Abstract
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.
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