We study the single-spin asymmetry, $A_N(t)$, arising from Coulomb-nuclear interference (CNI) at small 4-momentum transfer squared, $-t=q^2$, aiming at explanation of the recent data from the PHENIX experiment at RHIC on polarized proton-nucleus scattering, exposing a nontrivial $t$-dependence of $A_N$. We found that the failure of previous theoretical attempts to explain these data, was due to lack of absorptive corrections in the Coulomb amplitude of $pA$ elastic scattering. Our prominent observation is that the main contribution to $A_N(t)$ comes from interference of the amplitudes of ultra-peripheral and central collisions.
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