Calculation of orbital fractional parentage coefficients for five particles in translationally invariant basis

Abstract

In this work we present an independent scheme of the O(4) group transformation suitable for the calculation of orbital fractional parentage coefficients (OFPC) for N particle systems composed of N − 1 and 1 particle subsystems or N−2 and 2 particle subsystems, where the presented subsystems have their own intrinsic clusterization. Simple expressions for the corresponding five-particle harmonic oscillator transformation brackets (5HOB) used for the OFPC calculation are presented. The method does not require the calculation of the full expression of the 5HOB matrix. Instead of the full 5HOB matrix calculation, it is enough to calculate the 5HOB eigenvector matrix M and the diagonal eigenvalue matrix F . Examples of few body fermion systems, where this technique can be applied, are shown. Calculations of the 5HOB are fast and produce results with small numerical uncertainties.