$\it{Ab}$ $\it{initio}$ nuclear many-body perturbation calculations in the Hartree-Fock basis

TL;DR

This paper applies many-body perturbation theory in the Hartree-Fock basis to calculate properties of closed-shell nuclei using realistic nuclear forces, demonstrating good convergence and agreement with experimental data.

Contribution

It introduces a perturbative approach in the Hartree-Fock basis for nuclear structure calculations with realistic interactions, including a novel correction method for the one-body density.

Findings

Higher-order corrections are small relative to leading order.

Results show good agreement with other methods and experimental data.

The approach efficiently computes nuclear properties with reasonable convergence.

Abstract

Starting from realistic nuclear forces, the chiral N$^3$LO and JISP16, we have applied many-body perturbation theory (MBPT) to the structure of closed-shell nuclei, $^4$He and $^{16}$O. The two-body N$^3$LO interaction is softened by a similarity renormalization group transformation while JISP16 is adopted without renormalization. The MBPT calculations are performed within the Hartree-Fock (HF) bases. The angular momentum coupled scheme is used, which can reduce the computational task. Corrections up to the third order in energy and up to the second order in radius are evaluated. Higher-order corrections in the HF basis are small relative to the leading-order perturbative result. Using the anti-symmetrized Goldstone diagram expansions of the wave function, we directly correct the one-body density for the calculation of the radius, rather than calculate corrections to the occupation propabilities of single-particle orbits as found in other treatments. We compare our results with other methods where available and find good agreement. This supports the conclusion that our methods produce reasonably converged results with these interactions. We also compare our results with experimental data.