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.     

Isotope dependence of particle-decay rates of muonic molecular ions (d3,4Heμ) J=1 below (dμ)1s-3,4He threshold

Rates of particle-emitting decay of the resonant state of the muonic molecular ion (dHe) _J=1 lying below the (d)_1s-He threshold can decay to the d-He scattering state. The resonant state is estimated by scattering calculations with the non-adiabatic coupled-rearrangement-channel method. Strong isotope dependence of the decay rates of (d³He) _J=1 and (d⁴He) _J=1 is predicted, though the calculated radiative decay rates of the states are almost the same. In (d³He) _J=1, the particle decay width is three times larger than the radiative decay width, while the two types of decay widths are almost the same in (d⁴He) _J=1. This results in a strong hindrance of the branching ratio of the radiative decay of (d³He) _J=1 compared with the case of (d⁴He) _J=1. This is consistent with a recent observation of the radiative decay of the two molecular states.     

Study of the trapping of positive muons by extended defects in aluminum

PulsedSR spectra were measured with surface ⁺ in neutron irradiated aluminum as a function of specimen temperature above room temperature. It was found that the depolarization rate of ⁺ increases and the precession frequency decreases as the specimen temperature is raised. This fact was attributed to the trapping of ⁺ by radiation induced voids and suggests the importance of ⁺-surface interactions in the case of voids.     

μ+ Knight shift in Be

A first principles calculation of the Knight shift of a ⁺ in beryllium was carried out using a cellular multiple scattering technique (Keller 1972, 1977). The main conclusion is that the ⁺ induces the segregation of one state (of each spin) from the conduction band to lower energies, a molecular orbital of the ⁺ and its nearest neighbours. This state is occupied (with two antiparallel spin electrons) but it has less than 35% of ⁺ character. The screening is then completed with the conduction electrons properly. The observed Knight shift is then the sum of a diamagnetic shielding and a typical enhanced spin susceptibility term of opposite sign and smaller value.     

Future μCF program with pulsed muons at UTMSL/KEK and RIKEN/RAL

The present paper summarizes new experimental proposals on muon catalyzed fusion (CF) research with a sharply pulsed negative muon beam now available at the UTMSL/KEK facility and soon to be available in a more extensive way at the RIKEN/RAL facility. Special emphasis is placed on (1) CF studies on ultra-pure D-T mixture, (2) slow ^– beam production via CF, and (3) some exotic CF phenomena.     

Surviving extrema for the action on the twisted SU(∞) one point lattice

We give a simplified construction of twist eating configurations, based on a theorem due to Frobenius. These configurations are defined through the equation:U U U ⁺ U ⁺ =exp(2in /N) withU SU(N), =1 tod andn an antisymmetric matrix with integer entries. In the (Twisted)-Eguchi-Kawai model they yield extrema some of which survive forN. Comparison is made with the Monte Carlo data of the internal energy in the small coupling region.     

Development of a very low energy μ+ beam at PSI

At PSI we are investigating the technique of decelerating an existing very intense secondary beam of surface ⁺ (4 MeV) to an energy of 10 eV using appropriate moderators. These ⁺ can then be used as a source of a tertiary beam of low energy muons with tunable kinetic energy between 10 eV and 10 keV.With a 1000 A layer of solid Argon deposited on an Al substrate we obtain a moderation efficiency (with respect to the number of incoming surface ⁺) of the order of 10^–4.Results of our investigations and the present status of the project are presented together with future plans and possibilities.     

Poincaré Algebra and Space-Time Critical Dimensions for Paraspinnings Strings

In this paper, we paraquantize the spinning string theory in the Neveu-Shwarz model. Unlike the Ardalan and Mansouri work [Phys. Rev. D, Vol. 9, (1974) 3341], the paraquantum system is such that both the center of mass variables and the excitation modes of the string verify paracommutation relations. The commutators of the Poincaré algebra are satisfied, except the [p ,p ] one, since one can only write [p ,p ]= 0, for Q1. Because of the relation [x ,x ] =,0 and with the sole use of the trilinear relations, we find existence possibilities of spinning strings defined in a noncommutative space-time at space-time dimensions other than D=10.     

