Daniel R. Phillips

We consider scenarios in which a shallow bound state undergoes breakup by a probe whose energy is high compared to the binding energy. The first two scenarios, which serve as warm-up exercises, involve a single heavy particle bound to a light particle, analogous to a core nucleus bound to a neutron. We show that in quasifree kinematics, the leading effect comes from the heavy particle being knocked out by the probe, with corrections suppressed by inverse powers of the probe momentum. This formally justifies extracting neutron form factors from high-energy deuteron breakup in quasifree kinematics. In scenario 1, the probe is a local current; in scenario 2, it is hadron scattering. In scenarios 3 and 4 we consider, respectively, a local current and hadron scattering, but now on a three-body bound state of a heavy particle and two light particles. Hard knockout of the heavy particle leaves two low-energy particles behind, which can interact with one another. In all four scenarios, we prove that the amplitude is dominated by the nearby on-shell pole of the heavy-particle propagator and derive a closed-form expression for this contribution. When two bodies are left behind, the leading amplitude is the product of the scattering of the two light particles, a dynamical function depending on the probe, and a real function related to the bound-state wave function. Thus, quasifree removal of a core nucleus from a system with halo neutrons provides access to on-shell data on multineutron interactions. The resulting amplitudes are relativistic and satisfy unitarity for the remnant subsystem exactly. We also provide complementary nonrelativistic derivations. While the derivations are for spinless particles, the generalization to spin is straightforward, since the results depend only on quasifree knockout kinematics; we make no assumptions about the interparticle dynamics.

A century ago, Wigner’s SU(4) symmetry was introduced to explain the properties of atomic nuclei. Despite recent revived interest, its impact on nuclear structure, transitions, and reactions has not been fully explored. Here, we show that a variety of high-fidelity nuclear interactions predict nuclear states that have ≥ 90 % probability of being in a single SU(4) irreducible representation. Meanwhile, our analysis of axial current operators in chiral effective field theory ( χ EFT ) reveals that one-body currents at low momentum transfer act only within SU(4) irreducible representations, while two-body currents connect different representations. These selection rules interfere with the expected convergence pattern of the χ EFT expansion and explain key phenomenological observations, e.g., the unnaturally large two-body corrections to the axial-current matrix elements in eight-body nuclei.

Bayesian analyses of the convergence pattern of Effective Field Theories (EFTs) enable estimation of the uncertainty induced by a truncated expansion. When an EFT that has been calibrated to data is used to make a prediction this truncation uncertainty enters the posterior predictive distribution twice: directly from the finite-order calculation of the predicted quantity and indirectly through the posterior probability distributions of the EFT low-energy constants (LECs) determined by the calibration. In this work, we focus on the interplay of these two sources of uncertainty. We do this in the context of a toy EFT that we fit to pseudodata and use to make predictions. Direct EFT truncation uncertainty and LEC uncertainty are correlated in predictions when the predicted quantity is correlated with the observables used to fit the LECs. Here this results in the overall theoretical uncertainty in the EFT prediction being smaller than either the uncertainty induced by the truncation error or that stemming from the LECs alone.

We examine the relationship between the asymptotic normalization coefficient (ANC) of ⁶ Li and other low-energy observables in the α –deuteron system. Our analysis uses a set of calculations carried out within the ab initio no core shell model with continuum (NCSMC) using a variety of inter-nucleon interactions and basis sizes, and yielding ⁶ Li deuteron separation energies between 1.3 and 1.8 MeV (Hebborn et al 2022 Phys. Rev. Lett. 129 042503). These NCSMC calculations show that the square of the ANC is strongly correlated with the separation energy over this range. In this work, we investigate the origin of this correlation using the phenomenological R -matrix, a single-channel potential and a perturbative approach. We show that this correlation occurs because the depth of the α –deuteron central potential changes by only a small relative amount as the separation energy varies. We then investigate if the ANC can be accurately extracted from α –deuteron phase shifts in an ideal case in which low-energy data are available and there are no experimental errors. We find that both R -matrix and Coulomb-modified effective-range theory (CM-ERE) yield extracted ANCs close to, although not exactly equal to, the NCSMC value, provided the extrapolation is constrained by the known position of the bound-state pole and at least three terms are included in the fit function. The R -matrix approach converges faster than the CM-ERE as the number of parameters increases and is also more robust against the inclusion of low-energy and high-energy phase shift data. Finally, our study also shows that a naive quantification of uncertainties by comparing different truncations used in both theories is not accurate, and suggests the accuracy of ANCs extracted from phase shift data needs further investigation.