A new procedure to construct hyperspherical harmonics is presented in which the matrix of the multidimensional hyperangular Laplacian is diagonalized in the single-particle oscillator basis. It is shown that this matrix can be constructed and diagonalized prior to the elimination of spurious states in small subspaces, and that calculations of only the two-body operators is required. As a result, the hyperspherical basis can be constructed much faster than in the procedure introduced earlier [N. K. Timofeyuk, Phys. Rev. C 65, 064306 (2002)], which is based on recursive elimination of hyperradial excitations. The applicability of the proposed method is demonstrated for the systems made of up to ten identical bosons with zero spin using two different two-body potentials. In particular, it has been applied to some $\alpha$-particle nuclei for which the projection of their $0^{+}$ wave functions into the “condensed state wave function” have been calculated.

• Received 31 July 2008
• Corrected 26 November 2008

DOI:https://doi.org/10.1103/PhysRevC.78.054314