γ-Ray polarimetry with conversions to e+e− pairs: Polarization asymmetry and the way to measure it

Abstract

We revisit the measurement of the polarization fraction, P , and the measurement of the polarization angle of partially linearly-polarized gamma rays using their conversion to e + e − pairs in the field of a nucleus. We show that an inappropriate definition of the azimuthal angle, ϕ, used to reference the orientation of the final state degrades the precision of the measurement of P , by comparison to the optimal case where the bisector angle of the electron and of the positron momenta is used. We then focus on the lowest part of the energy spectrum, below ≈ 10 MeV, where a large part of the statistics lie for a cosmic source. We obtain the value of the polarization asymmetry, A, of pair conversion at threshold and we show that in the case where the correct expression is used for ϕ, the measured value of A tends to the limit.

HARPO, a gas TPC active target for high-performance γ-ray astronomy; demonstration of the polarimetry of MeV γ-rays converting to Bernard1 2019Nuclear Instruments and Methods in Physics Research Section A: Self Cite10040View full textAdd to dashboardCite

“…In the case of interest of a final state consisting of three particles (even when the recoil cannot be measured), the definition of the azimuthal angle, φ, is an issue. We determined the bisector φ +− = (φ + + φ − )/2 of the azimuthal angles of the direction of the electron, φ − , and of the positron, φ + , to be the optimal choice [27]. We demonstrated that with that angle definition, our generator is the only one, to our knowledge, to match the known asymptotic expressions for A at low and at high energies [24].…”

“…We implemented the moments' method to obtain an optimal measurement of the polarisation modulation factor A × P . In the case of the simple 1D differential cross section, the method is equivalent to a maximum likelihood fit of the 1D differential cross section dσ/dφ ∝ (1 + A × P cos(2(φ − φ 0 ))) [11,27]. In the case of the full 5D differential cross section, an additional gain in the precision of the measurement of A × P of a factor of two-to-three is obtained [11,27].…”

“…In the case of the simple 1D differential cross section, the method is equivalent to a maximum likelihood fit of the 1D differential cross section dσ/dφ ∝ (1 + A × P cos(2(φ − φ 0 ))) [11,27]. In the case of the full 5D differential cross section, an additional gain in the precision of the measurement of A × P of a factor of two-to-three is obtained [11,27]. In the case of interest of a final state consisting of three particles (even when the recoil cannot be measured), the definition of the azimuthal angle, φ, is an issue.…”

Polarimetry and high angular resolution gamma-ray observations in the MeV regime using a novel detector concept

“…This enabled us to access the geometry of the gamma-ray conversion, in particular, the azimuthal angle of the conversion plane of the event. It has been shown [13] that the precision of the measurement of the polarisation fraction depends on choosing optimally the angle that is measured and that the highest precision can be achieved if the bisector angle of the electron and of the positron momenta is used. The geometry of the conversion can be seen on the left of Figure 4.…”

“…MeV polarimetry using a TPC Deirdre Horan Figure 3: Examples of events recorded in the HARPO detector from [13]. From left to right are plotted events corresponding to a Compton scattering, a pair conversion and a triplet conversion.…”