Study of quantum electron diffraction for the LISA test-mass charging

The future Laser Interferometer Space Antenna (LISA) for gravitational wave detection in space and the precursor LISA Pathfinder missions rely on metal test masses (TMs) playing the role of free-falling geodesic-reference and interferometer end mirrors. Charge deposited on the TMs by high-energy particles of galactic and solar origin couples with stray electric fields thus perturbing the free-falling geodesic motion. In previous works it has been shown that sub-keV electrons play a relevant role for TM charging. In particular, electrons with energies below 100 eV show a wave-like behavior when impacting on the gold coatings of the TMs and electrode-housing (EH), the capacitive position sensor/actuator that surrounds the TMs. We aim at studying the effects of quantum diffraction of electrons on LISA Pathfinder and LISA TMs and EH gold lattice. We calculate the quantum diffraction probability of electrons with energies < 100 eV impinging on gold lattice from different directions by using the methods of quantum mechanics. The effects of electron quantum diffraction on LISA TM charging are reported here for the first time. This work is also of interest for the second-generation LISA-like space interferometers and for all space missions whose performance relies on free-falling metal test masses.