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A numerical method to integrate the time-dependent Hartree-Fock Bogoliubov(TDHFB) equations with Gogny interaction is proposed. The feasibility of theTDHFB code is illustrated by the conservation of the energy, particle numbers,and center-of-mass in the small amplitude vibrations of oxygen 20. The TDHFBcode is applied to the isoscalar quadrupole and/or isovector dipole vibrationsin the linear (small amplitude) region in oxygen isotopes (masses A = 18,20,22and 24), titanium isotopes (A = 44,50,52 and 54), neon isotope (A = 26), andmagnesium isotopes (A = 24 and 34). The isoscalar quadrupole and isovectordipole strength functions are calculated from the expectation values of theisoscalar quadrupole and isovector dipole moments.

Linear Responses in Time-dependent Hartree-Fock-Bogoliubov Method with Gogny Interaction