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New developments in ion cooling and ion bunching allow the trapping of radioactive ions from a low energy beam, in a very short time scale and with very good efficiency. The performances of Radio Frequency Quadrupole (RFQ) coolers, recently developed in several laboratories in Europe and USA, are now better known. In the present study, a RFQ device will be used to inject 6He+ ions in a transparent Paul trap. The ion beam will be delivered by the SPIRAL facility at GANIL. The careful measurement of the β-recoil ion coincidence spectrum is sensitive to the angular correlation parameter a, which depends on the coupling constants of the weak hamiltonian. It should be equal to −1/3 if the interaction is only of axial vector type (V-A theory). Deviation from this value would imply a new tensor-like interaction involving a new exchange boson thus introducing new physics beyond the Standard Model.