Analysis of the angular distribution for the elastic scattering of \(\alpha \) particles from tritium at an energy of 84.2 MeV

New experimental angular distribution data are reported for the \(\alpha \)+t elastic scattering at \(E_\textrm{lab}(\alpha ) = 84.2\) MeV (\(E_\textrm{cm} = 36.09\) MeV) covering both forward and backward scattering angles. An analysis was carried out using the coupled-reaction-channels (CRC) formalism including the transfer of a proton between the two triton cores. Automatic searches on the parameters of the \(\alpha \)+t optical model potential of volume Woods-Saxon form, together with the spectroscopic factor (SF), were performed using the code SFRESCO. The inclusion of a proper core-core (t+t) potential was found to be important and led to slightly higher values of the SF being obtained. The deduced value of the SF for the \(\alpha \) \(\rightarrow \) t+p overlap (1.33 ± 0.05) agrees very well with that found earlier for the mirror system \(^3\)He+n. However, both are lower than the value of 2.0 predicted by the shell model. The asymptotic normalization coefficient (ANC) was also deduced and the variations of the SF and \(\text {ANC}^2\) as a function of the radius of the t+p binding potential appear to be different, that of the SF being almost linear while the \(\text {ANC}^2\) increases approximately exponentially with increasing binding potential radius. Nevertheless, the best fit value of the \(\text {ANC}^2\) = 45.5 ± 1.8 \(\text {fm}^{-1}\) was found to be close to those obtained theoretically by Monte Carlo calculations.