Confirmation of some formulas related to spin coherence time

Abstract

This paper considers two sets of formulas related to a Spin Coherence Time (SCT) case with only vertical oscillations in a purely electric ring, the first derived by the author for the field index m > 0 and the second by Ivan Koop for the field index m = 0. I argue that a continuous transition can exist from one set to the other (contrary to appearances), and assume that a necessary condition for the transition is that both sets of formulas follow from the same equation. I demonstrate that they do follow when one takes into account that the first set of formulas holds only for times much larger than the period of the vertical oscillations. This demonstration confirms the correctness of the formulas and the equation.