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本文利用BES III的离线软件系统，对J/ψ→γηc→γ??进行蒙特卡罗模拟，通过比较单举道和遍举道蒙特卡罗样本，对末态粒子进行筛选，选择效率是BES II的1．5倍；同时，得到的衰变道ηc→??的分支比在误差范围内与蒙特卡罗的输入值一致.根据目前BES III上J/ψ样本的统计量，按照本文提出的方案，预计可以得到2144±26个ηc→??的事例.利用螺旋度的分析方法计算出各级衰变粒子在其母粒子坐标系下的角分布，遍举道蒙特卡罗的拟合结果与理论计算结果在误差范围内一致.本文的测量结果对实验上高精度测量该衰变道及BES III上实验数据分析具有重要意义.“,”The Monte Carlo simulation of J/ψ→γηc→γ??is performed at the BES III offline software system.The final states of the decay channel are selected by comparing the inclusive Monte Carlo with the exclusive Monte Carlo,and the efficiency is 1 .5 times as that of BES II.The branching fraction ofηc→??obtained by this method is consistent with the input value of Monte Carlo within the statistical errors.2 144±26 events number ofηc→??can be obtained when applying the procedure of the paper to the J/ψ data sample collected at BES III.A method of Helicity is used to calculate the angular distribution of all the particles in their mother frame,and the results are consistent with the fitting results of the exclusive Monte Carlo sample within the statistical errors.The result of this paper is meaningful for the high precision measurement of the channel and the data analysis at BES III experiment.