Determination of mean theoretical γ-ray linear polarizations over large area detectors

In order to determine the polarization sensitivity of any γ-ray Compton polarimeter, it is necessary to know the theoretical γ-ray linear polarizations of some selected transitions, at a set nominal angle (often 90°). It is clear that the use of theoretical polarization values due to point detectors is inaccurate when scattering crystals subtending large solid angles are used. ng has been used to determine sets of attenuation factors Q2, Q4, N2, and N4, arising from the mean values of P2(cos θ), P4(cos θ), P2(2)(cos θ), and P4(2)(cos θ), respectively, (used in polarization angular distribution formulae) over several surfaces and for different geometries. Firstly, for a circular surface (replicating that of a surface barrier or cylindrical germanium detector) whose central axis is in turn at 30°, 45°, 60° and 90° to a second axis. Next, for a square surface (replicating, to first order, that of a planar germanium or silicon double sided strip detector, DSSD) whose central axis is at 90° to a second axis. Finally, for a circular surface whose central axis is at 90° to the central axis of a square surface. All sets of attenuation factors were applied to the polarization angular distribution formula, with firstly a2=−1 and secondly a2=5/7 and a4=−12/7. In every case, the polarization obtained was unity (as expected) to a high degree of accuracy, proving the correctness of all sets of attenuation factors. The attenuation factors were then applied to selected transitions with known a2 and a4 to determine the change in the mean polarization from theoretical point detector values. found that, by inserting analytical values of Q2 and Q4, for a circular surface, in the polarization angular distribution formula, N2 and N4 can be determined, at any chosen θ, (except 0° or 180°) by setting P(θ)=1, with a2=−1 and a2=5/7, a4=−12/7. Because those modeling results with a square surface in the calculation could be duplicated by a circular surface of the same area, it is suggested that a similar procedure could be applied to many shapes which replicate the front scattering surface of any polarimeter.