Ab initio study of the radii of oxygen isotopes

TL;DR

This work addresses the challenge of computing nuclear radii in ab initio frameworks by applying nuclear lattice effective field theory (NLEFT) with high-fidelity N$^3$LO chiral interactions to the oxygen isotopes $^{16}$O–$^{20}$O. A key contribution is the partial pinhole algorithm, which mitigates the Monte Carlo sign problem and enables reliable imaginary-time extrapolations to extract both charge and matter radii, including a prediction of $r_{ m ch}(^ {20} ext{O}) = 2.810(32)$ fm. The results show that charge radii for $^{16}$O–$^{18}$O align with experimental data, while matter radii agree with electron- and proton-scattering extractions but differ from cross-section–based methods, highlighting model dependencies in the latter. The study demonstrates the broader applicability of the partial pinhole technique to other observables and larger systems, offering precise theoretical benchmarks and insights into nuclear structure such as possible alpha-cluster configurations in $^{16}$O.

Abstract

We present an {\em ab initio} study of the charge and matter radii of oxygen isotopes from $^{16}$O to $^{20}$O using nuclear lattice effective field theory (NLEFT) with high-fidelity N$^3$LO chiral interactions. To efficiently address the Monte Carlo sign problem encountered in nuclear radius calculations, we introduce the {\em partial pinhole algorithm}, significantly reducing statistical uncertainties and extending the reach to more neutron-rich and proton-rich isotopes. Our computed charge radii for $^{16}$O, $^{17}$O, and $^{18}$O closely match experimental data, and we predict a charge radius of $2.810(32)$ fm for $^{20}$O. The calculated matter radii show excellent agreement with values extracted from low-energy proton and electron elastic scattering data, but are inconsistent with those derived from interaction cross sections and charge-changing cross section measurements. These discrepancies highlight model-dependent ambiguities in the experimental extraction methods of matter radii and underscore the value of precise theoretical benchmarks from NLEFT calculations.

Figures (7)

• Figure 1: Left: Charge radii of oxygen isotopes calculated using the partial pinhole algorithm with the N$^3$LO interaction as functions of the projection time $\tau$. The black squares, red circles, blue upward triangles, and green downward triangles represent the results for $^{16}$O, $^{17}$O, $^{18}$O, and $^{20}$O, respectively. The solid lines denote fits using a double-exponential function, with the shaded bands indicating the 1$\sigma$ uncertainties. Right: Diamonds indicate the charge radii deduced from electron scattering data for $^{16}$O (black), $^{17}$O (red), and $^{18}$O (blue). Horizontal lines represent the extrapolated values at $\tau \to \infty$ from the left panel, with shaded bands showing the $1\sigma$ uncertainties.
• Figure 2: Left: Matter radii of oxygen isotopes calculated using the partial pinhole algorithm with the N$^3$LO interaction as functions of the projection time $\tau$. The black squares, red circles, blue upward triangles, and green downward triangles represent the results for $^{16}$O, $^{17}$O, $^{18}$O, and $^{20}$O, respectively. The solid lines denote fits using a double-exponential function, with the shaded bands indicating the 1$\sigma$ uncertainties. Right: Diamonds indicate the matter radii deduced from electron scattering and proton scattering data for $^{16}$O (black), $^{17}$O (red), $^{18}$O (blue), and $^{20}$O (green). Horizontal lines represent the extrapolated values at $\tau \to \infty$ from the left panel, with shaded bands showing the $1\sigma$ uncertainties.
• Figure S1: Nuclear binding energies $B$ from NLEFT in comparison to experimental data. The red circles summarise the results with ten minimal sets of 3NFs, and blue squares represent binding energies from Ref. Elhatisari:2022zrb_sm. The error bars show standard deviations.
• Figure S2: Schematic figure to show the additional finite volume effects introduced by the periodic boundary conditions. The frame $O'$ is a periodic copy of the frame $O$.
• Figure S3: Charge radii of $^{16}$O (top) and $^{17}$O (bottom) calculated with simple Hamiltonian as function of the projection time $\tau$. The black squares and red circles represent the results from the partial pinhole and the pinhole algorithm, respectively. The insets show the average phase factor for the partial pinhole and the pinhole algorithms as functions of the projection time $\tau$.