  The new data of the elastic scattering of $^{6}$He+$^{12}$C at about 40
MeV/nucleon are analyzed in the eikonal approximation. The $^{6}$He+$^{12}$C
phase-shift function is evaluated completely without any {\it ad hoc}
assumption by a Monte Carlo integration, which makes it possible to use a
realistic 6-nucleon wave function for a halo nucleus $^{6}$He. The effect of
the breakup of $^6$He on the elastic differential cross sections as well as the
optical potential is studied at different energies from 40 to 800 MeV/nucleon.
PACS number(s): 24.10.-i; 21.60.Ka; 25.60.Bx; 25.10.+s Keywords: Eikonal;
Glauber; Monte Carlo; Halo; Breakup
