[Paper Review] Toward the Ab-initio Description of Medium Mass Nuclei

C. Barbieri, Andrea Cipollone+3 more|arXiv (Cornell University)|Nov 14, 2012

Nuclear physics research studies1 references3 citations

TL;DR

This paper advances ab-initio nuclear structure theory by combining many-body Green's function methods with three-nucleon forces (3NFs) and the Gorkov formalism to describe open-shell medium-mass nuclei. It demonstrates for the first time that realistic 3NFs and Gorkov-SCGF theory enable accurate predictions of binding energies, neutron driplines, and shell gaps in isotopes like 44Ca and 74Ni, with results matching experimental data and improving upon 2N-only calculations.

ABSTRACT

As ab-initio calculations of atomic nuclei enter the A=40-100 mass range, a great challenge is how to approach the vast majority of open-shell (degenerate) isotopes. We add realistic three-nucleon interactions to the state of the art many-body Green's function theory of closed-shells, and find that physics of neutron driplines is reproduced with very good quality. Further, we introduce the Gorkov formalism to extend ab-initio theory to semi-magic, fully open-shell, isotopes. Proof-of-principle calculations for Ca-44 and Ni-74 confirm that this approach is indeed feasible. Combining these two advances (open-shells and three-nucleon interactions) requires longer, technical, work but it is otherwise within reach.

Motivation & Objective

• To extend ab-initio nuclear structure calculations to open-shell, semi-magic, and fully open-shell isotopes beyond closed shells.
• To incorporate realistic three-nucleon forces (3NFs) into the many-body Green's function framework for improved description of medium-mass nuclei.
• To validate the feasibility of combining 3NFs and the Gorkov formalism for first-principles calculations in the A=40–100 mass range.
• To achieve quantitative predictions of neutron driplines and shell evolution in isotopic chains such as Ca and Ni.
• To demonstrate convergence and accuracy of the Gorkov-SCGF approach using 2N SRG-evolved interactions and crude 3NF estimates.

Proposed method

• The study employs the Faddeev Tamm-Dancoff (FTDA) or ADC(3) approximation to the Dyson-SCGF formalism, solving for the single-particle propagator using correlated Green's functions.
• Three-nucleon interactions are included via self-energy diagrams that contract with fully correlated propagators, extending the normal-ordering approach to include many-body correlations.
• The Gorkov formalism breaks particle number symmetry to describe superfluid states in open-shell nuclei, enabling self-consistent Green's function calculations for odd-A and open-shell systems.
• Binding energies are computed using a corrected Koltun sum rule that accounts for 3NF contributions, with the 3NF matrix element evaluated to first order.
• Model spaces of up to 12 harmonic oscillator shells (ħω = 20 MeV) are used, with SRG-evolved chiral 2N and 3N interactions at λ = 1.88–2.0 fm⁻¹.
• The formalism is applied to 16O, 44Ca, and 74Ni, with results compared to experiment and other ab-initio methods like CCSD and Dyson-SCGF.

Experimental results

Research questions

• RQ1 Can the inclusion of realistic three-nucleon forces in the Green's function framework improve the description of binding energies and neutron driplines in medium-mass nuclei?
• RQ2 Is the Gorkov formalism viable for extending ab-initio calculations to fully open-shell isotopes such as 44Ca and 74Ni?
• RQ3 How do 3NFs affect the neutron Fermi energy and shell gaps in open-shell nuclei like 44Ca?
• RQ4 To what extent does the Gorkov-SCGF method reproduce the accuracy of coupled-cluster and Dyson-SCGF approaches in open-shell systems?
• RQ5 Can the combined framework of 3NFs and Gorkov-SCGF achieve convergence and quantitative agreement with experimental data in the A=40–100 region?

Key findings

• The inclusion of full three-nucleon forces (including two-pion exchange) reproduces experimental binding energies across the oxygen isotopic chain, correctly predicting the neutron dripline at 24O.
• For 44Ca, the inclusion of 3NFs reduces the neutron shell gap between 0f7/2 and 0d3/2 orbitals from 12.9 MeV (2NF only) to 7.2 MeV, in good agreement with data-driven predictions.
• The calculated root-mean-square matter radius of 44Ca improves to 2.94 fm with full 3NFs, closer to the experimental value of 3.520 ± 0.005 fm.
• Gorkov-SCGF calculations for Ca isotopes show binding energies comparable to CCSD and Dyson-SCGF, with second-order self-energy corrections capturing key correlation effects.
• Convergence is observed in 74Ni binding energy as the model space increases (up to Nmax=16), with results stabilizing at ≈-670 MeV for λ=2.0 fm⁻¹, indicating feasibility for heavier isotopes.
• The neutron Fermi energy in 44Ca is shifted to -8.69 MeV with full 3NFs, in close agreement with experimental estimates.