Measurements of J/ψ decays into 2(π+π−)η and 3(π+π−)η

Based on a sample of 5.8×107J/ψ events taken with the BESII detector, the branching fractions of J/ψ→2(π+π−)η and J/ψ→3(π+π−)η are measured for the first time to be (2.26±0.08±0.27)×10−3 and (7.24±0.96±1.11)×10−4, respectively.