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

TL;DR

This study systematically analyzes capture thresholds in fusion reactions using time-dependent Hartree-Fock theory, achieving close agreement with experimental barrier heights and improving predictions of fusion cross sections.

Contribution

First systematic application of TDHF to compute capture thresholds for 144 fusion systems involving nearly spherical nuclei, enhancing predictive accuracy over empirical models.

Findings

Calculated capture thresholds closely match measured barrier heights.

Inclusion of ~1 MeV excitation energy improves data reproduction.

TDHF results have smaller rms deviation than empirical potentials.

Abstract

With the time dependent Hartree-Fock (TDHF) theory, capture thresholds $E_{\rm cap}$ for 144 fusion systems with nearly spherical nuclei are systematically studied for the first time. We find that for the reactions between doubly-magic nuclei, the calculated $E_{\rm cap}$ 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 calcualtions, which is smaller than the results from three empirical nuclear potentials. Together with Siwek-Wilczy\'{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 $^{40}$Ca+$^{48}$Ca, $^{16}$O+$^{208}$Pb, $^{40}$Ca+$^{90,96}$Zr, $^{28}$Si+$^{96}$Zr and $^{132}$Sn+$^{40,48}$Ca.