Time-dependent Hartree-Fock-Bogoliubov calculations using a Lagrange mesh with the Gogny interaction

A new numerical method of calculating the Hartree-Fock-Bogoliubov (HFB) and time-dependent HFB (TDHFB) with the Gogny interaction is proposed. The three-dimensional harmonic-oscillator (3DHO) basis functions are replaced by one-dimensional spatial grid points of Lagrange mesh plus two-dimensional harmonic-oscillator basis functions in the perpendicular plane to the direction of the spatial grid points [Lagrange mesh and harmonic oscillator (LMHO)]. By using the LMHO, the calculations of the HFB and TDHFB are carried out in the typical nuclei of ²⁰O and ³⁴Mg as an illustration of the feasibility of the TDHFB formulation with the LMHO. The strength functions of the quadrupole vibrations ($K=0$) are obtained and are compared with the ones calculated with the 3DHO.