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

The reaction mechanisms of the two-neutron transfer reaction $^{12}$C($^6$He,$^4$He) have been studied at E$_{\mathrm{lab}}=30$ MeV at the TRIUMF ISAC-II facility using the Silicon Highly-segmented Array for Reactions and Coulex (SHARC) inside the TRIUMF-ISAC Gamma-Ray Escape-Suppressed Spectrometer (TIGRESS). In the past, the two-neutron transfer ($^{6}$He,$^{4}$He) angular distributions were often analyzed as a one-step process using a simple di-neutron plus core configuration for the $^{6}$He nucleus. In this work, the transfer angular distribution to the 2$^+_2$ 8.32 MeV state in $^{14}$C is studied using a realistic 3-body $^6$He model and advanced shell model calculations for the carbon structure, allowing to calculate the relative contributions of the simultaneous and sequential two-neutron transfer. The reaction model provides a good description of the data set and shows that while the simultaneous process is the dominant transfer mechanism, the sequential transfer contribution cannot be neglected.