ABSTRACT
May we briefly outline the philosophy of the muon method. The basis is nonconservation of parity in weak interactions. It is known that unstable lepton — positive muon decays by scheme: ¡i+ —> e+ + ve -f v^. The average life of the muon is TM « 2.2 x 10~6s. As shown in the theory of weak interactions, for the muon at rest the angular distribution of decay positrons of the specified energy is characterized by the following form:
(4.1)
Herein F — total probability of decay. The polar axis is chosen along the muon spin direction; 6 — angle between positron impulse and muon spin direction, and, finally, e = Ee+/Emax — normalized positron energy (Emax « 53 MeV). The scheme and
decay pattern are given in Figure 4.1a. It is clear from the above-stated that, if sufficient statistics are gathered, then it is possible to determine the muon polarization P = (a). Distributing events over short decay time intervals (£¿,í¿+i), which are named as temporal channels, it is possible to obtain histogram that describes functional dependence P{t). The measurement accuracy is mainly determined by the collection of statistics. So, the principal scheme of the muon method is extremely simple. An ensemble of muons with polarization P(0) is provided in a target, and further its temporal dependence P( t ) is studied. The orthodox scheme is as follows. Time (to = 0) when muon comes to the target is registered, and a 'dock' is actuated. Further, counters ('positron telescope') registers a time ¿i of the decay. Within interval AT = t\ - to only one muon is in the target (if more than one muon are in the target the event is rejected). After the statistics are gathered (usually 106108 decays) a histogram that determines P(t) is constructed. So, in the classical scheme, the muon ensemble is formed as a result of gathering a large number of measurements on single quantum objects. It is clear that the behaviour of (cr(t)} is completely determined by the local magnetic field on muon which is generated by both external and internal fields in a substance. Since muon can stop at any point of a sample the experiment provides an averaged pattern over the whole target. It should be also noted that initial polarization P(0) does not virtually change in the time of muon thermalization: ¿therm ~ 10~10 s. Actually, an angular frequency of muon spin precession is u » 0.85 x 105B s_ 1 , and, therefore, in field B ~ 15 kG the turning angle in a time of ¿therm is <¿> = tctftherm < 0.04 radian. Beams of polarized muons are generated in proton accelerators. The proton beam comes to a meson forming target where positive and negative pions of 2.6 x 10"8 s life are produced. Magnetic lenses separate beam 7r+ during the decay of which polarized / i + are formed. The decay scheme is given in Figure 4.1a, b. Further, the muon beam is directed to the target. The muon impulse is pM « 102 MeV/s for standard schemes. The free path of such muons in a substance is / % 10 g/cm2 (which is
about 1 cm for copper), and therefore, such beams are usually retarded by filters (of graphite, frequently) prior to getting to the target. In another option, muons from 7r+ 'caught' on the meson forming target surface are separated into a muon beam. They are characterized by relatively moderate impulse pM « 29.8 MeV/s. Their free path is about 0.15 g/cm2 (for copper it corresponds to / « 0.017 cm). So, characteristic thicknesses of metallic targets vary from 10~2 to 0.3-0.5 cm.
