Complex-dimensional invariant delta functions and lightcone singularities

Invariant delta functions (including imaginary-mass case) defined in a complexn-dimensional space-time are explicitly calculated in position space. It is proposed to define products of invariant delta functions in the ordinary Minkowski space by analytically continuing the correspondingn-dimensional ones ton=4. The (not only leading but also non-leading) lightcone singularities of [(x; m ²)]², (x; m ²)⁽¹⁾(x; m ²), and [⁽¹⁾(x; m ²)]² are shown to be unambiguously determined in this way.     

Determination of the nuclear parameters of155Gd excited states using the Mössbauer effect

From Mössbauer spectra of GdAlO₃ and GdVO₄ above and below the Néel temperature and fitted using a transmission integral, we have determined the following parameters of the 86.5 keV and 105 keV levels:g(86)/g(0)=+1.217±0.005,Q(86)/Q(0)= +0.10±0.02,g(105)/g(0)=–0.55±0.02,Q(105)/Q(0)=+0.74±0.02, r ²₁₀₅/ r ²₈₆=+1.30±0.05. The linewidth observed for the 105 keV transition is less than the calculated natural linewidth.     

Existence of Resonances for Metric Scattering in Even Dimensions

Suppose _g is the (negative) Laplace–Beltrami operator of a Riemannian metric g on ⁿ which is Euclidean outside some compact set. It is known that the resolvent R()=(– _g –²)^–1, as the operator from L ² _comp( ⁿ ) to H ² _loc( ⁿ ), has a meromorphic extension from the lower half plane to the complex plane or the logarithmic plane when n is odd or even, respectively. Resonances are defined to be the poles of this meromorphic extension. We prove that when n is 4 or 6, there always exist infinitely many resonances provided that g is not flat. When n is greater than 6 and even, we prove the same result under the condition that the metric is conformally Euclidean or is close to the Euclidean metric.     

Ozone production in oxygen by means of F2-laser irradiation at λ=157.6 nm

Ozone is generated in pure oxygen (p5 kPa), synthetic air (p7 kPa) and oxygen-argon mixtures (p3 kPa) by irradiation of these gases with the VUV light of a repetitively pulsed (f _L15 Hz) F₂-laser at =157.6 nm with maximum about 4 mJ/pulse. An absorption photometer measurement operating at 253.7 nm (Hg line) determines the ozone concentration as a function of oxygen and/or additive gas pressure, the repetition frequency of the laser and the wall temperature of the reaction chamber. The temporal development of the ozone concentration as a function of these parameters is calculated by means of rate equations for the species O(³ P), O₂(X ³ _g ^– ), O₃(¹ A ₁), O(¹ D), O₂(a ¹_g), O₂(b ¹ _g ⁺ ) and vibrationally excited O ₃ ^* (¹ A ₁) and the photon distribution. The maximum concentration of O₃ in the sealed-off chamber reaches 1.6% in pure O₂, 4.1% in air and 1.2% in a 1:5 O₂-Ar mixture at 3 kPa. The annihilation of O₃ by the wall and temperature dependent volume processes (300 KT395 K) is studied and the experimental and theoretical results are compared.     

Jauch-Piron system of imprimitivities for phonons. I. Localizability in discrete space

This paper is devoted to a discussion of the notion of localizability for phonons, i.e., quasiparticles arising from the harmonic vibrations of a system ofn atoms bound to one another by elastic forces. The natural tools for the analysis of localizability are the projection operatorsÊ() acting on the Hilbert space of one-phonon states, where is an arbitrary subset of the set that consists ofn vectors specifying the equilibrium positions ofn atoms. The expectation value ofÊ() is the probability that the phonon belongs to the atoms whose equilibrium positions are characterized by the elements of . For a strongly localizable phonon all of the projection operatorsÊ() commute with one another, whereas in the case of a weakly localizable phonon the operatorsÊ(₁) andÊ(₂) do not commute when ₁ and ₂ overlap. With the aid of the Jauch-Piron quantum theory of localization in space, the present paper describes the method of obtainingÊ() and also shows that if in the system ofn atoms there exist normal modes of zero frequency, then the phonon is only weakly localizable. Given the explicit expression forÊ(), one can define the number-of-phonons operator as well as the quasiparticle analogue (given in a companion paper) of the Wigner distribution function.     

