Computing nuclear response functions with time-dependent coupled-cluster theory

TL;DR

This work develops and applies a time-dependent coupled-cluster framework to compute nuclear response functions ab initio by real-time evolution, capturing correlations beyond mean-field. The method connects the Fourier transform of the time-dependent transition moment to the spectral response, enabling linear and nonlinear analyses of electromagnetic dipole excitations. Validation against static Lorentz integral transform calculations shows overall agreement within a few percent for key sum rules, while the approach also reveals real-time density fluctuations and nonlinear phenomena such as chaos under strong fields. The results illuminate giant and pygmy dipole resonances in light to neutron-rich nuclei and demonstrate the potential for TDCC to extend ab initio reaction dynamics, with planned improvements including three-nucleon forces and continuum treatments.

Abstract

We compute nuclear response functions by solving the time-dependent A-body Schrödinger equation, recording the time-dependent transition moment and extracting spectral information via Fourier transforms. The solution of the time-dependent many-body problem accounts for correlations on top of the mean field by taking advantage of a time-dependent formulation of coupled-cluster theory. As a validation, we focus on electric dipole transitions in $^4$He and $^{16}$O and compare moments of the response function distribution to the results of an equivalent static framework, finding negligible discrepancies. We investigate how proton and neutron densities evolve in time, and we see the traditional picture of soft and giant dipole resonances as collective oscillations of protons and neutrons emerging from our calculations in $^{16}$O and $^{24}$O. This method also allows us to investigate the behavior of the nucleus in the presence of a strong electric field. In that regime, the behavior of the system becomes chaotic. Qualitatively, the spectral information obtained in this limit is in line with previous time-dependent mean-field results.

Figures (15)

• Figure 1: Convergence of the dipole moment with CVODE's relative tolerance size for $^{16}$O and $N_{\rm max} = 6$.
• Figure 2: Time-dependent dipole moment for $^{4}$He and $^{16}$O as a function of time for $N_{\rm max} = 6$.
• Figure 3: Convergence of the response with model-space size for $^4$He.
• Figure 4: Convergence of the response with model-space size for $^{16}$O.
• Figure 5: Comparison between the static and time-dependent results for the dipole polarizability $\alpha_D$, the non-energy-weighted sum rule $m_0$ and the energy-weighted sum rule $m_1$ in $^4$He for different model-space sizes.