Pauli Blocking effects in Nilsson states of weakly bound exotic nuclei

The description of weakly bound nuclei using deformed few-body models has proven to be crucial in the study of reactions involving certain exotic nuclei. However, these core+valence models face the challenge of applying the Pauli exclusion principle, since the factorisation of the system does not allow complete antisymmetrization. Therefore, states occupied by core nucleons should be blocked for the valence nucleons. We aim to study $^{17}$C and $^{19}$C, which are good examples of weakly bound exotic nuclei with significant deformation where the valence shell is partially filled. The structure of $^{17}$C and $^{19}$C is described with deformed two-body models where a Nilsson Hamiltonian is constructed using Antisymmetrized Molecular Dynamic calculations of the cores. Different methods of blocking occupied Nilsson states are considered using the Bardeen$-$Cooper$-$Schrieffer formalism: without blocking, total blocking and partial blocking. The latter also takes into account pair correlations to some extent. These models are later used to study $^{16}$C$(d,p)^{17}$C, $^{17}$C$(p,d)^{16}$C and $^{18}$C$(d,p)^{19}$C transfer reactions within the Adiabatic Distorted Wave Approximation. In the first case, the results are compared with experimental data. A good reproduction of the structure of $^{17}$C is found, significantly improving the agreement in the $^{16}$C$(d,p)^{17}$C reaction including blocking effects. The $^{19}$C spectrum is better reproduced considering blocking, in particular, the partial blocking method that considers the pairing interaction provides the best description. Promising results are shown for the study of transfer reactions involving weakly bound exotic nuclei, by highlighting the effect of blocking occupied Nilsson states. We envision to extend the models to the study of breakup reactions and to newly discovered halo nuclei.