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We propose a fully quantum-mechanical method of treating four-body nuclearbreakup processes in scattering of a projectile consisting of threeconstituents, by extending the continuum-discretized coupled-channels method.The three-body continuum states of the projectile are discretized bydiagonalizing the internal  Hamiltonian of the projectile with the Gaussian basis functions. For  $^6$He+$^{12}$C scattering at 18 and 229.8 MeV, the validity of the method istested by convergence of the elastic and breakup cross sections with respect toincreasing the number of the basis functions. Effects of the four-body breakupand the Borromean structure of $^6$He on the elastic and total reaction crosssections are discussed.Comment: 5 pages, 6 figures, uses REVTeX 4, submitted to Phys. Rev.

physical review. c. nuclear physics/physical review. c, nuclear physics

Continuum-discretized coupled-channels method for four-body nuclear breakup in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mi mathvariant="normal">He</mml:mi><mml:mprescripts /><mml:none /><mml:mn>6</mml:mn></mml:mmultiscripts><mml:mo>+</mml:mo><mml:mmultiscripts><mml:mi mathvariant="normal">C</mml:mi><mml:mprescripts /><mml:none /><mml:mn>12</mml:mn></mml:mmultiscripts></mml:mrow></mml:math>scattering

Continuum-discretized coupled-channels method for four-body nuclear breakup inHe6+C12scattering