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The reaction mechanisms of the two-neutron transfer reaction$^{12}$C($^6$He,$^4$He) have been studied at 30 MeV at the TRIUMF ISAC-IIfacility using the SHARC charged-particle detector array. Optical potentialparameters have been extracted from the analysis of the elastic scatteringangular distribution. The new potential has been applied to the study of thetransfer angular distribution to the 2$^+_2$ 8.32 MeV state in $^{14}$C, usinga realistic 3-body $^6$He model and advanced shell model calculations for thecarbon structure, allowing to calculate the relative contributions of thesimultaneous and sequential two-neutron transfer. The reaction model provides agood description of the 30 MeV data set and shows that the simultaneous processis the dominant transfer mechanism. Sensitivity tests of optical potentialparameters show that the final results can be considerably affected by thechoice of optical potentials. A reanalysis of data measured previously at 18MeV however, is not as well described by the same reaction model, suggestingthat one needs to include higher order effects in the reaction mechanism.

Two-neutron transfer reaction mechanisms in $^{12}$C($^6$He,$^{4}$He)$^{14}$C using a realistic three-body $^{6}$He model