Elimination the centre-of-mass motion in the nuclear shell-model with isospin

An efficient procedure for large-scale calculations of the two-particle translational invariant coefficients of fractional parentage (CESO’s) for several j-shells with isospin is presented. The approach is based on a simple enumeration scheme for antisymmetric many-particle states and efficient algorithms for calculation of the coefficients of fractional parentage for a single j-shell and several j-shells with isospin. The CESO’s may be obtained by diagonalizing the centre-of-mass Hamiltonian in the basis set of antisymmetric A-particle oscillator functions with singled out dependence on intrinsic coordinates of two last particles and choosing the subspace of its eigenvectors corresponding to the minimal eigenvalue equal to 3/2. An arbitrary number of oscillator quanta can be involved. The characteristics of the introduced CESO’s basis are investigated.