The definitions used for the k0-constant, the coincidence correction factorc and the detector efficiency ef in the k0-method for NAA provide no means to interprete or correct for interference by artificial peaks. In this paper, extended descriptions for the detector efficiency are proposed to deal with escape peaks. For sum peaks caused by true coincidence, a k1-constant is defined as an alternative for the k0-constant, by separating the k0 into a part related to activation and a part related to spectrometry. The k1-constant is based on experimental data, just like the k0-constant.