Method to test Lorentz invariance in electron-capture decay by measuring a neutrino recoil force

Due to hypothetical Loretz invariance violation, additional terms arise in the differential rate for neutrino radiation accompanying electron capture by polarized nuclei. These terms, as well as the parity-violating term, can be probed by measurement of a small recoil force acting on a radioactive sample. An expression for this force is obtained for the case of allowed Gamow–Teller transitions. We discuss prospects to measure the force by using the methods of the magnetic resonance force microscopy, present a list of the most suitable isotopes and give the numerical estimates for mass and activity of required radioactive samples. (paper)