Shell model approach to construction of a hyperspherical basis for A identical particles: Application to hydrogen and helium isotopes

A new method to construct hyperspherical functions basis for A identical particles, beyond the minimal approximation, is presented. This method is based on the link between the hyperspherical function method (HSFM) and the oscillator no-core shell model and uses a Slater determinant representation of the hyperspherical functions. It is shown that, because of this representation, the HSFM matrix elements are related to the inverse Laplace transforms of the oscillator shell model matrix elements, on the condition that the center-of-mass motion and the hyperradial excitations are removed from the shell model states. The applicability of the proposed method is demonstrated for the case of the 3-7H and 4-10He isotopes