[Paper Review] Pionless Effective Field Theory in Few-Nucleon Systems

Johannes Kirscher|arXiv (Cornell University)|Jun 1, 2015

Nuclear physics research studies10 references3 citations

TL;DR

This dissertation develops pionless effective field theory (pEFT) to systematically compute low-energy observables in few-nucleon systems up to next-to-leading order (NLO), using the Resonating Group Method (RGM) with full Coulomb treatment. It achieves precise predictions for triton and alpha particle properties, demonstrates convergence in binding energy and radius correlations, and provides model-independent estimates for trinucleon binding energy splitting.

ABSTRACT

A systematic description of low-energy observables in light nuclei is presented. The effective field theory formalism without pions is extended to: i) predictions with next-to-leading-order (non-perturbatively) accuracy for the 4-helium binding energy B(α), the triton charge radius, and the 3-helium-neutron scattering length; ii) phase shifts for neutron-deuteron scattering and α-neutron low-energy scattering at leading order; iii) the ground states of the 5-helium (with and without Coulomb interaction) and 6-helium isotopes up to next-to-leading order; The convergence from leading- to next-to-leading order of the theory is demonstrated for correlations between: i) the triton binding energy B(t) and the triton charge radius; ii) B(t) and the 4-helium binding energy B(α); Furthermore, a correlation between B(t) and the scattering length in the singlet S-wave channel of neutron-helium-3 scattering is discovered, and a model-independent estimate for the trinucleon binding energy splitting is provided. The results provide evidence for the usefulness of the applied power-counting scheme, treating next-to-leading-order interactions nonperturbatively and four-nucleon interactions as, at least, one order higher. The 5- and 6-helium ground states are analyzed with a power-counting scheme which includes the momentum-dependent next-to-leading order vertices perturbatively. All calculations include a full treatment of the Coulomb interaction. The assessment of numerical uncertainties associated with the solution of the few-body equation of motion through the Resonating Group Method parallels the report of the results for light nuclei in order to establish this method as practical for the analysis of systems with up to six particles interacting via short-range interactions.

Motivation & Objective

• To extend pionless effective field theory (pEFT) to next-to-leading order (NLO) for accurate predictions of low-energy observables in light nuclei.
• To systematically assess convergence of pEFT by analyzing correlations between triton binding energy, charge radius, and alpha particle binding energy.
• To compute ground states of 5He and 6He, including Coulomb effects, using a power-counting scheme that treats NLO interactions nonperturbatively.
• To provide a model-independent estimate of the trinucleon binding energy splitting using pEFT correlations.
• To validate the RGM as a practical and reliable method for few-body systems with up to six nucleons, including uncertainty quantification.

Proposed method

• Formulates pionless EFT with a power-counting scheme that treats NLO two- and three-nucleon interactions nonperturbatively, and four-nucleon interactions as higher order.
• Applies the Resonating Group Method (RGM) to solve the few-body Schrödinger equation with a non-orthogonal Gaussian basis in configuration space.
• Uses a variational ansatz for the triton wave function composed of Gaussian-type basis functions with different width parameters, labeled by clustering and orbital structure.
• Solves the generalized eigenvalue problem for the Hamiltonian and norm matrices to obtain energy eigenvalues and expansion coefficients of the wave function.
• Incorporates the full Coulomb interaction in all calculations, including for 5He and 6He, using a consistent RGM framework.
• Quantifies numerical uncertainties via systematic basis truncation and convergence checks, ensuring robustness of results.

Experimental results

Research questions

• RQ1 Can pionless EFT at NLO provide accurate and systematically improvable predictions for the triton binding energy and charge radius, with controlled uncertainties?
• RQ2 What is the correlation between the triton binding energy and the 4-helium binding energy in pEFT, and does it support the convergence of the power-counting scheme?
• RQ3 How does the inclusion of momentum-dependent NLO vertices affect the description of 5- and 6-helium ground states in pEFT?
• RQ4 Can a model-independent estimate of the trinucleon binding energy splitting be derived from pEFT correlations without relying on phenomenological inputs?
• RQ5 To what extent does the RGM with a Gaussian basis and full Coulomb treatment provide a reliable and practical framework for few-body nuclear systems up to A=6?

Key findings

• The pEFT power-counting scheme successfully demonstrates convergence in the correlation between triton binding energy and triton charge radius, supporting its systematic nature.
• A strong correlation is found between the triton binding energy and the 4-helium binding energy, with NLO corrections improving agreement with experimental data.
• The model-independent estimate for the trinucleon binding energy splitting is derived from pEFT correlations, providing a theoretical benchmark without phenomenological input.
• The 5- and 6-helium ground states are computed with NLO interactions treated perturbatively, showing consistent convergence and agreement with known trends.
• The RGM implementation with a Gaussian basis and full Coulomb treatment yields numerical uncertainties that are well-controlled and systematically improvable, validating its use for A=6 systems.
• The inclusion of highly localized Gaussian basis functions (e.g., γ₁=11.1 fm⁻², γ₂=8.2 fm⁻²) has minimal impact on the ground state energy, indicating that the dominant physics is captured by broader, more delocalized components.