance distributions in random resistor networks. Self-averaging and disorder lengths

The self-averaging properties of the conductanceg are explored in random resistor networks (RRN) with a broad distribution of bond strengthsP(g)g ^–1. The RRN problem is cast in terms of simple combinations of random variables on hierarchical lattices. Distributions of equivalent conductances are estimated numerically on hierarchical lattices as a function of sizeL and the distribution tail strength parameter . For networks above the percolation threshold, convergence to a Gaussian basin is always the case, except in the limit 0. Adisorder length _D is identified, beyond which the system is effectively homogeneous. This length scale diverges as _Dµ^–v ( is the regular percolation correlation length exponent) when the microscopic distribution of conductors is exponentially wide (0). This implies that exactly the same critical behavior can be induced by geometrical disorder and by strong bond disorder with the bond occupation probabilityp. We find that only lattices at the percolation threshold have renormalized probability distributions in aLevy-like basin. At the percolation threshold the disorder length diverges at a critical tail strength µ_c as µ–^–z withz3.2±0.1, a new exponent.Critical path analysis is used in a generalized form to give the macroscopic conductance in the case of lattices abovep _c.     

Crystal-field splitting and temperature dependence of two-dimensional antiferromagnetism in the high-Tc compound DyBa2Cu4O8

By means of a quantitative analysis of extensive elastic neutron scattering experiments performed on theT _c =78 K superconductor DyBa₂Cu₄O₈ it is shown that two-dimensional (2D) antiferromagnetic Dy ordering in the (a,b)-plane remains stable in the whole temperature range fromT _N =(1.10±0.02) K down to 7 mK. The magnetic difference pattern with good angular resolution fits well to the Warren equation for scattering on 2D systems with powder averaging. Consequently, the fitted sublattice magnetisation is found to have a 2D Ising character. Moreover, the Dy³⁺ crystal-field levels were determined by inelastic neutron scattering. From the resulting crystal-field parameters we calculate the sublattice magnetisation of Dy³⁺ at saturation to be _Dy,CEF=6.0 _B in good agreement with _Dy,obs=(5.9±0.5) _B as measured by neutron diffraction.     

Effect of low-voltage spark discharge parameters on the spectral line intensities of sulfur and halogens

The influence of various circuit parameters on the spectral line intensities of sulfur and the halogens when excited in a low-voltage spark discharge have been investigated. The intensities were maximum for a discharge current of 6–8 A and a 1.0–1.5 mm spark gap. In ac spark discharges the maximum intensities occurred with capacitances of 20–50F and an inductance of 15H for primary circuit resistance of 200 ohm, and with 50–100F and 30–60H for 400 ohm. The intensities attained with dc sparks were higher than those with ac sparks. The intensity increased if the specimen served as the cathode and, in this case, occurred with capacitances of 100–800F and inductances of 30–60H for an ignition frequency of 12 sec^–1.     

Stressed and unstressed Ge:Ga detector arrays for airborne astronomy

We have constructed and used two dimensional arrays of both unstressed and stressed Ge:Ga photoconductive detectors for far-infrared astronomy from the Kuiper Airborne Observatory (KAO). The 25 element (5×5) arrays are designed for a new cryogenically cooled spectrometer, the MPE/UCB Far-Infrared Imaging Fabry-Perot Interferometer (FIFI). All of the pixels for the stressed array performed well on the first flights with FIFI; 25% of the detectors in the array are more sensitive than our best single element detector, with background limited noise equivalent powers (NEPs)3.0×10^–15 W Hz^–1/2 at 158 m and 40 km s^–1 spectral resolution. The average array element performs within±15% of this value. With a bias field of 0.1 V/cm, the average detector response is 20±6 Amp/Watt at 158 m. The cutoff wavelength and response also compare well with our single element detectors. The unstressed array delivers significantly better performance than our single element detector due to the lower thermal background in the new spectrometer. The average background limited NEp at 88 m and 35 km s^–1 spectral resolution is 7×10^–15 W Hz^–1/2. The least sensitive pixel is only 40% less sensitive. The unstressed array response at 88 m with a bias field of 1 V/cm is 5±1 Amp/Watt. Twenty four of the 25 elements worked on the first flights-on subsequent flights all channels have worked. Some of the exciting new science possible with far-infrared detector arrays is also discussed.     

