ON THE WAY TOWARDS INCREASING THE PREDICTIVE POWER OF THE NUCLEAR MEAN FIELD THEORIES: EVALUATION OF TWO-BODY MATRIX ELEMENTS

In this paper we collect a number of technical issues that arise when constructing the matrix representation of the most general nuclear mean field Hamiltonian within which "all terms allowed by general symmetries are considered not only in principle but also in practice". Such a general posing of the problem is necessary when investigating the predictive power of the mean field theories by means of the well-posed inverse problem. [J. Dudek et al., Int. J. Mod. Phys. E21 (2012) 1250053]. To our knowledge quite often ill-posed mean field inverse problems arise in practical realizations what makes reliable extrapolations into the unknown areas of nuclei impossible. The conceptual and technical issues related to the inverse problem have been discussed in the above-mentioned topic whereas here we focus on "how to calculate the matrix elements, fast and with high numerical precision when solving the inverse problem" [For space-limitation reasons we illustrate the principal techniques on the example of the central interactions].