Interaction of Tachyons with Matter

A new interaction mechanism of superluminal particles with matter is suggested. Tachyons are described by a real Proca field with negative mass square, coupled to a current of subluminal matter. The potential of a static point source in this field theory is a damped periodic function with 1/r-decay. We treat this potential as a perturbation of the Coulomb potential, and study its effects on cross-sections and energy levels. In the limit of large impact parameter, the periodicity of the potential has a pronounced effect on the classical cross-section, which gets singular at the accumulating extrema of the scattering angle. In this limit we define the cross-section wave mechanically, by semiclassical rainbow scattering. The impact of the tachyon potential on the energy levels of hydrogen and hydrogenic ions is calculated by means of Bohr-Sommerfeld quantization. Estimates for the tachyon mass (3 keV) and the coupling constant of the tachyon potential are derived on the basis of high-precision Lamb shift measurements.