  We show that the interplay between spin-orbit coupling and Zeeman splitting
in atomic systems can lead to the existence of bound states in the continuum
(BICs) supported by trapping potentials. Such states have energies falling well
within the continuum spectrum, but nevertheless they are localized and fully
radiationless. We report the existence of BICs, in some cases in exact
analytical form, in systems with tunable spin-orbit coupling and show that the
phenomenon is physically robust. We also found that BIC states may be excited
in spin-orbit-coupled Bose-Einstein condensates, where under suitable
conditions they may be metastable with remarkably long lifetimes.
