Error analysis based on nuclear liquid drop model

Cenxi Yuan

Published 2014-07-15, updated 2015-07-12Version 2

A new method is suggested to be used to estimate the statistical and systematic error of a theoretical model. As an example, such method is applied to analysis the total error of the nuclear binding energies between the observed values and the theoretical results from the liquid drop model (LDM). Based on the large number of data, the distribution of the error is supposed to be two normal distributions, standing for statistical and systematic error, respectively. The standard deviation of the statistical part, $\sigma_{stat}$, can be estimated by calculating with randomly generated parameters following normal distribution. The standard deviation of the systematic part, mean value of the statistical and systematic part can be obtain by minimizing the moments of the distribution of the total error with estimated $\sigma_{stat}$. The estimated distribution of the statistical and systematic error can well describe the distribution of the total error. The statistical and systematic error are estimated from LDM with and without the consideration of the shell effect. It can be seen that both statistical and systematic error are reduced after the inclusion of the shell correction.