Magnitude and Direction of $B_0$

This measurement of the polarization also provides ``free'' information about the magnitude and direction of the holding field.

As seen in Fig. 1, the magnitude of $B_0$ can be extracted from the frequency about which the EPR transitions occur. This has proven to be an incredibly precise measurement of the magnetic field in the location of the EPR measurement. For E02-013, this effectively means we very nearly measured the magnetic field about once a day.

Direction of the field, or the $^3$He spins, cannot be determined directly from these data. However, once the magnetic field direction is known, it is a simple matter to determine if the spins are aligned or anti-aligned with the holding field.

In the case of a frequency shift above the holding field shift (``well'' state, pictured in Fig. 1), the effective field seen by the alkali metal is the holding field plus the classical field of the polarized gas. For the ``hat state'' (not pictured), the field subtracts.

Recall that the magnetic moment for $^3$He is negative. This means that if the field is adding, then the spins are pointed opposite the magnetic field. Table 2.2 should clear this up.

Table 1: The States of the Spins. The alignment of the spins with the magnetic field can be determined from the shape of the EPR signal

State	Flip?	Spins
Hat	Flipped	Aligned
Well	Not Flipped	Anti-Aligned

The notation of +0 or +180 will be added to the run conditions spreadsheet and uploaded to the Wiki when I can get on the Wiki again.