The first search for ultra-high energy (UHE) neutrinos using a radio telescope was conducted by Hankins, Ekers and OSullivan (1996). This was a search for nanosecond duration radio Cherenkov pulses from electromagnetic cascades initiated by ultra-high energy (UHE) neutrino interactions in the lunar regolith, and was made using a broad-bandwidth receiver fitted to the Parkes radio telescope, Australia. At the time, no simulations were available to convert the null result into a neutrino flux limit. Since then, similar experiments at Goldstone, USA, and Kalyazin, Russia, have also recorded null results, and computer simulations have been used to model the experimental sensitivities of these two experiments and put useful limits on the UHE neutrino flux. Proposed future experiments include the use of broad-bandwidth receivers, making the sensitivity achieved by the Parkes experiment highly relevant to the future prospects of this field. We have therefore calculated the effective aperture for the Parkes experiment and found that when pointing at the lunar limb, the effective aperture at all neutrino energies was superior to single-antenna, narrow-bandwidth experiments, and that the detection threshold was comparable to that of the double-antenna experiment at Goldstone. However, because only a small fraction of the observing time was spent pointing the limb, the Parkes experiment places only comparatively weak limits on the UHE neutrino flux. Future efforts should use multiple telescopes and broad-bandwidth receivers.
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