Effects of periodic matter in kaon regeneration

We study the effects of periodic matter in kaon regeneration, motivated by the possibility of parametric resonance in neutrino oscillations. The large imaginary parts of the forward kaon-nucleon scattering amplitudes and the decay width difference $\Delta\Gamma$ prevent a sizable enhancement of the $K_L\to K_S$ transition probability. However, some interesting effects can be produced using regenerators made of alternating layers of two different materials. Despite the fact that the regenerator has a fixed length one can obtain different values for the probability distribution of the $K_L$ decay into a final state. Using a two-arm regenerator set up it is possible to measure the imaginary parts of the $K^0(\bar{K}^0)$-nucleon scattering amplitudes in the correlated decays of the $\phi$-resonance. Combining the data of the single-arm regenerator experiments with direct and reverse orders of the matter layers in the regenerator one can independently measure the CP violating parameter $\delta$.