  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.
