The 3He(α,γ)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(α,γ)7Be cross section has been performed at the INFN Gran Sasso underground laboratory by both the activation and the prompt γ detection methods. The present work reports full details of the prompt γ detection experiment, focusing on the determiPrep...