[en] A model for the long-spacing detector of a gamma-density-tool has been developed. It is based on 15-group, diffusion theory and on a point source situated in an infinite medium. The model has been compared with more accurate transport theory calculations and reasonable agreement was observed for the energy flux spectrum, provided the medium contains only limited concentration of elements heavier than Ca, provided the source energy is in the range 0.5 to 2 MeV and provided the source-detector distance multiplied by the attenuation coefficient of the medium at source energy is larger than 4 and less than 10. The model has been used to calculate energy build-up factors and calibration curves for the long-spacing detector, and reasonable agreement was obtained. It has been investigated how the calibration curves depend upon medium composition, source-detector distance, and energy width of detection window. A not too sucessful attempt has also been made to use the model for the determination of the photo-electric factor PEF. While a unique relation between LITH/LS and PEF was observed, it did not agree well with the relation reported in the literature. (author)