Polarization of strangeness Arizona muon

The longitudinal polarization of strangeness Arizona muon, namely, the 236 MeV/c ⁺ from the K^{+ +} v decay, has been measured to search for right-handed weak current in the strangeness changing process. The polarization has been determined to be –0.967±0.047.We are grateful to Professors T. Nishikawa, S. Ozaki, A. Kusumegi, and H. Sugawara of KEK for their encouragement and support during the course of this experiment. We are grateful to the operating crew of the KEK proton synchrotron and its experimental facilities for their cooperation during the experiment. This work is partially supported by the Grant-in-Aid of the Ministry of Education, Science and Culture.     

Energy and momentum in general relativity

In general relativity, conservation of energy and momentum is expressed by an equation of the form /x= 0, where –gT represents the total energy, momentum, and stress. This equation arises from the divergence formula dV _v = (/x ^v )d ⁴ d. Here we show that this formula fails to account properly for the system of basis vectors e(x). We obtain the (invariant) divergence formula e dV _v = e (/x ^v + )d ⁴ d. Conservation of energy and momentum is therefore expressed by the covariant equation (/x ^v ) + = 0. We go on to calculate the variation of the action under uniform displacements in space-time. This calculation yields the covariant equation of conservation, as well as the fully symmetric energy tensor . Finally, we discuss the transfer of energy and momentum, within the context of Einstein's theory of gravitation.     

The paramagnetic state (μ+e−) in silicon and tellurium at high temperature

The paramagnetic state (⁺e^–) in Si and Te was observed in a longitudinal magnetic field. The mean lifetimes of these states were obtained: _Si = 1.45(3) s, _Te = 12.5(8) s at 290 K, _Te = 12(2) s at 250 K.     

μ +SR in solids — trends and expectations

Conventional ⁺SR studies are classified according to their relation with Solid State Physics, and an attempt is made to identify current trends in the field of ⁺SR in solids. Desirable trends and development in ⁺SR techniques are also discussed shortly. Rather than risk attempts at predicting the future [1] of ⁺SR in solids, it is perhaps prudent merely to identify trends in the field and let individual readers to extrapolate. We shall start with trends in the main stream conventional ⁺SR and then discuss some desirable technical development.     

Leptonic decays of vector mesons and a possible μ+μ− resonance

The possible existence of a vector leptonic resonance (⁰) in the ^+– system is considered. We discuss the effect such a resonance would have on the g factor of the muon and also on the ratio of the partial widths of the muonic and electronic decay modes (R_V = (V ^+–)/G (V e⁺ e^–)) of the neutral vector mesons ⁰,,,, and. From the experimental values of R and R, the following values are obtained for the mass, coupling constant, and partial decay widths of the resonance: M = 872 ± 60 MeV, f²/4 = 4 ± 2) ·10^–4, ( ^{0 + –}) = 0.12±0.06 MeV, and (^{0 0 +–}) = 0.13±0.06 MeV.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 39–43, May, 1977.     

Investigation of muon states in silicon and germanium by field-quenching and RFμSR

The temperature dependence of the three states of positive muons in the semiconductors with diamond structure ( ⁺ in diamagnetic states ^d and paramagnetic muonium Mu and Mu^*) have been investigated on six Si (pure, B and P doped) and four Ge (ultrapure, CZ-grown undoped, Ga and Sb doped) single crystals by longitudinal field-quenching and radio-frequency ⁺SR. Clear evidence for the transition Mu^{* d} is found. The influence of light-induced charge-carriers is shown to be quite different in p- and n-type material.The work has been supported by the Bundesministerium für Forschung und Technologie in Bonn, Germany, under contract no. 03-SE3STU.     

Muon-pair formation in the collision of polarized hadrons

The angular dependence of the differential cross section of muon-pair formation in hadron-hadron collisions a₁+a₂+^–+X is investigated in general form, attention being directed mainly toward those contributions to the differential cross section which are determined by the vector polarization of the incident hadron a₁. The specific mechanism of processes a₁ + a₂ ⁺ + ^– +X is not given in detail here, but use is made of such general properties as the conservation of electromagnetic hadron current and the invariance of the electromagnetic interaction of hadrons with respect to spatial reflections.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 88–91, July, 1982.     

