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Potential for measurement of the tensor electric and magnetic polarizabilities of the deuteron in storage-ring experiments with polarized beams

Measurement of the tensor electric and magnetic polarizabilities of the deuteron is of great interest, especially in connection with the possibilities of COSY and GSI. These polarizabilities can be measured in storage rings by the frozen spin method providing a disappearance of g-2 precession. This method will be used in the planned deuteron electric-dipole-moment experiment in storage rings. The tensor electric polarizability of the deuteron significantly influences the buildup of the vertical polarization in the above experiment. The spin interactions depending on the electric dipole moment, the tensor electric polarizability, and main systematical errors caused by field misalignments have very different symmetries. For the considered experimental conditions, the sensitivity to the deuteron EDM of $1\times10^{-29} e\cdot$cm corresponds to measuring the both of tensor polarizabilities with an accuracy of $δα_T\approxδβ_T\approx5\times10^{-42}$ cm$^3$. This conservative estimate can be improved by excluding the systematical error caused by the field instability which is negligible for the measurement of the tensor polarizabilities. To find the tensor magnetic polarizability, the horizontal components of the polarization vector should be measured.