Towards Universal Learning: Recommendations from the Learning Metrics Task Force. Summary Report

Abstract

We define the transformation brackets connecting the wave functions for two particles in an harmonic oscillator common potential with the wave functions given in terms of the relative and centre of mass coordinates of the two particles. With the help of these brackets we show that all matrix elements for the interaction potentials in nuclear shell theory can be given directly in terms of Talmi integrals. We obtain recurrence relations and explicit algebraic expressions for the transformation brackets that will permit their numerical evaluation.