# Density-constraint Time-dependent Hartree-Fock-Bogoliubov method

## TL;DR

This paper introduces the Density-constraint Time-dependent Hartree-Fock-Bogoliubov (DC-TDHFB) method, which incorporates pairing correlations to improve predictions of fusion cross-sections in superfluid nuclear systems.

## Contribution

The paper develops and applies the DC-TDHFB method, extending the density-constraint approach to include superfluidity effects in fusion reactions.

## Key findings

- DC-TDHFB reproduces experimental fusion data well.
- The method aligns with TDHFB fusion thresholds.
- Phase-lock mechanisms influence fusion outcomes.

## Abstract

Background: The Density-constraint Time-dependent Hartree-Fock method is currently the tool of choice to predict fusion cross-sections. However, it does not include pairing correlations, which have been found recently to play an important role. Purpose: To describe the fusion cross-section with a method that includes the superfluidity and to understand the impact of pairing on both the fusion barrier and cross-section. Method: The density-constraint method is tested first on the following reactions without pairing, $^{16}$O+$^{16}$O and $^{40}$Ca+$^{40}$Ca. A new method is developed, the Density-constraint Time-dependent Hartree-Fock-Bogoliubov method. Using the Gogny-TDHFB code, it is applied to the reactions $^{20}$O+$^{20}$O and $^{44}$Ca+$^{44}$Ca. Results: The Gogny approach for systems without pairing reproduces the experimental data well. The DC-TDHFB method is coherent with the TDHFB fusion threshold. The effect of the phase-lock mechanism is shown for those reactions. Conclusions: The DC-TDHFB method is a useful new tool to determine the fusion potential between superfluid systems and to deduce their fusion cross-sections.