Novel chiral Hamiltonian and observables in light and medium-mass nuclei

Abstract

Background: Recent advances in nuclear structure theory have led to the availability of several complementary ab initio many-body techniques applicable to light and medium-mass nuclei as well as nuclear matter. After successful benchmarks between different approaches, the focus is moving to the development of improved models of nuclear Hamiltonians, currently representing the largest source of uncertainty in ab initio calculations of nuclear systems. In particular, none of the existing two-plus three-body interactions is capable of satisfactorily reproducing all the observables of interest in medium-mass nuclei.Purpose: A novel parameterisation of a Hamiltonian based on chiral effective field theory is introduced. Specifically, three-nucleon operators at next-to-next-to-leading order are combined with an existing (and successful) two-body interaction containing terms up to next-to-next-to-next-to-leading order. The resulting potential is labelled NN+3N (lnl). The objective of the present work is to investigate the performance of this new Hamiltonian across light and medium-mass nuclei.Methods: Binding energies, nuclear radii and excitation spectra are computed using state-of-the-art no-core shell model and self-consistent Green's function approaches. Calculations with NN+3N (lnl) are compared to two other representative Hamiltonians currently in use, namely NNLOsat and the older NN+3N (400).Results: Overall, the performance of the novel NN+3N (lnl) interaction is very encouraging. In light nuclei, total energies are generally in good agreement with experimental data. Known spectra are also well reproduced with a few notable exceptions. The good description of ground-state energies carries on to heavier nuclei, all the way from oxygen to nickel isotopes. Except for those involving excitation processes across the N = 20 gap, which is overestimated by the new interaction, spectra are of very good quality, in general superior to those obtained with NNLOsat. Although largely improving on NN+3N (400) results, charge radii calculated with NN+3N (lnl) still underestimate experimental values, as opposed to the ones computed with NNLOsat that successfully reproduce available data on nickel. Conclusions:The new two-plus three-nucleon Hamiltonian introduced in the present work represents a promising alternative to existing nuclear interactions. In particular, it has the favourable features of (i) being adjusted solely on A = 2, 3, 4 systems, thus complying with the ab initio strategy, (ii) yielding an excellent reproduction of experimental energies all the way from light to medium-heavy nuclei and (iii) well behaving under similarity renormalisation group transformations, with negligible four-nucleon forces being induced, thus allowing large-scale calculations up to medium-heavy systems. The problem of the underestimation of nuclear radii persists and will necessitate novel developments.

Model nuclear energy density functionals derived from ab initio calculations

“…We chose the interaction NNLO sat [30] for the two-body and three-body sector. We made this choice since this interaction has been optimised to reproduce ground state energies and radii for isotopes up to mass A = 24 and it has been shown to predict accurate saturation properties also for larger isotopes and for infinite nuclear matter [48,49,50,51]. 16 The SCGF calculations were performed using a basis of spherical harmonic oscillator wave functions with oscillator energy ω=20 MeV.…”

Global Sensitivity Analysis of Bulk Properties of an Atomic Nucleus

“…It is not clear why. The NNLO sat interaction [20] reproduces experimental binding energies and charge radii for nuclei up to mass A ∼ 50 [4,5,9,16], while the 1.8/2.0 (EM) interaction [21,22] reproduces binding energies and low-lying energy spectra up to mass A ∼ 100 [4,7,8,10,12,15] while radii are underestimated.…”

“…Introduction.-How do properties of atomic nuclei depend on the underlying interaction between protons and neutrons? Recent ab initio computations of nuclei [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] have revealed that observables such as binding energies, radii, spectra, and decay probabilities are very sensitive to the values of the low-energy constants (LECs) in chiral Hamiltonian models with two-and three-nucleon forces [17][18][19]. Certain interaction models work better than others, but only for selected types of observables and in limited regions of the Segré chart.…”

“…Unfortunately, the number of model samples required for statistical computing increases exponentially with the number of uncertain LECs. A global sensitivity analysis of the ground-state energy and charge radius 16 O, based on a realistic next-to-next-to-leading order (NNLO) chiral Hamiltonian with 16 LECs, requires more than one million model evaluations. Similar numbers can be expected for Markov Chain Monte Carlo sampling of Bayesian marginalization end evidence integrals [23][24][25].…”

“…See Fig. 1 for a demonstration of the SP-CC method applied to 16 O and the variation of a single LEC (details are given below). We will use SP-CC to analyze the description of the 16 O ground-state energy and charge radius across a large domain of relevant LECs.…”