Energy band structure of CdSnAs2 and CdGeAs2

The energy band structure of CdSnA₂ and CdGeAs₂2 is calculated by the empirical-pseudopotential method, taking account of spin-orbital interaction. The calculated parameters – E_g = 0.25, _cr = 0.05, _s.o = 0.44 for CdSnAs₂ and E_g = 0.55, _cr = 0.20, and _s.o = 0.33 for CdGeAs₂ (all in eV) — are in good agreement with experiment. The conclusion drawn in a series of experimental works that there are additional minima close to the bottom of the CdSnAs₂ conduction band is not confirmed in the calculation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 78–82, December, 1981.     

The Efficiency of the Formation of Singlet Oxygen by a Sensitizer Based on Zinc Phthalocyanine

Using zinc octa(diethoxyphosphenylmethyl)phthalocyanine as an example, we determined experimentally the quantum yield of generation of singlet oxygen () which makes it possible to evaluate quantitatively the efficiency of photogeneration of ¹O₂ and the influence of biomolecules on this parameter. It is shown that the efficiency of generation of singlet oxygen by the sensitizers used in photodynamic therapy depends on their state in a solution and increases with disaggregation of the dye and its interaction with biomolecules. It is established that phthalocyanine in an aqueous buffer solution sensitizes the formation of ¹O₂ with the quantum yield = 0.16 ± 0.02. On introduction of the detergent Triton X100 into the buffer solution of phthalocyanine, increases up to 0.48 ± 0.07. In a microheterogeneous medium (buffer + albumin) = 0.42.     

Thermal expansion,sound velocities,specific heat and pressure derivative ofT c in YBa2Cu3O7

We report measurements, between helium and room temperature, of the thermal expansion (T), sound velocitiesv _L (T) andv _T (v) and specific heatC(T) of YBa₂Cu₃O₇ samples, all cut from the same sintered pellet. A linear term in (T) is resolved at low temperatures. It is compared with a corresponding term in the low temperature specific heat and, using the bulk modulus from our sound propagation measurements, a Grüneisen parameter of usual size (1.2±0.4) is derived-in conformity with the possible existence of non-superconducting carriers well belowT _c . Longtime drift effects in the length of the sample between 30 K and 60 K point to the vicinity of a structural instability. The Debye temperature derived fromC(T) amounts to about 450 K atT=T _c =91 K and forT0 approaches 350 K, in agreement with the value deduced fromv _L (T) andv _T (T). The superconducting transition is indicated by anomalies with idealized discontinuities and C. A thermodynamic relation between and C yields the relative pressure derivative ofT _c ,t _p =T _c ^–1 (T _c /p) _p0=+(0.7±0.2)·10^–7 kbar^–1.     

Critical Region for Droplet Formation in the Two-Dimensional Ising Model

We study the formation/dissolution of equilibrium droplets in finite systems at parameters corresponding to phase coexistence. Specifically, we consider the 2D Ising model in volumes of size L ² , inverse temperature > _c and overall magnetization conditioned to take the value m L ² –2m v _L , where _c ^–1 is the critical temperature, m =m () is the spontaneous magnetization and v _L is a sequence of positive numbers. We find that the critical scaling for droplet formation/dissolution is when v _L ^3/2 L ^–2 tends to a definite limit. Specifically, we identify a dimensionless parameter , proportional to this limit, a non-trivial critical value _c and a function such that the following holds: For < _c , there are no droplets beyond log L scale, while for > _c , there is a single, Wulff-shaped droplet containing a fraction _c =2/3 of the magnetization deficit and there are no other droplets beyond the scale of log L. Moreover, and are related via a universal equation that apparently is independent of the details of the system.     

Weak density of states

Let L be a quantum logic, here an orthoalgebra, and let be a convex set of states on L. Then generates a base-normed space, and the dual-order unit-normed space contains a canonically constructed homomorphic copy of L, denoted by e(L). A convex set of states on L is said to be ample provided that every state on L is obtained by restricting an element of the base of the bi-dual order unit-normed space to e(L). For a quantum logic L we show that a convex set of states is ample if and only if is weakly dense in the convex set of all states on L. The notion of ampleness is then discussed in the context of Gleason-type theorems for W^* algebras and JBW algebras and also in the context of classical logics.Dedicated to Prof. Peter Mittelstaedt on the occasion of his sixtieth birthday. Research supported by the Swiss National Science Foundation.     

