The accurate and efficient simulation of coupled neutron-photon problems is necessary for several important radiation detection applications. Examples include the detection of nuclear threats concealed in cargo containers and prompt gamma neutron activation analysis for nondestructive determination of elemental composition of unknown samples. In these applications, high-resolution gamma-ray spectrometers are used to preserve as much information as possible about the emitted photon flux, which consists of both continuum and characteristic gamma rays with discrete energies. Monte Carlo transport is the most commonly used modeling tool for this type of problem, but computational times for many problems can be prohibitive. This work explored the use of coupled Monte Carlo-deterministic methods for the simulation of neutron-induced photons for high-resolution gamma-ray spectroscopy applications. A method was developed for the implementation of coupled neutron-photon problems into RAdiation Detection Scenario Analysis Toolbox (RADSAT), a computer code that couples the complementary strengths of discrete-ordinate and Monte Carlo approaches to obtain high-resolution detector responses. Central to this work was the development of a method for generating multi-group neutron-photon cross-sections in a way that separates the discrete and continuum photon emissions so that the key signatures in neutron activation analysis (i.e., the characteristic line energies) are preserved. The mechanics of the cross-section preparation method are described and contrasted with standard neutron-gamma cross-section sets. These custom cross-sections were then applied to several benchmark problems using the method developed in this work. Multi-group results for neutron and photon flux are compared to MCNP results. Finally, calculated responses of high-resolution spectrometers were compared. The added computational efficiency of the coupled Monte Carlo-deterministic method and the positive agreement achieved in the code-to-code verification make the integration of the coupled neutron-photon method into RADSAT a promising endeavor.