Variational calculations are pet-formed to search for bound rovibrational s
tates of diatomic molecules formed from alkali atoms and helium in the very
shallow (2)Sigma electronic ground state. Examination of a recent set of p
otential surfaces and several older potentials indicates that all pairs pos
sess a single very diffuse bound state with J = 0. Such marginally bound st
ates will have profound effects on low energy collisions between alkali ato
ms and helium atoms. The sensitivity of these states with respect to retard
ation effects has been studied. The variational calculations employ a basis
set of generalized Laguerre functions and new analytical expressions for k
inetic energy matrix elements.