MAX is a proposed Laue lens gamma-ray telescope taking advantage of Bragg diffraction in crystals to concentrate incident photons onto a distant detector. The Laue lens and the detector are carried by two separate satellites flying in formation. Significant effort is being devoted to studying different types of crystals that may be suitable for focusing gamma rays in two 100 keV wide energy bands centered on two lines which constitute the prime astrophysical interest of the MAX mission: the 511 keV positron annihilation line, and the broadened 847 keV line from the decay of 56Co copiously produced in Type Ia supernovae. However, to optimize the performance of MAX, it is also necessary to optimize the detector used to collect the source photons concentrated by the lens. We address this need by applying proven Monte Carlo and event reconstruction packages to predict the performance of MAX for three different Ge detector concepts: a standard coaxial detector, a stack of segmented detectors, and a Compton camera consisting of a stack of strip detectors. Each of these exhibits distinct advantages and disadvantages regarding fundamental instrumental characteristics such as detection efficiency or background rejection, which ultimately determine achievable sensitivities. We conclude that the Compton camera is the most promising detector for MAX in particular, and for Laue lens gamma-ray telecopes in general.
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