Coherent radio pulses from showers in different media: A unified parametrization

We study the frequency and angular dependences of Cherenkov radio pulses originated by the excess of electrons in electromagnetic showers in different dense media that are being given consideration as targets for ultra high energy neutrino detection such as ice, salt and the lunar regolith. By means of a simple model of shower development we rederive the scaling of the electric field spectrum with the properties of the media such as density, radiation length, Moli\`ere radius, critical energy and refraction index. We compare the predictions of the scaling relations to the numerical results obtained in our own developed GEANT4-based Monte Carlo simulation, and address in a quantitative manner the predictive power of the scaling relations. We also give a unified parametrization of the frequency spectrum and angular distribution of the electric field in ice, salt, and the lunar regolith, in terms of the relevant properties of the media to be used in practical applications. We establish the applicability of our parametrizations. Our formulas are useful for estimates of the acceptance of current and future neutrino detectors using the radio technique, and for many other practical applications.