This proposal aims at performing the most sensitive search for exotic tensor type interactions contributing to the weak interaction involving the lightest quarks. The observation of such contributions would provide a signature for new physics beyond the standard electroweak model whereas their non-observation will provide the tightest constraints on the couplings associated with those interactions. The search will be performed through high precision measurements of the full beta-energy spectrum in the decay of 6He nuclei. The main instrumental effect which has precluded these measurements to be performed so far, associated with the back-scattering of beta particles on detectors, is eliminated by improving and implementing calorimetric techniques in which the active volume of particle detectors fully enclose the decay source.