Abstract: The continuum-discretized coupled-channels (CDCC) method [1] was developed in the 80s to study nuclear reactions for three-body systems, composed by a two-body projectile plus a target nucleus. In the 2000s the CDCC formalism was extended to four-body systems [2-6] in order to study reactions induced by the two-neutron halo Borromean nuclei 6He(4He+n+n) and 11Li (9Li +n+n). Two different approaches were used to build the states of the three-body projectile: Pseudo-State (PS) methods [2,3,7,8] and the binning procedure [4]. The four-body CDCC can be also applied to other three-body projectiles such as the stable, although weakly-bound, Borromean nucleus 9Be(α+α+n) [7,9,10,11] and the Borromean p-rich nucleus 17Ne(15O+p+p) (in progress). Also, we have applied the formalism to reactions induced by the Brunnian nucleus 10C(α+α+p+p) [12], adopting a three-body model 10C(8Be+p+p) that assumes 8Be is in its ground state (a very narrow resonance only 92 keV over the α-α threshold). A comparison between methods to build the projectile states will be shown, along with the comparison with experimental data. The reaction dynamics, as the binding energy of the projectile increases, will be discussed. 

[1] M. Yahiro et al., Prog. Theor. Phys. Suppl. 89, 32 (1986); N. Austern et al., Phys. Rep. 154, 125 (1987).

[2] T. Matsumoto, T. Egami, K. Ogata, Y. Iseri, M. Kamimura, M. Yahiro, Phys. Rev. C (2006) 73, 051602(R).

[3] M. Rodríguez-Gallardo, J. M. Arias, J. Gómez-Camacho, R. C. Johnson, A. M. Moro, I. J.

Thompson,  J. A. Tostevin, Phys. Rev. C 77 (2008) 064609.

[4] M. Rodríguez-Gallardo, J. M. Arias, J. Gómez-Camacho, A. M. Moro, I. J. Thompson, J. A. Tostevin, Phys. Rev. C 80, (2009) 051601(R).

[5] M. Cubero, J. P. Fernández-García, M. Rodríguez-Gallardo et al., Phys. Rev. Lett. 109 (2012)  262701.

[6] J. P. Fernández-García, M. Cubero, M. Rodríguez-Gallardo et al., Phys. Rev. Lett. 110 (2013)  142701.

[7] P. Descouvemont, T. Druet, L.F. Canto,  M.S. Hussein, Phys. Rev. C 91 (2015) 024606.

[8] J. Casal, M. Rodríguez-Gallardo, and J.M. Arias, Phys. Rev. C 88 (2013) 014327.

[9] J. Casal, M. Rodríguez-Gallardo, and J.M. Arias, Phys. Rev. C 92 (2015) 054611.

[10] A. Arazi, J. Casal, M. Rodríguez-Gallardo et al, Phys. Rev. C 97 (2018) 044609.

[11] V. Soukeras, O. Sgouros, A. Pakou et al., Phys. Rev. C 102 (2020) 064622.    

[12] R. Linares, Mandira Sinha, E.N. Cardozo et al., Phy. Rev. C 103 (2021) 044613.