We have examined 2.4 × 109 events recorded by the Chicago Air Shower Array-Michigan Muon Array (CASA-MIA) experiment for evidence of ultra-high-energy (100 TeV) neutral particle and gamma-ray emissions from the Crab Nebula and Pulsar between 1990 March 4 and 1995 October 9. No such emissions have been detected. Over this interval, the 90% confidence level integral flux limits for continuous emission above 141 TeV are 2.08 × 10-14 cm-2 s-1 for any neutral particle (which can produce a detectable air shower) and 9.21 × 10-15 cm-2 s-1 for gamma rays. There is no evidence of transient emission on timescales of 1 day or longer. The 90% confidence level integral flux limit for emission on a single day is conservatively estimated to be 4.40 × 10-12 cm-2 s-1 for any neutral particle and 5.09 × 10-12 cm-2 s-1 for gamma rays. There is no evidence for emission from the pulsar at the radio period on intervals of 1 day or longer. The 2 σ (97.7% confidence) limit on the pulsed flux on the most significant day is 3.29 × 10-12 cm-2 s-1 for any neutral particle with mass less than 21 MeV, and 8.31 × 10-12 cm-2 s-1 for gamma rays. For an interval of 162 sidereal days beginning 1992 March 1, the pulsed flux limit was 2.39 × 10-13 cm-2 s-1 for any neutral particle with mass less than 21 MeV, again above 141 TeV.
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