  The gamma-ray pulsar PSR B1509-58 and its surrounding nebulae have been
observed with the CANGAROO 3.8m imaging atmospheric Cherenkov telescope. The
observations were performed from 1996 to 1998 in Woomera, South Australia,
under different instrumental conditions with estimated threshold energies of
4.5 TeV (1996), 1.9 TeV (1997) and 2.5 TeV (1998) at zenith angles of ~30 deg.
Although no strong evidence of the gamma-ray emission was found, the lowest
energy threshold data of 1997 showed a marginal excess of gamma-ray--like
events at the 4.1 sigma significance level. The corresponding gamma-ray flux is
calculated to be (2.9 +/- 0.7) * 10^{-12}cm^{-2}s^{-1} above 1.9 TeV. The
observations of 1996 and 1998 yielded only upper limits (99.5% confidence
level) of 1.9 * 10^{-12}cm^{-2}s^{-1} above 4.5 TeV and 2.0 *
10^{-12}cm^{-2}s^{-1} above 2.5 TeV, respectively. Assuming that the 1997
excess is due to Very High-Energy (VHE) gamma-ray emission from the pulsar
nebula, our result, when combined with the X-ray observations, leads to a value
of the magnetic field strength ~5 micro G. This is consistent with the
equipartition value previously estimated in the X-ray nebula surrounding the
pulsar. No significant periodicity at the 150ms pulsar period has been found in
any of the three years' data. The flux upper limits set from our observations
are one order of magnitude below previously reported detections of pulsed TeV
emission.
