Tidal symmetry in nuclear reactions: application to the scattering of polarised projectiles

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Abstract
A partial diagonalisation of a coupled-channels system is obtained for arbitrary momentum-independent interactions and excitation energies when the angular momentum dependence of the centrifugal barrier is treated approximately. This is a consequence of the 'tidal symmetry' of the interaction, that is, the invariance of the interaction with respect to rotations of the interacting particles about their relative coordinate. Closed expressions are found for the transition amplitudes of the full coupled-channels system as a function of those of a reduced coupled-channels calculation involving only spin-zero states. In particular it is found for elastic scattering that the projection of the spin along the recoil direction is conserved. A consequence of this is that the tensor analysing powers obey the shape effect model relations in a strong-coupling non-adiabatic situation. The consequences for inelastic scattering are also discussed.