  In two recent papers (R. Kshetri, JINST 2012 7 P04008; ibid., P07006), a
probabilistic formalism was introduced to predict the response of encapsulated
type composite germanium detectors like the SPI (spectrometer for INTEGRAL
satellite). Predictions for the peak-to-total and peak-to-background ratios are
given at 1.3 MeV for the addback mode of operation. The application of the
formalism to clover germanium detector is discussed in two separate papers (R.
Kshetri, JINST 2012 7 P07008; ibid., P08015). Using the basic approach
developed in those papers, for the first time we present a procedure for
calculating the peak-to-total ratio of the cluster detector for gamma-energies
up to 8 MeV. Results are shown for both bare and suppressed detectors as well
as for the single crystal and addback modes of operation. We have considered
the experimental data of (i) peak-to-total ratio at 1.3 MeV, and (ii) single
detector efficiency and addback factor for other energies up to 8 MeV. Using
this data, an approximate method of calculating the peak-to-total ratio of
other composite detectors, is shown. Experimental validation of our approach
(for energies up to 8 MeV) has been confirmed considering the data of the SPI
spectrometer. We have discussed about comparisons between various modes of
operation and suppression cases. The present paper is the fifth in the series
of papers on composite germanium detectors and for the first time discusses
about the change in fold distribution and peak-to-total ratio for sophisticated
detectors consisting of several modules of miniball, cluster and SPI detectors.
Our work could provide a guidance in designing new composite detectors and in
performing experimental studies with the existing detectors for high energy
gamma-rays.
