text: The decay of the positive muon into a positron and two neutrinos occurs via the weak interaction process after a mean lifetime of
  τ = 2.197034(21) μs:
  Parity violation in the weak interaction leads in this more complicated case (three body decay) to an anisotropic distribution of the positron emission with respect to the spin direction of the μ at the decay time. The positron emission probability is given by
  where  is the angle between the positron trajectory and the μ-spin, and  is an intrinsic asymmetry parameter determined by the weak decay mechanism. This anisotropic emission constitutes in fact the basics for the μSR technique.
  The average asymmetry  is measured over a statistical ensemble of implanted muons and it depends on further experimental parameters, such as the beam spin polarization , close to one, as already mentioned. Theoretically  =1/3 is obtained if all emitted positrons are detected with the same efficiency, irrespective of their energy. Practically, values of  ≈ 0.25 are routinely obtained.
  The muon spin motion may be measured over a time scale dictated by the muon decay, i.e. a few times τ, roughly 10 µs. The asymmetry in the muon decay correlates the positron emission and the muon spin directions. The simplest example is when the spin direction of all muons remains constant in time after implantation (no motion). In this case the asymmetry shows up as an imbalance between the positron counts in two equivalent detectors placed in front and behind the sample, along the beam axis. Each of them records an exponentially decaying rate as a function of the time t elapsed from implantation, according to
  with  for the detector looking towards and away from the spin arrow, respectively. Considering that the huge muon spin polarization is completely outside thermal equilibrium, a dynamical relaxation towards the equilibrium unpolarized state typically shows up in the count rate, as an additional decay factor in front of the experimental asymmetry parameter, A. A magnetic field parallel to the initial muon spin direction probes the dynamical relaxation rate as a function of the additional muon Zeeman energy, without introducing additional coherent spin dynamics. This experimental arrangement is called Longitudinal Field (LF) μSR.
  A special case of LF μSR is Zero Field (ZF) μSR, when the external magnetic field is zero. This experimental condition is particularly important since it allows to probe any internal quasi-static (i.e. static on the muon time-scale) magnetic field of field distribution at the muon site. Internal quasi-static fields may appear spontaneously, not induced by the magnetic response of the sample to an external field They are produced by disordered nuclear magnetic moments or, more importantly, by ordered electron magnetic moments and orbital currents.
  Another simple type of μSR experiment is when implanted all muon spins precess coherently around the external magnetic field of modulus , perpendicular to the beam axis, causing the count unbalance to oscillate at the corresponding Larmor frequency  between the same two detectors, according to
  Since the Larmor frequency is , with a gyromagnetic ratio  Mrad(sT), the frequency spectrum obtained by means of this experimental arrangement provides a direct measure of the internal magnetic field intensity distribution. The distribution produces an additional decay factor of the experimental asymmetry A. This method is usually referred to as Transverse Field (TF) μSR.
  A more general case is when the initial muon spin direction (coinciding with the detector axis) forms an angle  with the field direction. In this case the muon spin precession describes a cone which results in both a longitudinal component, , and a transverse precessing component,  , of the total asymmetry. ZF μSR  experiments in the presence of a spontaneous internal field fall into this category as well.