Parallel and anti-parallel echoes in beam spin echo experiments - I. Litvin (Results in Physics, 2019)
The refocusing of velocity-dependent spin-phase is the basic phenomenon behind helium and neutron spin echo beam experiments. In this paper we present quantum and classical descriptions of the spin echo phenomenon and show that non-adiabatic transitions, such as those which take place during rotation of the magnetic field axis between the two arms of a helium spin echo setup, lead to echo conditions without reversing the magnetic field orientation between the two arms. The usual spin echo conditions, created by reversing the magnetic field orientation, do not require such non-adiabatic transitions. These two echo conditions are termed parallel and anti-parallel spin echoes, respectively. We derive the dependence of the relative intensity of the two echoes on the scattering geometry of the setup and show experimental results which verify the co-existence of the two echo conditions, the theoretically derived expressions for their relative intensity and the effect of an additional spin rotator coil introduced within the non-adiabatic transition region.