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One widely-explored mechanism for producing astrophysical $\gamma$-ray bursts is the accretion of a comet onto a neutron star. We have re-examined the event rates for such collisions and find them to be dominated (by a factor of 100) by a previously-overlooked source: impacts due to encounters between field neutron stars penetrating the Oort Clouds of other stars. If comet clouds are common, then such collisions should (i) be frequent, with up to 4000 active sources in the Milky Way; (ii) be detectable by GRO/BATSE to distances of $\sim$1 kpc, (iii) display a Galactic distribution, (iv) be space-correlated with repetition frequencies of months to years, and (v) exhibit a wide range of peak luminosities and luminosity time histories. Based on the statistics of soft $\gamma$-ray repeaters (SGRs), the estimates of neutron star space densities, and the sensitivity of the GRO/BATSE instrument, we estimate that there should be $\sim20$ detectable SGRs within 1 kpc. Compared to the 3 repeaters that have been observed to date, we therefore conclude that either comet impacts on neutron stars are not the cause of SGRs, or the fraction of stars in the Galaxy with Oort Clouds is $\sim15$\%.
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