Ab initio calculations of six-body systems

Abstract

For description of physical proterties of many-body systems besides the physical part of the problem, requires efficient mathematical and computational methods. One of the hugest projects with an emphasis on computational and algorithmic developments in nuclear physics, was UNEDF project [1,2], carried out in USA from 2006 to 2012. This project revealed the complexity of many-body systems and the limitations of the models which were used. As an example calculations of 12C, required supercomputer resources with more than 100,000 cores. Here for basis antisymmetrisation Slater determinants were employed. The method of Slater determinants is quite simple method of antisymmetrisation of N fermion systems, but it gives a huge basis states used in calculations and therefore may require superpowerfull computer resources. One of the possible solution of the problem- to create efficient models of many-body systems which allows to optimize the use of computer resources. For the solution of the problem, method of binary cluster model can be applied. The approach is based on a simple enumeration scheme for antisymmetric N particle states, and I suggest an efficient method for constructing the eigenvectors of two-particle transposition operator PN1;N in a subspace where N1 and N2 = N −N1 nucleons basis states are already antisymmetrized [4]. Using this method we can distinguish totally asymmetrical N particle states from the other states with lower degree of antisymmetry. Calculations were performed for systems composed of six nuclei.