Entropy andp-particle observables. I. The general program

An information-theoretic notion of entropy is proposed for a system ofN interacting particles which assesses an observer's limited knowledge of the state of the system, assuming that he or she can measure with arbitrary precision all one-particle observables and correlations involving some numberp of the particles but is completely ignorant of the form of any higher-order correlations involving more thanp particles. The idea is to define a generic measure of entropyS[ ] = –Tr log for an arbitrary density matrix or distribution function , and then, given the trueN-particle, to define a reduced _R ^P which reflects the observer's partial knowledge. The result, at any timet, is a chain of inequalitiesS[ _R ¹ ]S[ _R ² ]...S[ _R ^N ]S[], with true equalityS[ _R ^p ]=S[ _R ^p+1 ] if and only if the true factorizes exactly into a product of contributions involving all possiblep-particle groupings. It follows further than (1) if, at some initial timet ₀, the true factorizes in this way, thenS[ _R ^p (]S[ _R ^p (t ₀)] for all finite timest>t ₀, with equality if and only if the factorization is restored, and (2) the initial response of the system must be to increase itsp-particle entropy.     

Massive spin-two particle in a gravitational field

The spin-two particle is described by a symmetric tensorh subject to the subsidiary conditionsh = h =0. Their covariant generalization and the wave equation have been obtained directly from the Eulerian variational equations by algebraic methods only. In addition to the tensor fieldh a symmetric third-rank tensor = as well as a vector fieldA have been added, neither of which enter in the final result. The Lagrangian function is taken as a linear sum of all combinations which can be constructed from these functions, as well as terms involving the curvature tensor and its two possible contractions. Variation with respect toh , andA independently gives the Euler equations. Combining the various trace equations and choice of arbitrary constants yields the subsidiary conditions, while the Euler equations themselves give the connection between the auxiliary functions and the tensorh as well as the generalization of the wave equationD D h + 2R h -R h -R h +g R h +Rh =m ² h Finally, variation with respect tog yields the energy-momentum tensor.     

Contribution to the theory of positive muon diffusion in metals at low temperature

We study the temperature dependence of the ⁺ diffusion in a metal within the small polaron theory. The geometry of the strain field due to an impurity is shown to strongly influence the ⁺ diffusion properties. We reanalyzed part of the Al data.Part of this work was done at the French Atomic Commission at Grenoble.The author is much indebted to his muon spin rotation collaborators at CERN for numerous discussions. He would likt to thank A.M. Stoneham for his letters and the ⁺SR group at LAMPF for its support.     

μ + Residual polarization in water,CS2, C6F6 and hydrocarbons under strong decoupling fields

The ⁺ decay asymmetry was measured as a function of longitudinal magnetic field (LF) between zero and 10 kG in spin decoupling experiments on muons in water, c-hexane, CS₂, C₆F₆, C₆H₆ etc. The results were compared both with the diamagnetic polarization,P _D, measured by transverse-field (TF) experiments ⁺SR, and with the asymmetry observed in ⁺ spin resonance experiments under longitudinal field. These results have been interpreted in terms of spin conversion and chemical reactions of muonium (Mu) with paramagnetic species such as free radicals in the muon track or spur. It is argued that spin-conversion reactions are responsible for the so-called missing fraction of ⁺ polarization in various media.     

Matter and light wave interferometry in gravitational fields

We consider the problem of finding the quantum mechanical phase associated with the propagation of a particle in a given external gravitational field, and conclude that it ism ds. In weak fieldsh this allows us to calculate the gravitationally induced phase on a freely traveling particle as 1/2 h P dx whereP is the ordinary momentum. This formula has the expected Newtonian limit and is then used to calculate effects in matter wave interferometry such as those due to gravity waves and the dragging of the ether frame by rotating bodies. Light wave interferometry is then considered and is shown to be also described by 1/2 h K dx , whereK is the wave vector of the light, and the integral is along the path of the ray. Matter and light wave interferometry are compared in various cases.A preliminary version of this work was presented at the Grenoble Workshop on Neutron Interferometry, June 1978.