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.
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