  Recently, a square-integrable discrete basis, obtained performing a simple
analytical local scale transformation to the harmonic oscillator basis, has
been proposed and successfully applied to study the properties of two-body
systems. Here, the method is generalized to study three-body systems. To test
the goodness of the formalism and establish its applicability and limitations,
the capture reaction rate for the nucleosynthesis of the Borromean nucleus 6He
(4He + n + n) is addressed. Results are compared with previous publications and
with calculations based on actual three-body continuum wave functions, which
can be generated for this simple case. The obtained results encourage the
application to other Borromean nuclei of astrophysical interest such as 9Be and
12C, for which actual three-body continuum calculations are very involved.
