Session S06: Nuclear Theory II

Proton-deuteron correlation functions from pionless effective field theory

High-energy collisions of nucleons or nuclei provide fascinating insights into the nature of the strong interaction.  Interestingly, not only can one learn from such processes about quantum chromodynamics (QCD) under extreme conditions, but also about the nuclear interaction at much lower energies, by measuring correlations among hadrons that are produced in the collision.  Recently, experiments have advanced to study three-body systems in this way, going beyond just two-hadron correlations.  A solid understanding of the theory governing the process is crucial to use measurements in order to constrain nuclear and other hadronic interactions.

This contribution presents such a theoretical study for the proton-deuteron (pd) correlation function, calculated in Pionless effective field theory (Pionless EFT) using a formalism that fully accounts for the underlying three-body dynamics in the system.  Pionless EFT is designed to capture the universal low-energy features of few-nucleon systems that arise from the fact that the two-nucleon scattering lengths are unnaturally large, and it has been used to make a number of predictions for low-energy few-nucleon processes.  In particular, the systematic inclusion of electromagnetic corrections, relevant for studying the pd system, is well understood within Pionless EFT.  In this work, the formalism is extended to calculate the pd correlation function up to next-to-leading order in the EFT expansion.   

Tritium β-decay and pp fusion in Pionless Effective Field Theory

At low energies, pp fusion, which is relevant for stellar and Big Bang nucleosynthesis, and tritium β-decay both depend on a two-nucleon axial current contribution described by the low-energy constant L_1,A at next-to-leading order (NLO). Using pionless effective field theory, we compute the Fermi and Gamow-Teller matrix elements of tritium β-decay up to NLO. We then extract the L_1,A parameter from the tritium half-life and use it to predict the transition matrix element for pp fusion. We will also discuss the consequences of Wigner-SU(4) symmetry in the calculation of the Fermi and Gamow-Teller matrix elements for tritium β-decay.   

Ab initio calculation of the 3He(α,γ)7Be astrophysical S factor

The ³He(α,γ)⁷Be reaction is an important part of ongoing processes occuring in all stars like our very own sun. In the fusion reaction network of the sun, the ³He(α,γ)⁷Be reaction is key to determining the ⁷Be and ⁸B neutrino fluxes resulting from the pp-II chain . In standard solar model (SSM) predictions of these neutrino fluxes, the low-energy ³He(α,γ)⁷Be S factor, S₃₄(E), is the largest source of uncertainty from nuclear input. The SSM uses S₃₄(E) near the Gamow peak energy, roughly 18 keV, which cannot be experimentally measured since the Coulomb force between ³He and ⁴He suppresses the fusion reaction at such low energies. Theoretical calculations are needed to guide the extrapolation to the solar energies of interest.  To this end, I will present ab initio calculations of the ³He(α,γ)⁷Be reaction using the no-core shell model with continuum starting from two- and three-nucleon chiral interactions. To demonstrate that the NCSMC provides an accurate S factor, I will also compare NCSMC ³He + ⁴He elastic-scattering cross sections with those recently measured by the SONIK collaboration.   

Towards a Nuclear Mass Model Rooted in Chiral Effective Field Theory

Nuclear mass models have a long history. They come in many flavors, ranging from those based on macroscopic phenomenology to those based on microscopic mean field treatments. The most sophisticated of these have root-mean-square deviations lower than 0.5 MeV. However, apart from a few exceptions (e.g. the density functionals by Navarro Perez et al., arXiv:1801.08615 and by Zurek et al., arXiv:2307.13568), they are lacking a direct connection to  quantum chromodynamics.

We start with a Hamiltonian from chiral effective field theory at next-to-next-to leading order and readjust its low-energy coefficients such that (symmetry breaking) Hartree-Fock computations yield binding energies. To make computationally viable the task of minimizing the root-mean-square deviation between the Hartree-Fock and experimental binding energies, we make use of model order reduction and construct Hartree-Fock emulators. This short talk presents the first results of this project.   

Shape coexistence in neutron-rich N = 20 nuclei

Neutron-rich nuclei exhibit deformed ground states at neutron number N=20 and beyond. Coupled-cluster computations based on interactions from chiral effective field theory show that deformed and nearly spherical shapes coexist in neon and magnesium nuclei in this region of the nuclear chart.    

Non-Relativistic Effective Field Theory of Narrow S-Wave Resonances with No Auxiliary Field

We present a potential in the context of effective field theory (EFT) that allows sharp resonances to form without the use of dimer fields. We show that our theory leads to the same results previously proved for the on-shell T-matrix of such states and demonstrate that this potential leads to a scattering amplitude which up to next-to-leading order is renormalizable on and off mass shell. We show that this potential leads to the corresponding T-matrix for the bound state and is also renormalizable for the bound state on and off mass shell up to next-to-leading order.