1. An apparatus that provides an absolute nuclear material assay of an unknown source that emits neutrons, comprising: a multigate neutron multiplicity counter detecting neutrons emitted from the source and grouped with respect to time, and collecting a number of neutrons within a defined time window to derive neutron multiplet count data, the multigate counter further measuring the multiplet count in a measurement as a function of lifetime and neutron number; a processor of a plurality of processors coupled to the multiplicity counter and executing code to iteratively solve a plurality of coupled algebraic equations for five unknown parameters of the source using the first three moments of a fission chain distribution, wherein the parameters comprise mass, multiplication, alpha ratio, detector efficiency, and time constant (lambda), and wherein the first three moments are corrected with respect to the impact of instrument dead time on the count distributions of the emitted neutrons; another processor of the plurality of processors coupled to the multiplicity counter executing code that fits the time constant parameter to the actual time dependence of the moments to reduce the unknown parameters to four parameters of mass, multiplication, alpha ratio, and detector efficiency; and yet another processor of the plurality of processors coupled to the multiplicity counter that executes code that compares truncated data moments with untruncated and truncated theoretical moments to provide an estimation of a parameter of the four parameters and to allow for solution of the remaining three parameters using the first three moments.