Search for the forbidden decays {eta}{yields}3{gamma} and {eta}{yields}{pi}{sup 0}{gamma} and the rare decay {eta}{yields}{pi}{sup 0}{pi}{sup 0}{gamma}{gamma}

A new upper limit is presented for the branching ratio (BR) of {eta}{yields}3{gamma}. This decay is not allowed by charge-conjugation invariance. We have determined that BR({eta}{yields}3{gamma})<4x10{sup -5}. We also obtained BR({eta}{yields}{pi}{sup 0}{gamma}{yields}3{gamma})<9x10{sup -5}; this decay mode is absolutely forbidden, as it violates conservation of angular momentum. Finally, we have established that BR({eta}{yields}{pi}{sup 0}{pi}{sup 0}{gamma}{gamma})<1.2x10{sup -3} in a restricted diphoton-energy region. All three upper limits are at the 90% confidence level. They were obtained by using the Crystal Ball multiphoton spectrometer at the AGS and are based on the analysis of 28 million {eta} mesons produced in the {pi}{sup -}p{yields}{eta}n reaction close to threshold.