Basic Muon Properties
Follow this link for a very brief summary of the muon's properties
such as charge, spin, mass etc. The figure also shows
abbreviated cartoons of the reactions in which muons
are created and destroyed, described in more detail below.
If you want some really detailed and authoritative
information about the properties of the muon, go visit the
of the Particle Data Group,
where you can find essentially everything that is known about
Muons are produced in various high energy processes and
elementary particle decays such as
but µSR requires low energy muons in order to stop the beam
in samples of convenient thickness, and these are available
in the required intensities only from the ordinary two-body
decay of charged
from which the muon emerges (in the rest frame of the pion)
with a momentumof 29.79 MeV/c and a kinetic energy of 4.119 MeV.
The lifetime of a free charged pion is 26.03 ns.
The most remarkable feature of
positive pion decay
is that it maximally violates Parity symmetry,
causing the µ+ to be emitted
with perfect spin polarization.
This is the greatest advantage of µSR as a magnetic resonance
technique: whereas NMR and ESR rely upon a
thermal equilibrium spin polarization,
usually achieved at low temperatures in strong magnetic fields,
begins with a perfectly polarized probe, regardless of conditions
in the medium to be studied. It also implies that muon spin degrees of
freedom usually start their evolution as far from thermal equilibrium as
Most µ+ beams
today are literally emitted from
positive pion decay at rest in the surface layer of the primary target where
the pions themselves are produced by collisions of high energy protons
with target nuclei -- hence the common mnemonic name,
The propensity of the muon decay positron to be emitted along
the spin of the µ+ is another consequence of
P-violation in the weak interaction
which allows us to read out the information encoded in the evolution
of an initially polarized muon spin ensemble.
The information is delivered to the experimenter
in the form of rather high energy (up to 52 MeV) positrons
which readily penetrate sample holders, cryostats or ovens
and the detectors used to establish the time and direction of the muon
The decay probability of the muon depends
as shown here
upon the fraction x of the maximum possible
total relativistic e+ energy
of 52.83 MeV and the angle between the muon spin direction
and the direction of e+ emission.
The asymmetry factor a increases monotonically with
the e+ energy and is 100% for the maximum energy.
Note that a changes sign at low energy;
however, very few positrons are emitted with such low energies (see above)
and those which are will usually not be detected.
In any real experiment, some of the lower energy positrons
do not penetrate intervening material to trigger the detectors,
or are ``curled up'' by applied magnetic fields, so that the
efficiency f(x) for detecting positrons is energy dependent,
forcing an integration over E(x) a(x)
f(x) dx to obtain the average asymmetry.
This, combined with the finite solid angle of any real detectors,
renders the experimental maximum asymmetry Ao
an empirical parameter to be determined by measurement on a
sample known not to produce any muon depolarization
but otherwise identical in every respect to that under
investigation. Obviously, this calibration can never be perfect;
in general one should not believe any absolute calibration
of Ao to better than about 5% of itself.
It is perhaps unfortunate that a is traditionally known as the
``asymmetry'' (rather than perhaps the ``anisotropy'')
since this term does not connote polarization (of a spin ensemble)
to most people in the magnetic resonance community. However, at this
point we are stuck with the term, much as we are stuck with the
technical misnomer ``muonium.''
Jess H. Brewer
Last modified: Tue Sep 30 15:09:39 PDT 2003