  A complete discrete set of spherical single-particle wave functions for
studies of weakly-bound many-body systems is proposed. The new basis is
obtained by means of a local-scale point transformation of the spherical
harmonic oscillator wave functions. Unlike the harmonic oscillator states, the
new wave functions decay exponentially at large distances. Using the new basis,
characteristics of weakly-bound orbitals are analyzed and the ground state
properties of some spherical doubly-magic nuclei are studied. The basis of the
transformed harmonic oscillator is a significant improvement over the harmonic
oscillator basis, especially in studies of exotic nuclei where the coupling to
the particle continuum is important.
