Difference between revisions of "Dynamic Relaxation"
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Therefore it behooves us to model the resultant relaxation functions. |
Therefore it behooves us to model the resultant relaxation functions. |
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The simplest cases are when either the muon '''hops''' between sites with different ''static'' magnetic fields and/or the muon is at a fixed site with a randomly '''fluctuating''' local magnetic field. In either case we usually assume that the field at each hop or after each fluctuation is selected ''randomly'' from an easily modeled distribution <math>\cal{D}(\vec{B})</math> -- ''e.g.'' a Gaussian distribution of field ''magnitudes'', <math>\cal{D}(|B|) |
The simplest cases are when either the muon '''hops''' between sites with different ''static'' magnetic fields and/or the muon is at a fixed site with a randomly '''fluctuating''' local magnetic field. In either case we usually assume that the field at each hop or after each fluctuation is selected ''randomly'' from an easily modeled distribution <math>\cal{D}(\vec{B})</math> -- ''e.g.'' a Gaussian distribution of field ''magnitudes'', <math>\cal{D}(|B|) = {1 \over \sqrt{2\pi} \Delta} \exp\left[- {1\over2} \left(B-B_0 \over \Delta \right)^2\right] </math>, with a direction randomly selected from an isotropic distribution. |
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Revision as of 12:59, 13 September 2022
So far we have treated only the behavior of the muon polarization at fixed locations where the local magnetic fields are static. This is often not the case, and situations in which the muons are hopping between different sites and/or the local fields at those sites are fluctuating comprise many of the most interesting µSR studies.
Therefore it behooves us to model the resultant relaxation functions.
The simplest cases are when either the muon hops between sites with different static magnetic fields and/or the muon is at a fixed site with a randomly fluctuating local magnetic field. In either case we usually assume that the field at each hop or after each fluctuation is selected randomly from an easily modeled distribution [math]\displaystyle{ \cal{D}(\vec{B}) }[/math] -- e.g. a Gaussian distribution of field magnitudes, [math]\displaystyle{ \cal{D}(|B|) = {1 \over \sqrt{2\pi} \Delta} \exp\left[- {1\over2} \left(B-B_0 \over \Delta \right)^2\right] }[/math], with a direction randomly selected from an isotropic distribution.
