Low energy capture cross sections are calculated within a microscopic many-body approach using an effective Hamiltonian derived from the Argonne V18 potential. The dynamics is treated within Fermionic Molecular Dynamics (FMD) which uses a Gaussian wave-packet basis to represent the many-body states. A phase-shift equivalent effective interaction derived within the Unitary Correlation Operator Method (UCOM) that treats explicitly short-range central and tensor correlations is employed. As a first application the 3He(alpha,gamma)7Be reaction is presented. Within the FMD approach the microscopic many-body wave functions of the 3/2- and 1/2- bound states in 7Be as well as the many-body scattering states in the 1/2+, 3/2+ and 5/2+ channels are calculated as eigenstates of the same microscopic effective Hamiltonian. Finally the S-factor is calculated from E1 transition matrix elements between the many-body scattering and bound states. For 3He(alpha,gamma)7Be the S-factor agrees very well, both in absolute normalization and energy dependence, with the recent experimental data from the Weizmann, LUNA, Seattle and ERNA experiments. For the 3H(alpha,gamma)7Li reaction the calculated S-factor is about 15% above the data.
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