  The precise determination of astrophysical S-factors is essential for a
detailed understanding of the nucleosynthesis in its various facets. It is
discussed how the Lorentz integral transform (LIT) method can be applied for
such a determination. The astrophysical S-factor for the proton-deuteron
radiative capture is considered as test case. The importance of a specific
many-body basis used for the LIT equation solution is pointed out. The
excellent results of the test are discussed.
