Long-range behaviour in hyperspherical formalism

It is shown that hyperspherical harmonics can be represented in a form typical of traditional microscopic cluster models. This allows those hyperharmonics that are responsible for long-range behaviour of valence nucleons in loosely-bound nuclei to be selected. The hyperspherical cluster model based on such hyperharmonics is tested for $^5$He using a simplified description of the $^4$He core and two versions of the Volkov potential which give $^5$He as either bound or unbound. The study has confirmed that it is possible to get a converged solution for binding energy, r.m.s. radius, overlap integral and asymptotic normalization coefficient with small number of basis functions for bound $^5$He. The values obtained of these quantities are very close to those calculated in a microscopic cluster model.