  A probability model has been presented for understanding the operation of an
array of encapsulated germanium detectors generally known as composite
detector. The addback mode of operation of a composite detector has been
described considering the absorption and scattering of gamma-rays. Considering
up to triple detector hit events, we have obtained expressions for
peak-to-total and peak-to-background ratios of the cluster detector, which
consists of seven hexagonal closely packed encapsulated HPGe detectors. Results
have been obtained for the miniball detectors comprising of three and four
seven hexagonal closely packed encapsulated HPGe detectors. The formalism has
been extended to the SPI spectrometer which is a telescope of the INTEGRAL
satellite and consists of nineteen hexagonal closely packed encapsulated HPGe
detectors. This spectrometer comprises of twelve detector modules surrounding
the cluster detector. For comparison, we have considered a spectrometer
comprising of nine detector modules surrounding the three detector
configuration of miniball detector. In the present formalism, the operation of
these sophisticated detectors could be described in terms of six probability
amplitudes only. Using experimental data on relative efficiency and fold
distribution of cluster detector as input, the fold distribution and the
peak-to-total, peak-to-background ratios have been calculated for the SPI
spectrometer and other composite detectors at 1332 keV. Remarkable agreement
between experimental data and results from the present formalism has been
observed for the SPI spectrometer.
