Systematic study of capture thresholds with time dependent Hartree-Fock theory

With the time dependent Hartree-Fock (TDHF) theory, capture thresholds Ecap for 144 fusion systems with nearly spherical nuclei are systematically studied. We find that for the reactions between doubly magic nuclei, the calculated Ecap are very close to the extracted barrier heights from measured fusion excitation functions. For the fusion reactions with nearly spherical nuclei, an excitation energy of about 1 MeV at the capture position need to be considered to better reproduce the data due to the lower excitation threshold. The rms deviation with respect to the barrier heights is only 1.43 MeV from the TDHF calculations, which is smaller than the results from three empirical nuclear potentials. Together with Siwek-Wilczy {n} \'{n}{}ski formula in which the three parameters are determined by the TDHF calculations, the measured fusion cross sections at energies around the barriers can be well reproduced for seven fusion reactions ⁴⁰Ca+⁴⁸Ca, ¹⁶O+²⁰⁸Pb, ⁴⁰Ca+90,96Zr, ²⁸Si+⁹⁶Zr, and ¹³²Sn+40,48Ca.