Anisotropy of the low temperature resistivity of hexagonal single crystalline spin glass systems

The impurity contribution to the resistivity in zero field (T) of dilute hexagonal single crystals of ZnMn, CdMn and MgMn has been studied in the mK range on samples cut parallel () and perpendicular () to thec-axis, using a SQUID technique for the measurements. Typical spin glass behavior is found in (T) as well as (T) for all alloys, with Kondo like logarithmic increases at higher temperatures and maxima atT _m at lower temperatures, indicating the influence of impurity interactions. The differences in the corresponding isotropic resistivity _poly(T) between the three systems can qualitatively be understood within the framework of a theoretical model by Larsen, describing (T) as a function of universal quantitiesT/T _K and _RKKY/T _K , where _RKKY is the RKKY-interaction strength andT _K the Kondo temperature. With respect to the two lattice directions studied, the behavior of (T and (T is anisotropic in the Kondo regime as well as in the range where ordering becomes important. While the anisotropy in the Kondo slope can be understood by an anisotropic unitarity limit, the understanding of the anisotropy in region where impurity interactions are important remains problematic.Dedicated to Prof. Dr. S. Methfessel on the occasion of his 60th birthday     

A study of a fullyc-axis oriented dc-sputtered thin film of YBa2(Cu0.98 57Fe0.02)3O6.8 by means of CEMS,XRD and SEM

A fullyc-axis oriented thin film of YBa₂(Cu_0.98 ⁵⁷Fe_0.02)₃O_6.8 prepared by planar dcsputtering has been investigated by means of Mössbauer spectroscopy. Room temperature⁵⁷Fe conversion electron Mössbauer spectra taken at different angles between the -ray direction and the normal (=c-axis) of the film show four subspectra: A (quadrupole splitting E _Q1.9 mm/s), B (E _Q1 mm/s), C (E _Q0.5 m/s) and D (E _Q1.6 mm/s). For subspectra A, B and C, we found the same hyperfine parameters as already published on other samples. The hyperfine parameters for subspectrum D are determined for the first time using a fully oriented sample. For D, we found the asymmetry parameter 0.6 andV _zz (the main component of the electric field gradient) lying in the a-b-plane.     

Analyticity properties of eigenfunctions and scattering matrix

For potentialsV=V(x)=O(|x|^–2–) for |x|,x³ we prove that if theS-matrix of (–, –+V) has an analytic extension to a regionO in the lower half-plane, then the family of generalized eigenfunctions of –+V has an analytic extension toO such that for |Imk|<b. Consequently, the resolvent (–+V–z ²)^–1 has an analytic continuation from ⁺ to {kOImk|<b} as an operator from _b ={f=e ^–b|x| g|gL ₂(³)} to _–b . Based on this, we define for potentialsW=o(e ^–2b|x|) resonances of (–+V, –+V+W) as poles of and identify these resonances with poles of the analytically continuedS-matrix of (–+V, –+V+W).The author would like to thank the Institute for Advanced Study for its hospitality and the National Science Foundation for financial support under Grant No. DMS-8610730(1)     

Spectral properties of random Schrödinger operators with unbounded potentials

We investigate spectral properties of random Schrödinger operators H = - + _n()(1 + |n|) acting onl ²(Z ^d), where _n are independent random variables uniformly distributed on [0, 1].Research partially supported by a Sloan Doctoral Dissertation Fellowship and NSERC under grant OGP-0007901Research partially supported by NSF grant DMS-9101716     

119Sn-mössbauer,IR, and DSC study of tin oxyfluoride glasses

The¹¹⁹Sn-Mössbauer spectra ofxSnO·(70–x)SnF₂·30P₂O₅ glasses (0 x70) measured at 78 K comprised a doublet due to Sn²⁺ (=3.30–3.36 mm s^–1, = 1.70–1.72 mm s^–1) and a weak singlet due to Sn⁴⁺ located at –0.23 mm s^–1 with respect to BaSnO₃. The and of Sn²⁺ were comparable to those of Sn₂P₂O₇. Small Debye temperatures (146 and 155 K) were obtained from the low-temperature measurements. These results indicate that Sn²⁺ and Sn₄₊ occupied interstitial sites, being loosely and ionically bonded to distorted PO_4–x F _x tetrahedra.     

