  Because accretion and merger shocks in clusters of galaxies may accelerate
particles to high energies, clusters are candidate sites for the origin of
ultra-high-energy (UHE) cosmic-rays. A prediction was presented for gamma-ray
emission from a cluster of galaxies at a detectable level with the current
generation of imaging atmospheric Cherenkov telescopes. The gamma-ray emission
was produced via inverse Compton upscattering of cosmic microwave background
(CMB) photons by electron-positron pairs generated by collisions of UHE cosmic
rays in the cluster. We observed two clusters of galaxies, Abell 3667 and Abell
4038, searching for very-high-energy gamma-ray emission with the CANGAROO-III
atmospheric Cherenkov telescope system in 2006. The analysis showed no
significant excess around these clusters, yielding upper limits on the
gamma-ray emission. From a comparison of the upper limit for the north-west
radio relic region of Abell 3667 with a model prediction, we derive a lower
limit for the magnetic field of the region of ~0.1 micro G. This shows the
potential of gamma-ray observations in studies of the cluster environment. We
also discuss the flux upper limit from cluster center regions using a model of
gamma-ray emission from neutral pions produced in hadronic collisions of
cosmic-ray protons with the intra-cluster medium (ICM). The derived upper limit
of the cosmic-ray energy density within this framework is an order of magnitude
higher than that of our Galaxy.
