The relation of Cerenkov time profile widths to the distance to maximum of air showers

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Abstract
The authors provide information to enable experimenters to interpret measurements of Cerenkov pulse widths (FWHM) in terms of the distance along the axis to air-shower maximum. The relations were calculated from Monte Carlo simulations for protons using a scaling model and rising cross sections. Primary energies of 1015, 1016, 1017 eV and zenith angles from 0 degrees to 40 degrees are covered. The results will be useful for radii of observation from 200 to 350 m and refer to sea level. The relations are sensitive to marked deviations from scaling-model behaviour on the approach to maximum; however, reasonable aerosol variations to not invalidate the results. The procedure frequently used to obtain the true widths by correcting the measured widths for the impulse response of the detector can lead to appreciable errors near a radius of 200 m. An alternative method is described.

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