Final results on the mu He-3-capture experiment and perspectives for mu p-capture studies

Muon capture on hydrogen gives a unique possibility for a measurement of the pseudo-scalar form factor g(p) (q(c)(2) = -0.88 m(mu)(2)) of the nucleonic weak current, thus providing a sensitive test of the QCD chiral symmetry perturbation theory which predicts the value of this form factor with a precision of Delta g(p)/g(p) similar or equal to 2%. For adequate comparison with theory, the muon capture rate Lambda(c) should be measured with a precision of Delta Lambda(c)/Lambda(c) less than or equal to 1%, that is an order of magnitude better than the precision of the present world data. We report on the project of an experiment designed to provide the required precision. Also, we present the final result of our previous experiment on a high precision measurement of the mu(3)He capture rate and compare this result with the PCAC prediction