Difference between revisions of "Static Longitudinal Field Relaxation"
(Created page with "Relaxonomy --> here ---- When the muon spin polarization <math>\vec{P}</math> is initially in the same direction as the applied magnetic field <math>\vec{B}</math>, we ca...") |
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When the muon spin polarization <math>\vec{P}</math> is initially in the same direction as the applied magnetic field <math>\vec{B}</math>, we call that the <math>z</math> direction. This is called the '''''longitudinal field''''' ('''LF''') geometry. The relaxation of <math>\vec{P}</math> is then described by |
When the muon spin polarization <math>\vec{P}</math> is initially in the same direction as the applied magnetic field <math>\vec{B}</math>, we call that the <math>z</math> direction. This is called the '''''longitudinal field''''' ('''LF''') geometry. The relaxation of <math>\vec{P}</math> is then usually described by |
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<center><math> g_{zz}(t) \; \equiv \; \langle P_z(0) \, P_z(t) \rangle </math></center> |
<center><math> g_{zz}(t) \; \equiv \; \langle P_z(0) \, P_z(t) \rangle </math></center> |
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where the lower case <math>g</math> is used (instead of the more general <math>G</math>) |
where the lower case <math>g</math> is used (instead of the more general <math>G</math>) |
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to designate a '''''static''''' relaxation function. ('''''Dynamic''''' cases will be treated later.) |
to designate a '''''static''''' relaxation function, just like in '''ZF'''. ('''''Dynamic''''' cases will be treated later.) |
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In the limit where <math>B \gg </math> any random local magnetic fields ('''RLMF'''), this formulation is valid. (At last, a "low-bogosity" case!) However, in modest applied fields (<i>B</i> <math> \sim </math> RLMF) it is subject to the same ''caveats'' as the '''ZF''' case, which see. |
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Revision as of 14:10, 15 September 2022
Relaxonomy --> here
When the muon spin polarization <math>\vec{P}</math> is initially in the same direction as the applied magnetic field <math>\vec{B}</math>, we call that the <math>z</math> direction. This is called the longitudinal field (LF) geometry. The relaxation of <math>\vec{P}</math> is then usually described by
where the lower case <math>g</math> is used (instead of the more general <math>G</math>) to designate a static relaxation function, just like in ZF. (Dynamic cases will be treated later.)
In the limit where <math>B \gg </math> any random local magnetic fields (RLMF), this formulation is valid. (At last, a "low-bogosity" case!) However, in modest applied fields (B <math> \sim </math> RLMF) it is subject to the same caveats as the ZF case, which see.
