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...") |
m |
||
| Line 2: | Line 2: | ||
---- |
---- |
||
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 |
||
<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> |
||
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>) |
||
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.) |
||
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. |
|||
Revision as of 15:10, 15 September 2022
Relaxonomy --> here
When the muon spin polarization [math]\displaystyle{ \vec{P} }[/math] is initially in the same direction as the applied magnetic field [math]\displaystyle{ \vec{B} }[/math], we call that the [math]\displaystyle{ z }[/math] direction. This is called the longitudinal field (LF) geometry. The relaxation of [math]\displaystyle{ \vec{P} }[/math] is then usually described by
where the lower case [math]\displaystyle{ g }[/math] is used (instead of the more general [math]\displaystyle{ G }[/math]) to designate a static relaxation function, just like in ZF. (Dynamic cases will be treated later.)
In the limit where [math]\displaystyle{ 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]\displaystyle{ \sim }[/math] RLMF) it is subject to the same caveats as the ZF case, which see.
