Since radionuclides have unique characteristic gamma-ray spectra, usually maintained as a set of (energy, counts/energy) ordered pairs, an explicit functional representation would be indisputably useful. In this paper, the Gamma Detector Response and Analysis Software has been used to simulate the gamma-ray spectra as it would be collected by an NaI detector for a set of 70 radionuclides. Gaussian radial basis function (RBF) networks that offer simple, closed-form expressions are then trained to represent each of these spectra. Hence, a library consisting of 70 RBF networks for the corresponding radionuclides has been built. The presence of these library-contained radionuclides in a given gamma-ray spectrum of an unknown source is identified by an algorithm that employs a linear combination of the library spectra to approximate the unknown spectrum. The combination coefficients are then determined by minimizing the squared deviation error function under convexity constraints.