A Monte Carlo technique for modeling the gamma-ray background spectra in space-based gamma-ray telescopes has been developed. The background spectrum is one of the key factors to the ultimate sensitivity that gamma-ray telescopes can achieve. The major sources of background are the diffuse cosmic gamma-ray flux, the Earth's atmospheric flux, and the decay of nuclei produced by spallation of cosmic rays, trapped protons and their secondary particles, the decay of nuclei produced by neutron capture and the de-excitation of excited states produced by inelastic scattering of neutrons. All of these sources are included in the model. The method for calculating the nuclear activation and decay component of the background combines the low Earth orbit primary proton and neutron flux, the production of secondary hadrons with GEANT, the spallation cross sections from Alice91 and YieldX, nuclear decay data from National Nuclear Data Center's (NNDC) Evaluated Nuclear Structure Data Files (ENSDF) database, and three-dimensional gamma-ray and beta particle transport with Electron Gamma-ray Shower version 4 (EGS4) using MORSE-CG. The background in the High Energy Astrophysics Observatory 3 (HEAO 3) gamma-ray instrument was modeled and compared to the measured background to validate the code. HEAO 3 is a space-based germanium spectrometer surrounded by active scintillators that provide shielding. Both the active and passive components of the HEAO 3 instrument are included in the simulation. The measured background from the HEAO 3 space instrument is compared with the simulation.; This Monte Carlo code handles the following decay types: electron capture, beta{dollar}-{dollar}, beta+, meta-stable isotopes and short lived meta-stable decay products, and isotopes that have branchings to both beta{dollar}-{dollar} and beta+. The code follows a cascade of photons to the ground state of the decay product, and propagates these photons and appropriate accompanying beta simultaneously. This model was applied to the design of an advanced Compton telescope (proposed as the ATHENA mission) to predict its performance capabilities. The effective area, background, and point spread function (the imaged response to a point source) were modeled for several configurations of this Compton telescope. Thus, the sensitivity of these different configurations of this Compton telescope were compared. The sensitivity of the best configurations of this advanced Compton telescope are {dollar}{lcub}sim{rcub}3times10sp{lcub}-7{rcub}{dollar} gamma-rays s{dollar}sp{lcub}-1{rcub}{dollar} cm{dollar}sp{lcub}-2{rcub}{dollar} which is nearly 100 times more sensitivity than previous gamma-ray instruments.
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