An annihilator is a nonzero density distribution that produces no external field for a particular source geometry. the annihilator describes quantitatively the non-uniqueness of potential field data because any amount of the annihilator can be added to a possible solution without affecting the field of the source. find a simple annihilator (rho) for a spherical mass of radius (a) as viewed from outside the sphere. let rho represent density contrast so that rho can reach negative values.