Why does precession occur in Muon Spectroscopy?

[Christopher Small]

I've been doing some research on Muon spectroscopy, and am not that far in the physics world yet. I've got kind of a fuzzy picture of what goes on, but could use some help in identifying some key concepts. The information I have been getting is from the following paper


Muon-Spin Rotation Studies of Electronic Properties of Molecular Conductors and Superconductors

Stephen J. Blundell

Department of Physics, Oxford University, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom

Received March 16, 2004




which I received from the American Chemical Society Data Base


What I have found thus far is that 100% polarized muons can be fired at a sample under study, and that the magnetic environment at the time of muon decay can have an effect on the emittance of positrons. Of prime importance to the theory of this form of study is the

propensity for the emitted positron to emerge predominantly along the direction of the muon spin when it decayed... the muon enters the sample with its spin pointing along the direction from which it came. If the muon is unlucky enough to decay immediately, then it will not have time to precess and a positron will be emitted preferentially into the backward detector. If the muon lives a little longer, it will have time to precess; therefore, for example, if it lives for half a revolution, the resultant positron will be preferentially emitted into the forward detector. Thus, the positron beam from an ensemble of precessing muons can be likened to the beam of light from a lighthouse.

Now my understanding is that since the muon has negative helicity, the spin axis points antiparallel to the direction of motion. Why does precession occur? Can anyone help clairify this or suggest a good resource?



Thanks

 

[ZapperZ]

Now my understanding is that since the muon has negative helicity, the spin axis points antiparallel to the direction of motion. Why does precession occur? Can anyone help clairify this or suggest a good resource?



Thanks

The precession occurs because the muon spin is not along the direction of the external magnetic field that the muon is in. This is why, if the muon decays too quickly to "sample" the surrounding field, it will not have time to precess.

However, in most cases, the muon lifetime is long enough (some people think it is too long and that's why neutron scattering is used in the study of many other materials) that the muon spectrum in a typical muSR spectroscopy will provide more of an "average" information of the magnetic orientation of the material being studied.

Zz.

 

[sir-pinski]

for your question. Precession occurs in Muon Spectroscopy because muons have an intrinsic magnetic moment, similar to that of a tiny bar magnet. When a muon enters a magnetic field, its magnetic moment will align itself with the field, causing it to precess or rotate around the direction of the field. This precession is similar to the way a spinning top precesses when it is tilted.

In the case of Muon Spectroscopy, the muon is fired at a sample and its magnetic moment aligns itself with the magnetic environment of the sample. As the muon decays, its spin direction affects the direction in which the emitted positron is preferentially detected. This is because the positron is emitted along the direction of the muon's spin at the time of decay.

To understand why precession occurs, it is helpful to think about the quantum mechanical nature of the muon. In quantum mechanics, particles can have both a spin and angular momentum, which are related to each other. When a muon enters a magnetic field, its spin and angular momentum will align with the field, causing it to precess. This precession is a result of the quantum mechanical properties of the muon and its interaction with the magnetic field.

I hope this helps clarify the concept of precession in Muon Spectroscopy. A good resource for further understanding would be a textbook on quantum mechanics or particle physics.