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.     

Slow and monoenergetic (3Heμ−)+ beam production and novel applications

Based upon the recent discovery at UT MSL/KEK, a new idea is proposed for producing a slow and monoenergetic (3.2 keV) (³He^–)⁺ ion beam by using particle decay of the (d³He) muon molecule formed during the (d) to³He transfer reaction. The proposed intense (³He) beam as well as the less intense (⁴He) beam will open up way to various new types of important CF experiments.     

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.     

Development of a μLCR facility at LAMPF

It has long been recognized thatLCR could profitably be done with the high intensity surface beam at LAMPF [1]. A spectrometer has been built that is matched to the LAMPF beam characteristics. The polarization information is obtained from a downstream array of counters while side counters, containing no polarization signal, monitor the ⁺ beam. Degraders select higher energy e⁺, thereby reducing rates and required counter segmentation while maintaining information content. We apply a ramped longitudinal field in addition to the static one to average over instabilities in the ⁺ beam. This field scan allows direct interpretation of data and does not require a prior estimate of the resonance structure of a sample. Flux coils monitor the applied ramp field and eddy-current induced fields. High average rate (2×10^{7 +}/s). good stability, and the versatile field scan permitted useful data to be collected from Cu, Al(Cu), Al, Si(Al), and polycrystalline Si targets.     

Muon diffusion and trapping by defects in electron-irradiated Nb and Ta

The transverse spin relaxation of positive muons ( ⁺) has been measured on Nb and Ta after irradiation with 3 MeV electrons. In high-purity Nb the ⁺ diffusivity derived from the trapping at irradiation-induced defects above 100 K is explained in terms of adiabatic hopping. At lower temperatures there is evidence for the dominating processes to be fewphonon incoherent tunnelling and coherent hopping. Annealing results in the formation of new defects capable of trapping the ⁺. In Ta at least two types of irradiation-induced defects capable of trapping ⁺ survive up to annealing temperatures of 400 K.     

Trilinear generally covariant equations

Field equations for n-frames h ^a that are possible in the theory of absolute parallelism are considered. It is shown that in three cases the equations can, after the substitution h ^a =H^pH ^a (H=det H ^a , p is an n-dependent constant), be written in a trilinear form that contains only the matrix H _a and its derivatives and not H ^a . It is shown that the equations are still regular for degenerate but finite matrices H _a if rank H _a 2.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 22–27, February, 1991.     

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.     

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.     

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.     

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.     

Paramagnetic shift of μ+ in MnO and its time dependence

Conclusion The paramagnetic shift K of ⁺ in MnO is measured from 140K to 420K. K is negative at 14OK, increases rapidly with increasing temperature, but does not show a linear relation to the susceptibility . At T = 170K and 230K, the value of K depends greatly on the fitting time-range of the spectrum. These features are explained by a site change of ⁺ caused by its diffusion and trapping in the crystal.     

A Strategy for a Vanishing Cosmological Constant in the Presence of Scale Invariance Breaking

Recent work has shown that complex quantum field theory emerges as a statistical mechanical approximation to an underlying noncommutative operator dynamics based on a total trace action. In this dynamics, scale invariance of the trace action becomes the statement 0 = Re Tr T , with T the operator stress energy tensor, and with Tr the trace over the underlying Hilbert space. We show that this condition implies the vanishing of the cosmological constant and vacuum energy in the emergent quantum field theory. However, since the scale invariance condition does not require the operator T to vanish, the spontaneous breakdown of scale invariance is still permitted.     

Search for right-handed currents in muon decay

We report new limits on right-handed currents, based on precise measurements of the endpoint of the e⁺ spectrum from ⁺ decay. Highly polarized ⁺ from the TRIUMF surface beam were stopped in pure metal foils within either an 1.1-T spin-holding logitudinal field, or a 70-gauss spin-precessing transverse field. Decay e⁺ emitted within 200 mrad of the beam direction were momentum-analyzed to ±0.2%. For the spin-held data, decay via (V-A) currents requires the e⁺ rate to approach zero in the beam direction at the endpoint. Measurement of this rate sets the 90%-confidence limits P />0.9959 and M(W_R)>380 GeV, where W_R is the possible right-handed gauge boson. For the spin-precessed data we independently determine a 90% confidence limit P />0.9918.We are indebted to the entire TRIUMF management and staff for their splendid support of this experiment. In its early stages we benefited from discussion with J. Brewer, R. Cahn, K. Crowe, and W. Wenzel. Rapid commissioning of the polarimeter was made possible by the superb efforts of the LBL support staff. This research was supported in part by the U.S. Department of Energy, Division of Basic Energy Sciences, Office of Energy Research under contracts W-7405-ENG-48 and AC02-ER02289.     

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.     

μ + SR studies of UM2Al3, M=Ni,Pd

Positive-muon spin rotation ( ⁺ SR) measurements have been carried out in the new heavy-fermion superconductors UM₂Al₃, M=Ni and Pd. In UNi₂Al₃ the observed ⁺ frequencies in zero applied field indicate commensurate antiferromagnetic (AF) ordering of U moments 0.1 _B /U atom. These moments coexist with superconductivity and have the highest values observed in an AF heavy-fermion superconductor. The absence of well-defined frequencies in zero-field ⁺ SR in the AF state of UPd₂Al₃ suggests symmetric ⁺ stopping sites. In this system ⁺ SR linewidths belowT _c yield a preliminary value of 8000 Å for the London penetration depth.     

The spectrum of a quasiperiodic Schrödinger operator

The spectrum (H) of the tight binding Fibonacci Hamiltonian (H _mn= _m,n+1+ _m+1,n + _m,n v(n),v(n)= ((n–1)), 1/ is the golden number) is shown to coincide with the dynamical spectrum, the set on which an infinite subsequence of traces of transfer matrices is bounded. The point spectrum is absent for any , and (H) is a Cantor set for 4. Combining this with Casdagli's earlier result, one finds that the spectrum is singular continuous for 16.On leave from the Central Research Institute for Physics, Budapest, Hungary     

Formation of muonium and a muonic radical in fullerene

Three distinct electronic states were detected for positive muons (⁺) after implantation into a C₆₀ powder sample. About 40% of the ⁺ remained in the bare (diamagnetic) state, essentially an interstitial charged point particle. The rest of the muons were found to thermalize predominantly in two muonium (Mu=⁺ e^–) atomic species. A vacuum Mu state, with hyperfine coupling close to that of free Mu, most likely at the molecular center, and a muonic substituted radical, i.e. a hydrogen-like Mu addition to double bonds on the carbon rings. This opens up a rich subfield of fullerene spectroscopy using muons.     

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.     

Positivity of entropy production in nonequilibrium statistical mechanics

We analyze different mechanisms of entropy production in statistical mechanics, and propose formulas for the entropy production ratee() in a state . When is steady state describing the long term behavior of a system we show thate()0, and sometimes we can provee()>0.     

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.