Ab initio symmetry-adapted approaches to nuclear reactions

TL;DR

The paper presents an ab initio, symmetry-guided framework (SA-NCSM with continuum) that unifies nuclear structure and reaction descriptions from light to medium-mass nuclei, leveraging a symmetry-adapted basis and chiral EFT interactions. By integrating Green's function and resonating-group methodologies, it yields nonlocal, energy-dependent optical potentials and reaction observables with quantified uncertainties, connecting microscopic structure to scattering, capture, and knockout processes. It demonstrates how deformation, clustering, and multi-particle excitations emerge naturally and influence cross sections, ANCs, SFs, and reaction rates for neutron, proton, and alpha-induced processes, including astrophysical reactions and beta-decay constraints on BSM physics. The work also develops uncertainty quantification approaches—Bayesian local-potential fitting and chiral-LEC variations—to provide credible error bars on predictions and guide future improvements toward heavier nuclei and more complete interactions. Overall, SA-NCSM with continuum offers a scalable, first-principles route to predictive structure–reaction theory with broad implications for nuclear physics, astrophysics, and tests of fundamental symmetries.

Abstract

In this review, we discuss recent applications of the ab initio symmetry-adapted no-core shell-model (SA-NCSM) theory for study and prediction of structure and reactions of stable and unstable nuclei from light to medium mass range. We explore structure properties of neutron-rich He, Mg, and Li isotopes, with a focus on nuclear collectivity, clustering, and spectroscopic factors, as well as multi-particle excitations of utmost significance in the proximity of the drip lines. In addition, we present extensions of the SA-NCSM with continuum for determining the microscopic structure of reaction fragments, which enables calculations of reaction cross sections for targets from the lightest $^{4,6}$He to $^{40}$Ca, rooted in first principles. We illustrate this for neutron and proton elastic scattering, deuteron and alpha capture reactions, and alpha knock-out reactions. Furthermore, we discuss microscopic optical potentials with uncertainty quantification, a critical ingredient in many reaction models, and reaction observables with uncertainties that stem from the underlying chiral potential. We also discuss the impact of alpha clustering on reactions of significance to nuclear astrophysics, as well as on beta decays and beyond-the-standard-model physics.

Figures (19)

• Figure 1: Microscopic description of deformation, rotations, vibrations, and clustering in the ab initio SA-NCSM framework with chiral EFT interactions, illustrated for $^{20}$Ne: (a) giant-resonance mode; rotational bands above (b) the ground state (g.s.) (which may also include a band above another $2^+$ state often referred to as "$K=2$"), (c) a negative-parity state (only the $1^-$ member of the band is shown), and an illustrative excited $0^+$ state of different deformation (sometimes referred to as a "$K=0$" band), together with (e) the $^{16}$O$+\alpha$ wavefunction with exact asymptotics at large distances. Excitation energies, along with the one-body density profiles for the most dominant shape in the body-fixed frame, are shown for a model space of $145$ million basis states (13 harmonic oscillator shells), which includes hundreds of nuclear shapes (the giant resonance shown by the monopole response function from Ref. Burrows_2025; the g.s. rotational band described in Ref. DytrychLDRWRBB20LauneyMD_ARNPS21; the first excited $1^-$ state from Ref. DreyfussLESBDD20 with extrapolated energy; inset adapted from Ref. LauneyMD_ARNPS21).
• Figure 2: SA-NCSM capabilities enable calculations beyond the oxygen isotopes, computations of B(E2) transition strengths without effective charges, and descriptions of states dominated by multi-particle excitations, with illustrative examples: (a) $B(E2)$ transition strengths for $^{21}$Mg and $^{21}$F in the SA-NCSM, compared to the experimental data of Ref. Ruotsalainen19 and to the results of other theoretical approaches (models that adopt proton and neutron effective charges are also labeled by the corresponding $\Delta e^{\pi, \nu}$; see Ref. Ruotsalainen19 for details). Figure from Ruotsalainen19, with permission. (b) Energy spectrum of $^{8}$He (ground state) and $^{10}$He showing a deformed 2p-2h configuration as energetically favored and dominant in the $^{10}$He ground state, with the corresponding one-body density profiles.
• Figure 3: Energy spectra (in MeV) and $B(E2)$ transition strengths (in W.u.) for (a) $^{28}$Mg and (b) $^{32}$Mg calculated in the SA-NCSM with the NNLO$_{\rm opt}$ chiral potential, with uncertainties reported from extrapolations to the infinite-size model space, as compared to experiment ("Expt."): PhysRevC.100.014322 for $^{28}$Mg and physics4030048 for $^{32}$Mg. Calculated states with 0p-0h dominance are shown in gray and with 2p-2h dominance in red. For $^{28}$Mg, calculated levels with no uncertainties (green) are reported in PhysRevC.100.014322; an experimental $(4^+)$ state is shown in red as a possible candidate that belongs to the 2p-2h rotational band. The one-body density profiles are shown to the right for the 2p-2h-dominated band (red).
• Figure 4: $B(E2)$ estimates for Mg isotopes calculated without effective charges using the microscopic interaction of Refs. DreyfussLDDBp12TobinFLDDB14 for the most deformed 0p-0h (blue) and 2p-2h (red) configurations (with no mixing between configurations) in the model space of 16 HO shells, as compared to experiment (black squares) and estimates from the SA-NCSM with NNLO$_{\rm opt}$ where available (green). Results for $^{21}$Mg are from Ruotsalainen19; results for $^{22}$Mg are from Henderson:2017dqc, where theoretical results are reported with model uncertainties and validated in smaller model spaces against the SA-NCSM with NNLO$_{\rm opt}$. Note that B(E2) estimates for $Z=12$ and $A>30$ are consistent with dominant 2p-2h configurations.
• Figure 5: (a) Single-nucleon overlaps of the $^7$Li ground state with the $^6\mathrm{Li}+{\rm n}$ in $N_{\rm max}=12$ for partial waves $p_{1/2}$ and $p_{3/2}$ vs. the separation between $^6\mathrm{Li}$ and the neutron, $r$, compared to the GFMC results from Ref. QMC_database. The dotted lines correspond to the exterior Whittaker function. The shaded bands indicate the uncertainty due to the $\hbar\Omega$ variance from 10 to 20 MeV (interior to exterior wavefunction matching radii differ for different $\hbar\Omega$, see text for details). For all but the first two points, the GFMC uncertainties are smaller than the marker size on the plot. Inset: SA-NCSM overlaps compared to a typical Woods-Saxon parameterization (see text for details). (b) Calculated SFs in $N_{\rm max}=12$ model space vs. the extrapolated neutron separation energies ($S_{\rm n}$) and the experimentally deduced SFs from Refs. WuosmaaSRGH2008Schiffer8Li1967Wuosmaa9Li2005. Uncertainties on extrapolated $S_{\rm n}$ are from variances in $\hbar\Omega$ and the use of SA model spaces. Uncertainties on the experimental $S_{\rm n}$ are smaller than the marker size. Figure adapted from Ref. sargsyan:23, with permission.