The 7Be((n,alpha ))4He Reaction Studied via THM for the Cosmological Li-Problem

7Be destruction channels during the Big Bang nucleosynthesis are currently a matter of study because of their influence on the primordial 7Li abundance. We have taken several approaches by means of the Trojan Horse method (THM) to investigate the most important reaction channels 7Be(eta,rho)7Li and 7Be(eta,alpha)4He. The 7Be(eta,alpha)4He reaction cross sections were firstly determined from the available THM data of the 7Li(rho,alpha)4He reaction with charge-symmetry hypothesis (CSH). We performed another THM experiment using a 7Be RI beam which did not require CSH. We also present the preliminary result of another experiment with an upgraded setup successfully observing both the 7Be(eta,rho)7Li and the 7Be(eta,alpha)4He reactions. The deduced reaction rates from those studies allows us to evaluate the impact on big bang nucleosynthesis and on the lithium problem.