A long-time tail for random walk in random scenery

Consider a simple random walk on ^d whose sites are colored black or white independently with probabilityq, resp. 1–q. Walk and coloring are independent. Letn _k be the number of steps by the walk between itskth and (k+1) th visits to a black site (i.e., the length of itskth white run), and let _k =E(n _k )–q ^–1. Our main result is a proof that (*) lim _k k ^d/2 _k = (1 –q)q ^{d/2 – 2}(d/2) ^d/2. Since it is known thatq ^{– 1} _k =E(n ₁ n _{k + 1} B) –E(n ₁ B)E(n _{k + 1} B), withB the event that the origin is black, (*) exhibits a long-time tail in the run length autocorrelation function. Numerical calculations of _k (1k100) ind=1, 2, and 3 show that there is an oscillatory behavior of _k for smallk. This damps exponentially fast, following which the power law sets in fairly rapidly. We prove that if the coloring is not independent, but is convex in the sense of FKG, then the decay of _k cannot be faster than (*).     

Electrical properties (dc and ac) of vanadium-borate glass

The results of an investigation into the temperature and frequency dependence of the electrical conductivity [dc and ac (10²–10⁵ Hz)] of glass of the composition 35% B₂O₃-15% CaO-20% V₂O₄-30% V₂O₅ (weight %) are discussed. The resistivity of the glass at T=300°K is =1.2·10¹¹ ·cm. The activation energy of the dc conductivity is E=(0.652±0.004) eV and equal to E for ₂ at high temperatures. The temperature-frequency dependences of the polarization component _p, the dielectric loss coefficient, and the permittivity are explained on the basis of the Fröhlich model proposed for uncoupled relaxation oscillators for which the heights of the potential barriers are uniformly distributed in some range of energies.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika. No. 3, pp. 35–38, March, 1981.     

Tunneling experiments on amorphous and crystalline superconducting tantalum films

The energy gap and the transition temperature of amorphous and crystalline superconducting Ta films are measured by tunneling experiments. The following values are obtained: 2(0)=0,65 meV,T _c=2,11 K for the amorphous state after quenched condensation and 2(0)=1,24 meV,T _c=4,06 K for the crystalline state after annealing at room temperature. The reduced energy gap 2(0)/kT _c=3,58 demonstrates that amorphous Ta films are weak-coupling superconductors. The crystallization of the amorphous Ta films takes place at 250 K.     

Radiative and Nonradiative Deactivation of the 1Δ g State of Molecular Oxygen in Solutions of Saturated Hydrocarbons

The luminescence of singlet molecular oxygen (¹ _g or ¹O₂) caused by the ¹ _g ³ _g ^– transition in liquid saturated hydrocarbons from n-hexane to n-undecane is investigated. A model of quenching of the ¹ _g state of the oxygen molecule by the CH oscillations of the molecules of solvents is proposed, in which the rate constant of the nonradiative deactivation (k _nr) depends strongly on the average distance between the ¹O₂ and CH groups of the solvent. This experimental dependence can adequately be described by an exponential function with the distance parameter R ₀ = 0.15 , which indicates that the acceleration of quenching with the solvent density is a result of larger overlapping of the electron orbitals of oxygen and the CH groups. The detected increase in k _nr with temperature can also be explained qualitatively well within the framework of the model suggested. It is shown that the radiative rate constant (k _r of the ¹ _g ³ _g ^– transition does not depend on the distance between the ¹O₂ and CH groups and its change in a number of hydrocarbons is related to macroscopic parameters, in particular, the polarizability of the solvent.     

The theory of neutron scattering from mixed harmonic solids

In the intermediate valent cerium alloys Ce_1–xY_xPd₃, Ce(Pd_1–xRh_x)₃ and Ce(Pd_1–xAg_x)₃ the Gd³⁺-ESR shows a non-linear increase of the linewidth H(T) in the temperature range 4.2KT300K. The deviation from the linear Korringa law can be described by a reduced conduction electron density of states at the Gd site (which is a Ce lattice site) in the energy range E _4f (=width of the Ce 4f states). This supposition allows a determination of E _4f from the H(T)-data. For CePd₃:Gd³⁺ we find E _4f=(650±100) K. E _4f increases with Y- and Rh-concentration and decreases with Ag-concentration.