In fact, MM  was based on Kunstatter's study , in which the adiabatic invariant quantity ([I.sub.adb]) is expressed as follows:
Subsequently, using the adiabatic invariant quantity (3) and Bohr-Sommerfeld quantization rule,
The projection of the neutron magnetic moment on the magnetic field direction is an adiabatic invariant
. For fields of the order of tesla, depolarization is negligible, [10.sup.-25] in [10.sup.4] s.
The basic adiabaticity requirement is that the rate of a change of the field direction, has to be smaller compared to the Larmor frequency [omega] = [mu]B/h ([mu] is the magnetic moment of the neutron) then the projection of the spin on the field direction is approximately conserved; the projection of the neutron spin on the field direction is an adiabatic invariant
. In the design of the abBA experiment we will have a field configuration of B = [B.sub.0]x + [[dB]/[dz]]vtz where the x-axis is the axis of the spectrometer magnet and the z-axis is the beam axis, in two situations.
The code will be made faster by using the adiabatic invariants
for charged particle tracking in the electromagnetic field, which will markedly improve the uncertainties of our method.
Several simulation methods were used including commercial software (Simion), custom software, as well as analytical tools based on the use of adiabatic invariants
. Our results indicate that the proposed field geometry of the abBA spectrometer will be substantially immune to most systematic effects and that transport calculations using adiabatic invariants
agree well with solution of the full equations of motion.