Models, measurements, and effective field theory: proton capture on Beryllium-7 at next-to-leading order

Abstract

We employ an effective field theory (EFT) that exploits the separation of scales in the p-wave halo nucleus ${}^8\mathrm{B}$ to describe the process ${}^7\mathrm{Be}(p,\gamma {)}^8\mathrm{B}$ up to a center-of-mass energy of 500 keV. The calculation, for which we develop the lagrangian and power counting, is carried out up to next-to-leading order (NLO) in the EFT expansion. The power counting we adopt implies that Coulomb interactions must be included to all orders in ${\alpha }_{\mathrm{em}}$. We do this via EFT Feynman diagrams computed in time-ordered perturbation theory, and so recover existing quantum-mechanical technology such as the two-potential formalism for the treatment of the Coulomb-nuclear interference. Meanwhile the strong interactions and the E1 operator are dealt with via EFT expansions in powers of momenta, with a breakdown scale set by the size of the ${}^7$Be core, $\Lambda \approx 70$ MeV. Up to NLO the relevant physics in the different channels that enter the radiative capture reaction is encoded in ten different EFT couplings. The result is a model-independent parametrization for the reaction amplitude in the energy regime of interest. To show the connection to previous results we fix the EFT couplings using results from a number of potential model and microscopic calculations in the literature. Each of these models corresponds to a particular point in the space of EFTs. The EFT structure therefore provides a very general way to quantify the model uncertainty in calculations of ${}^7\mathrm{Be}(p,\gamma {)}^8\mathrm{B}$. We also demonstrate that the only N${}^2$LO corrections in ${}^7\mathrm{Be}(p,\gamma {)}^8\mathrm{B}$ come from an inelasticity that is practically of N${}^3$LO size in the energy range of interest, and so the truncation error in our calculation is effectively N${}^3$LO. We also discuss the relation of our extrapolated $S(0)$ to the previous standard evaluation.

68 pages, 10 figures, and 4 tables

References in corpus (7)

• Effective field theory description of halo nuclei
• alpha-alpha Scattering in Halo Effective Field Theory
• Universal properties and structure of halo nuclei
• Asymptotic normalization coefficients from ab initio calculations
• Radiative Neutron Capture on Lithium-7
• Causality constraints for charged particles
• Constraining Low-Energy Proton Capture on Beryllium-7 through Charge Radius Measurements

Cited by in corpus (11)

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• Solar fusion III: New data and theory for hydrogen-burning stars
• Ab initio informed evaluation of the radiative capture of protons on ${}^7$Be
• New Results for the p7Be-->8Bgamma Astrophysical S-factor from 10 keV to 5 MeV and Reactions Rate from 0.01 to 10 T9
• Coupled-channels treatment of ${}^7\mathrm{Be}(p,\gamma {)}^8\mathrm{B}$ in effective field theory
• Radiative proton capture on ${}^{15}\mathrm{N}$ within effective field theory
• Finite-Size Effects in Heavy Halo Nuclei from Effective Field Theory
• Non-Hermitian quantum mechanics approach for extracting and emulating continuum physics based on bound-state-like calculations: Detailed description
• A study of the fine-structure constant dependence of radiative capture in Halo-EFT