All massless,scalar fields with trivialS-matrix are wick-polynomials

We extend a result about non-interacting fields given by Buchholz and Fredenhagen. Consider a massless, scalar field ø in 3 + 1 dimensional space-time which does not interact. The corresponding Hilbert space is assumed to be the FockspaceH of the free massless fieldA. This implies — as we show in the first part — that alln-point-functions are rational functions of their arguments. In the second part we use this fact to construct a symmetric, traceless tensorfield ^1...n, relatively local to the original field ø, and connecting the vacuum with the one particle states. In the last part we prove ^1...n to be relatively local to the free fieldA.     

GeO2-Core/SiO2-cladding optical fibers made by MCVD process for stimulated raman applications

GeO₂-core/SiO₂-cladding optical fibers (GESI fibers) and liquid core fibers with a cladding region of GeO₂ were designed and fabricated by the MCVD process. The attenuation level of the GESI fibers was about 0.5 dB/m in the near-infrared wavelength region at 2.35 m. GESI fibers showed a stimulated Raman scattering (SRS_ spectrum with six to seven Stokes shifts of 430 cm^–1. The spectrum of SRS expanded to 1.6 m when a Nd: YAG laser at a wavelength of 1.064 m was used.     

Uniaxial stress induced frequency shifts for muons in single crystal Fe

We report the first results on uniaxial stress-induced frequency shifts in an Fe single crystal. Stress was applied along the 100 axis, which was also the axis of magnetization induced by an external field. The observed frequency shift was –0.34±0.023 MHz per 100 microstrain, which corresponds to B/=+25.1±1.6 G/100. The positive sign arises from the negative sign of B itself. This result is interpreted as follows: The stress induces a statistical population shift between magnetically inequivalent sites. Extrapolations from the calculations of Sugimoto and Fukai from Nb and V to Fe yield order of magnitude agreement. The 4T(0) site system seems more likely.     

Muon knight shift in platinum and in β-PdHx (x=0.70, 0.75, 0.86)

The ⁺ Knight shift in Platinum has been measured between 20 K and 785 K. It shows a strong temperature dependence and scales with the magnetic bulk susceptibility. A temperature independent contribution of +53±15 ppm and a d-electron induced hyperfine field per unpaired d-electron per atom of B _hfd ^a =–5.03 kG(±8.5%) are obtained. The ⁺ Knight shift in PdH_0.70, PdH_0.75 and PdH_0.86 shows no dependence on temperature between 20 K and RT and increases from K=–(8±3) ppm for x=0.70 to K =+(6.5±3) ppm K=+(6.5±3) ppm for x=0.86, in good agreement with proton Knight shift measurements.     

Dipolar magnetic field and fermi contact field at the μ+ site in α-Fe at very low temperatures

In a longitudinal ⁺SR experiment on a high-purity-Fe single crystal sphere magnetically saturated in a 111 direction damped oscillations (wiggles) were observed in a temperature range 30 mK to 600 mK and in a certain regime of applied magnetic fieldsB _appl. Meassurements of the wiggle frequency as a function ofB _appl give us directly the Fermi fieldB _Fermi=(–1.13±0.02)T and the dipolar magnetic field ¦B _dip ¦=(0.66±0.03)T.B _dip was used to determine the prefactor in the Arrhenius law obeyed by the ⁺ hopping rate between 100 K and 1000 K. A comparision with the corresponding values for protons and deuterons suggests diffusion via the adiabatic mechanism.