Power-moderated mean method in nuclear mass predictions

The power-moderated mean (PMM) method is a new method approved by the Consultative Committee for Ionizing Radiation for calculating a key comparison reference value and its associated standard uncertainty. The PMM method can exclude extreme data based on statistical criteria, and incorporates aspects of the arithmetic mean, the weighted mean, and the Mandel-Paule mean. For the data sets that are suspected of inconsistency, the PMM method can automatically adjust data uncertainties to achieve consistency, moderate the power of the uncertainties in the weighting factors, and thus allow for the calculation of an efficient and robust mean from any data set. The PMM method is applied for the first time to predict nuclear masses based on the mass predictions from various nuclear models. In the known nuclear region, where the theoretical mass predictions of different nuclear models are consistent within uncertainties, the PMM mass prediction approaches a weighted mean of different theoretical mass predictions. When extrapolating to the unknown region, the model uncertainties are underestimated and hence the theoretical mass predictions are inconsistent, the PMM mass prediction approaches an arithmetic mean of different theoretical mass predictions. Therefore, the PMM method provides a tool for a smooth transition of the mass prediction from the weighted mean to the arithmetic mean. The extrapolation performance of the PMM method is further verified by taking the mass predictions of the finite-range droplet model as the pseudoexperimental data, and it is found that the PMM mass predictions can agree with the pseudoexperimental data within uncertainties even far away from the known region, implying that the PMM method provides reliable uncertainty evaluations.