Optimization of semi-empirical mass formula co-efficients using least square minimization and variational Monte-Carlo approaches

In this paper, both least squares minimization (LSM) and variational Monte-Carlo techniques have been implemented to determine the co-efficients of semi-empirical mass formula (SEMF). First, the experimental binding energies (BEs) are determined for all the available nuclei from atomic mass evaluation (AME2016) data. Then, LSM technique is implemented in Gnumeric worksheet to minimize relative mean squared error (RMSE) to obtain the SEMF co-efficients by considering only the first three co-efficients which are deduced from liquid drop model. The mean percentage error (MPE) value, between obtained BEs from the optimized co-efficients and the experimental BEs, has been determined. Then, to emphasize the relevance of empirical terms, they have been introduced successively one after other and the procedure has been repeated. A reduction in MPE-value has been observed after each iteration. This same procedure has also been employed using Monte-Carlo approach to obtain SEMF co-efficients by minimizing RMSE-value as in variational principle.