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We show that in the plane-wave impulse approximation an incident proton cannot, in the case of elastic forward (q =0) scattering, change the polarization state (J,M) of a J =1 target nucleus from (1, +1) to (1, -1), where the direction of polarization is normal to the scattering plane. We then show that this double spin-flip process can take place when the effects of double scattering are taken into account. As a corollary, the spin-quadrupole moment of the deuteron must be zero.