We describe the cryogenic resonant gravitational wave detector of the Rome group, named Explorer, and report on its long term operation with sensitivity for short bursts in the range h congruent-to 7-10 X 10(-19). Explorer has mass M = 2270 kg and is equipped with a resonant capacitive transducer followed by a dc superconducting quantum interference device amplifier. It has been operated at T congruent-to 2.6 K in a cryostat cooled with superfluid helium. With a transducer voltage bias of 320 V (E = 6.15 MV/m) the two resonant modes have frequencies of 904.7 and 921.3 Hz with coupled quality factors, respectively, of 0.77 X 10(6) and 1.0 X 10(6). The description of the experimental apparatus and of its calibration is followed by the analysis of the noise and the calculation of the expected sensitivity of the detector: h congruent-to 8 X 10(-19) (under the assumption of bursts with duration of 1 ms). We then describe the data acquisition system and the techniques of data analysis, discussing the filtering algorithms. The last section reports the experimental results obtained during the operation of the detector from May 1990 to December 1991. During this period the data were recorded for more than two-thirds of the total time: we show the distributions of the data and the hourly averages of the sensitivity. The data taken from May 1991 to December 1991 have also been used to establish a new improved upper limit for the rate and strength of gravitational wave pulses; at h = 2 X 10(-17), for example, there are no more than 0.5 events/day as averaged over a period of 134 days.
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