One of the two main instruments of INTEGRAL, an ESA mission dedicated to ga
mma-ray astronomy, is the SPectrometer on INTEGRAL (SPI), which is mainly d
esigned for high-resolution spectroscopy of gamma-ray lines. It consists of
a cooled germanium-detector array with an energy resolution of 2 keV at 1.
33 MeV and will operate in the energy range 20 keV to 8 MeV. Radioactivity
induced in detector materials is recognised as an important limitation of i
nstrument sensivity for gamma-ray telescopes and heedful considerations of
this source of background are required. This study presents simulation resu
lts of background from the decay of radioactive nuclei produced by nuclear
reactions of cosmic protons and their secondaries within the materials surr
ounding the germanium detectors and the germanium itself. Numerical simulat
ions to calculate the nuclear activation and beta-decay components of the b
ackground have been performed by using the nuclear physical code TIERCE dev
eloped at CEA, Bruyeres-le-Chatel, Another Monte-Carlo code (GEANT) is used
to simulate the propagation of the beta particles from the nuclear decay a
nd the photons simultaneously emitted. This study presents background calcu
lations derived from the decay of radioactive nuclei and techniques for its
reduction. These calculations allowed us to determinate the SPI sensitivit
y.