The 3He(alpha,gamma)7Be process is a key reaction in both Big-Bang nucleosynthesis and p-p chain of Hydrogen Burning in Stars. A new measurement of the 3He(alpha,gamma)7Be cross section has been performed at the INFN Gran Sasso underground laboratory by both the activation and the prompt gamma detection methods. The present work reports full details of the prompt gamma detection experiment, focusing on the determination of the systematic uncertainty. The final data, including activation measurements at LUNA, are compared with the results of the last generation experiments and two different theoretical models are used to obtain the S-factor at solar energies.
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