Surface muons

Muonium (Mu) is the lightest hydrogen-like atom (mMu = 0.11 mH) available for chemical research it has a positive muon (/jl+, t = 2.2 fisec) as the nucleus. The muon spin resonance (/tSR) technique is described in several review articles (16, 99—102). Most of the research is performed in the condensed phases, but because of the development of the surface muon beams (103, 104), experiments in the gaseous phase have received more attention. At present three muonic fractions can be detected (1) fan, free muonium (2) fa, free n+, or Mu bound in a diamagnetic compound and (3) fa, Mu bound in a paramagnetic compound. In liquid phases, there is quite often a missing fraction, fa = 1 -fau - fa - fa ... 

K. Assamagan, C. Bronnimann, M. Daum, H. Forrer, R. Frosch, P. Gheno, R. Horisberger, M. Janousch, P. Kettle, T. Spirig, C. Wigger, Upper limit of the muon-neutrino mass and charged-pion mass from momentum analysis of a surface muon beam, Phys. Rev. D 53 (1996) 6065-6077. 

Picture of apparatus showing four e" counter telescopes. The target vessel is often a cryostat for low temperature studies. The counters shown are set up for "surface muons" and have holes in the forward pair to allow the incident beam to enter. 

Pion decay is mediated by the weak interaction and firll parity violation comes into play. In particular, the neutrino (here v ) always has left-handed chiral symmetry, meaning that its spin Sv (being h/2 like that of the muon) is oriented in the opposite direction to its linear momentum (pv)- The pion has spin zero. Conservation of momentum in its decay (eq. 2) requires that the neutrino (v ) and the muon (p,+) are ejected 180 apart in the rest frame of the pion. Since the orientation of is fixed to (Sy "T J. / v), the same must hold for the muon ( n i p - We thus get perfectly spin polarized muons with their spin directed opposite to their line of flight. The situation is illustrated in fig. 2. Under certain circumstances (to be discussed in the next section) the pion rest frame is identical with the laboratory fi-ame ( surface muon beam). The linear momentum given to the muon firom pion decay at rest is 29.8 MeV/c which corresponds to a kinetic energy of 4.1 MeV... 

Fig. 4. Raw muon spin rotation spectrum (analogue plot) observed out to very late times on a pulsed muon beam (RAL-BIS). Note the logarithmic vertical scale. Surface muons are stopped in pure Ag. Also visible is the distortion at early times due to the finite muon pulse width. (The data shown were taken at the time of commissioning the facility. Meanwhile, pulse structure has been improved and the time span over which...

We mentioned the MORE apparatus which offers some of the features of pulsed beam data collection for continuous beams. The acronym MORE stands for Muons On REquest. Its basic feature is a fast-switching electrostatic beam deflector (for surface muons only) which extracts one muon out of the beam and sends it towards a pSR spectrometer. After 10T i the system is ready for the next muon to be extracted. This ensrues that at any time only one muon is in the sample and the muon gate circuitry is not needed. Time resolution is not blurred by a finite pulse width when compared to a pulsed beam, but count rates are lower. The system runs parasitically on a beam line which delivers sruface muons to a conventional spectrometer when the beam deflector is off (which is most of the time). 

Collimation of the beam hardly works beyond a reduction of 50% in illuminated area, The collimator must be placed some distance in front of the sample to avoid that forward or backward detectors pick up positrons stemming from muons stopped in the collimator, The divergence of the muon beam and especially scattering of muons by the collimator and also in the start counter, the cryostat windows etc. break up the collimated beam again in the case of surface muons. 

The so called surface muon beams, where the beam energies are ca 4 MeV, are almost 100 % spin polarized. If the fractional populations of the Zeeman energy levels shown in Figure 7.3 are indicated by and +, at the time of implantation into the sample these populations are either = 1 and + = 0 or =0 and n+ = 1, depending on the direction of the longitudinal magnetic field with respect to the muon spin direction. The net polarization ... 

Two types of positive muon beams are possible (1) surface muons, arising from pions decaying at rest close to the surface of the production target, with a momentum of 28 MeV/c and a stopping range of 140 mg cm 2 (corresponding to a water layer 1.4 mm... 

---