Comparisons of two- and three-dimensional time-dependent Hartree-Fock calculations of the reactionsO16+O16andCa40+Ca40

Two-dimensional and three-dimensional time-dependent Hartree-Fock calculations have been performed over a wide range of angular momenta for ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ + ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ at $E_{\mathrm{lab}}=105\mathrm{}$ MeV and for ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ + ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ at $E_{\mathrm{lab}}=192\mathrm{}$ MeV. In all of the two-dimensional calculations it is assumed that the nuclear system is axially-symmetric about the line joining the mass centers of the colliding ions. Two very different two-dimensional, axially-symmetric models are considered. (a) In the first case, it is assumed that after the two ions interpenetrate the moment of inertia of the system attains the rigid-body value. (b) In the second model, each single-particle wave function is assumed to be multiplied by an extra phase factor which depends upon the azimuthal angle. This model yields an irrotational fluid flow. The results of time-dependent Hartree-Fock (TDHF) calculations with both of these models are compared with each other and with three-dimensional TDHF results. It is concluded that the two-dimensional calculations reproduce reasonably well the three-dimensional results for values of the angular momentum both below and above the three-dimensional fusion window. As the laboratory bombarding energy is decreased, there is better agreement between the two- and three-dimensional calculations, including cases in which the angular momentum is within the fusion region.