Simple yet accurate approximate formulae for the physically interesting complex eigenvalues for a delta function well plus linear potential are presented, and their results compared with numerical results accurate to twelve significant figures. By a semiclassical analysis the authors suggest and confirm the correct physical interpretation of states above the top of the well, and show that contrary to widely held views, in certain potentials with isolated real singular points the higher states have a longer lifetime than lower ones. The position probability density and the phase of the wavefunction are graphically displayed, as are numerical results for dimensionless electric field intensities from 10^-12 to beyond 10¹⁹².