Transformation Coefficients of Hyperspherical Harmonic Functions of an -Body System

Abstract.

Two algorithms are presented for calculating the transformation coefficients between hyperspherical harmonic functions constructed with different sets of Jacobi vectors. They have been tested in the case , where the transformation coefficients of states with grand angular quantum number up to have been studied. The applicability of the two algorithms to larger systems is discussed. The numbers of independent hyperspherical-spin-isospin states with given values, entering the expansion of the alpha-particle ground-state wave function, are also evaluated. The use of complete non-redundant bases is important for future accurate applications of the hyperspherical harmonic technique.