Intense positron sources from pair production of high energy prompt &ggr;‐rays from neutron capture reactions are described. A titanium‐platinum target placed in a thermal neutron flux of 3.3×1014n/cm2s was used in conjunction with the BILL beta spectrometer as a high intensity, monochromatic and tunable positron source. The system yielded a 2.5×106e+/s in 10cm of the focal plane with a momentum dispersion of &Dgr;p/p=1.5×10−3per cm. It was applied for the search for neutral resonances superimposed on the excitation function of elastice+e−(Bhabha) scattering. These resonances had been proposed as an explanation of the GSI positron lines from heavy ion reactions. No such resonances were found and very stringent limits were set for their intrinsic lifetimes. In addition, the possibility of constructing a very intense source of moderated positrons based on the same principle is discussed.