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.     

Development of a beam of very slow polarized muons

During the last few decades, a variety of methods has been developed which makes use of polarized positive muons as a microscopic probe of the magnetic properties of condensed matter (muon spin rotation, relaxation, resonance,SR). Until now, available beams for SR studies have delivered 100% polarized muons with energies in the MeV range, resulting in a deep penetration of the muons into the sample material under investigation. This presently limits the applications of theSR technique to the study of the bulk characteristics of matter. To be able to control the implantation depth, a very low energy beam of polarized muons is being developed at the Paul Scherrer Institute. Very slow polarized muons (kinetic energy 10 eV, polarization 90%) are obtained from the moderation of a high energy muon beam in a thin film of an appropriate condensed gas. These muons can be used as a source for a beam of tunable energy between a few tens of eV and some tens of keV. Implantation depths in the range of few to a few hundreds of nanometers can thus be achieved by varying the energy.     

Molecular-orbital X-rays from 1 GeV 208Pb + 208Pb and 209Bi + 209Bi collisions

We have measured the spectra of continuum X-rays above the characteristic K lines for 4.5 to 4.8 MeV/N ²⁰⁸₈₂Pb → ²⁰⁸₈₂Pb, Pb → Bi, Bi → Pb and Bi → Bi collisions. Above ≈400 keV X-ray energy the spectral shape and intensity agree roughly with calculations of Kirsch et al. for the 1sσ molecular-orbital (MO) X-ray spectrum from Pb-Pb. Deviations from the theory below ≈400 keV suggest transitions to other MO's.     

Change-of-variance sensitivities in regression analysis

Summary The change-of-variance function is defined for estimators of regression coefficients. Both an unstandardized and a standardized form of the change-of-variance sensitivity are introduced, and their relation with the corresponding gross-error-sensitivities is investigated. The problems of optimal robustness lead to the Hampel-Krasker and the Krasker-Welsch estimators. At the same time, also the scale parameter has to be estimated robustly. By means of the change-of-variance sensitivity, optimal robust redescending scale estimators are constructed.     

Muon Spin Rotation and Relaxation Experiments on Thin Films

The recent development at the Paul Scherrer Institute of a beam of low energy muons allows depth dependent muon spin rotation and relaxation investigations in thin samples, multilayers and near surface regions (low energy SR, LE-SR). After a brief overview of the LE-SR method, some representative experiments performed with this technique will be presented. The first direct determination of the field profile just below the surface of a high-temperature superconductor in the Meissner phase illustrates the power and sensitivity of low energy muons as near-surface probe and is an example of general application to depth profiling of magnetic fields. The evolution of the flux line lattice distribution across the surface of a YBa₂Cu₃O₇ film in the vortex phase has been investigated by implanting muons on both sides of a normal-superconducting boundary. A determination of the relaxation time and energy barrier to thermal activation in iron nanoclusters, embedded in a silver thin film matrix (500nm), demonstrates the use of slow muons to measure the properties of samples that cannot be made thick enough for the use of conventional SR. Other experiments investigated the magnetic properties of thin Cr(001) layers at thicknesses above and below the collapse of the spin density wave.     

Robust and accurate inference for generalized linear models

In the framework of generalized linear models, the nonrobustness of classical estimators and tests for the parameters is a well known problem, and alternative methods have been proposed in the literature. These methods are robust and can cope with deviations from the assumed distribution. However, they are based on first order asymptotic theory, and their accuracy in moderate to small samples is still an open question. In this paper, we propose a test statistic which combines robustness and good accuracy for moderate to small sample sizes. We combine results from Cantoni and Ronchetti [E. Cantoni, E. Ronchetti, Robust inference for generalized linear models, Journal of the American Statistical Association 96 (2001) 1022–1030] and Robinson, Ronchetti and Young [J. Robinson, E. Ronchetti, G.A. Young, Saddlepoint approximations and tests based on multivariate M-estimators, The Annals of Statistics 31 (2003) 1154–1169] to obtain a robust test statistic for hypothesis testing and variable selection, which is asymptotically χ²-distributed as the three classical tests but with a relative error of order O(n⁻¹). This leads to reliable inference in the presence of small deviations from the assumed model distribution, and to accurate testing and variable selection, even in moderate to small samples.     

Generation of very slow polarized muons by moderation

At the Paul Scherrer Institute very slow, nearly 100% polarized, positive muons with an energy of \sim\mbox10 eV are produced by moderating a secondary beam of surface muons in a thin film of an appropriate condensed gases. These epithermal muons can be used as a source of a tertiary beam of tunable energy between \sim\mbox10 eV and \sim\mbox20 keV. Such a beam allows the μSR technique to be extended to the study of thin films and surfaces. In order to be able to perform time differential μSR experiments we have developed an ultra‐thin detector that registers the passage of keV muons and permits to trigger the experiment. The results achieved so far demonstrate that first investigations of thin film samples can be performed with the present set‐up. This revised version was published online in August 2006 with corrections to the Cover Date.     

Formation of hydrogen impurity States in silicon and insulators at low implantation energies

The formation of hydrogenlike muonium (Mu) has been studied as a function of implantation energy in intrinsic Si, thin films of condensed van der Waals gases (N2, Ne, Ar, Xe), fused and crystalline quartz, and sapphire. By varying the initial energy of positive muons (mu+) between 1 and 30 keV the number of electron-hole pairs generated in the ionization track of the mu+ can be tuned between a few and several thousand. The results show the strong suppression of the formation of those Mu states that depend on the availability of excess electrons. This indicates that the role of H-impurity states in determining electric properties of semiconductors and insulators depends on the way in which atomic H is introduced into the material.