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Nuclear structure study with two- and three-nucleon contact interactions derived within low-energy EFT

Songlin Lyu, Francesco Amodio, Giovanni De Gregorio, Nunzio Itaco, Luigi Coraggio

TL;DR

The paper addresses whether a pionless EFT-derived nuclear Hamiltonian with $2NF$ and $3NF$ contact interactions can describe open-shell nuclear structure by deriving effective shell-model Hamiltonians for the $0p$ and $1s0d$ shells and benchmarking against experimental data and a ChPT-based Hamiltonian with pion-exchange terms. The approach uses $H_{ m eff}$ obtained via the Kuo-Lee-Ratcliff folded-diagram expansion for a valence space, including $2NF$ and $3NF$ contributions up to next-to-next-to-next-to-leading order and converting second-order three-body diagrams into density-dependent two-body forces. Across nuclei such as $^6$Li, $^{10}$B, $^{12}$C, $^{17}$O, and the oxygen isotopes, the LEEFT-based results generally fail to reproduce the spectra and shell evolution, whereas the ChPT-based Hamiltonian better captures level ordering and $2^+$ excitations, highlighting deficiencies in the pionless EFT at very low energies for mid-mass systems. The findings suggest that, at the extreme low-energy scale of pionless EFT, many-body forces beyond LO $3$NF become increasingly important with mass, limiting the ability to describe open-shell structure without higher-order operators or additional degrees of freedom.

Abstract

We present the results of the application of a nuclear potential consisting of two- and three-nucleon contact interactions in nuclear structure investigations. The nuclear Hamiltonian has been derived for a very low-energy regime within the framework of the effective field theory, its low-energy constants have been fitted to a few low-energy nucleon-nucleon experimental observables and the deuteron and 3H binding energies. Our goal is to validate the ability of this Hamiltonian to reproduce some important features of open-shell nuclei, and to this end we derive effective shell-model Hamiltonians for nuclei in the p- and sd-shell mass regions. The results of shell-model calculations with these effective Hamiltonians are then compared with experiment, and also with those obtained with a nuclear Hamiltonian derived within chiral perturbation theory, that includes also terms with one- and two-pion exchanges.

Nuclear structure study with two- and three-nucleon contact interactions derived within low-energy EFT

TL;DR

The paper addresses whether a pionless EFT-derived nuclear Hamiltonian with and contact interactions can describe open-shell nuclear structure by deriving effective shell-model Hamiltonians for the and shells and benchmarking against experimental data and a ChPT-based Hamiltonian with pion-exchange terms. The approach uses obtained via the Kuo-Lee-Ratcliff folded-diagram expansion for a valence space, including and contributions up to next-to-next-to-next-to-leading order and converting second-order three-body diagrams into density-dependent two-body forces. Across nuclei such as Li, B, C, O, and the oxygen isotopes, the LEEFT-based results generally fail to reproduce the spectra and shell evolution, whereas the ChPT-based Hamiltonian better captures level ordering and excitations, highlighting deficiencies in the pionless EFT at very low energies for mid-mass systems. The findings suggest that, at the extreme low-energy scale of pionless EFT, many-body forces beyond LO NF become increasingly important with mass, limiting the ability to describe open-shell structure without higher-order operators or additional degrees of freedom.

Abstract

We present the results of the application of a nuclear potential consisting of two- and three-nucleon contact interactions in nuclear structure investigations. The nuclear Hamiltonian has been derived for a very low-energy regime within the framework of the effective field theory, its low-energy constants have been fitted to a few low-energy nucleon-nucleon experimental observables and the deuteron and 3H binding energies. Our goal is to validate the ability of this Hamiltonian to reproduce some important features of open-shell nuclei, and to this end we derive effective shell-model Hamiltonians for nuclei in the p- and sd-shell mass regions. The results of shell-model calculations with these effective Hamiltonians are then compared with experiment, and also with those obtained with a nuclear Hamiltonian derived within chiral perturbation theory, that includes also terms with one- and two-pion exchanges.

Paper Structure

This paper contains 5 sections, 6 figures.

Table of Contents

  1. Introduction
  2. Outline of the theory
  3. Results
  4. Summary and conclusions
  5. Acknowledgments

Figures (6)

  • Figure 1: Behavior of 2NF for LEEFT potential at N$^3$LO and Reid interaction in the $^1{\rm S}_0$ channel.
  • Figure 2: In panel (a), calculated spectra of $^{6}$Li with LO and N$^3$LO LEEFT effective SM Hamiltonian compared with experiment. In panel (b), the same as in (a) but for ChPT and N$^3$LO $H_{\rm eff}$s.
  • Figure 3: Same as in Fig. \ref{['6Li']}, but for $^{10}$B
  • Figure 4: Same as in Fig. \ref{['6Li']}, but for $^{12}$C
  • Figure 5: In panel (a), calculated SP spectra of $^{17}$O with LO and N$^3$LO LEEFT effective SM Hamiltonian compared with experimental states with the largest SP component. In panel (b), the same as in (a) but for ChPT and N$^3$LO $H_{\rm eff}$s.
  • ...and 1 more figures