Abstract
Abstract 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.
Highlights
Neutron spin echo (NSE) and helium spin echo (HSE) are two beam techniques with exceptionally high energy resolution which have revolutionized the ability to study atomic scale bulk and surface dynamics [1,2]
To inhomogeneous broadening in NMR [10], this effect can be reversed and the macroscopic magnetization can be recovered if the second magnetic field, B2, produces a net phase change which exactly cancels out the spread of spin phases which existed before the particles entered the second field
We have shown in this paper that the fundamental mechanism, controlling the echo phenomenon in beam spin echo setups with nonadiabatic transitions, splits into two channels of constructive interference between the spin-phases accumulated during the beam propagation in the two-coil arms
Summary
Neutron spin echo (NSE) and helium spin echo (HSE) are two beam techniques with exceptionally high energy resolution which have revolutionized the ability to study atomic scale bulk and surface dynamics [1,2]. The internal nuclear state vector at a given time in each arm along its classical path, is expanded in the complete orthonormal set of eigenvectors of the spin Hamiltonian under a magnetic field oriented along the beam axis (see Fig.1 upper plot).
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