Details of a spin-polarized surface state on W(110) with a Dirac-cone-like dispersion are revealed by calculations of the spin- and layer-resolved density of states. After collisions of spin-polarized low-energy electrons, which impinge on the surface, with the surface-state electrons, correlated electron pairs are emitted, which have either parallel or antiparallel spins. Calculations of the corresponding reaction cross sections demonstrate, first, a spin-resolved mapping of the surface-state dispersion with surface-parallel momentum. Second, momentum distributions of the outgoing electron pairs with parallel and antiparallel spins allow a separation of Coulomb correlation and exchange effects.