Proton–proton fusion in lattice effective field theory

Abstract

The proton-proton fusion rate is calculated at low energy in a lattice effective field theory (EFT) formulation. The strong and the Coulomb interactions are treated non-perturbatively at leading order in the EFT. The lattice results are shown to accurately describe the low energy cross section within the validity of the theory at energies relevant to solar physics. In prior works in the literature, Coulomb effects were generally not included in non-perturbative lattice calculations. Work presented here is of general interest in nuclear lattice EFT calculations that involve Coulomb effects at low energy. It complements recent developments of the adiabatic projection method for lattice calculations of nuclear reactions.

Ab initio alpha–alpha scattering

“…We use the formalism of lattice effective field theory [11][12][13][14] and make use of a technique for elastic scattering and inelastic reactions on the lattice called the adiabatic projection method [15][16][17][18][19]. In the following we present the first ab initio calculation of 4 He + 4 He scattering, going up to next-to-next-to-leading order in chiral effective field theory.…”

Ab initioCalculation of thenp→dγRadiative Capture Process

“…For the analogous weak interactions of multinucleon systems, considerably less is known from experiment but these processes are equally important. The weak two-nucleon interactions currently contribute the largest uncertainty in calculations of the rate for proton-proton fusion in the Sun [11][12][13][14][15][16][17], and in neutrino-disintegration of the deuteron [18], which is a critical process needed to disentangle solar neutrino oscillations. Given the phenomenological importance of electroweak interactions in light nuclei, direct determinations from the underlying theory of strong interaction, quantum chromodynamics (QCD), are fundamental to future theoretical progress.…”

Nucleon-deuteron scattering using the adiabatic projection method

“…For the general case see Ref. [15,23]. In our three-body system one ↑ and one ↓ fermions are bound together and make a dimer state.…”

“…[9,10] that would allow future studies involving nuclear clusters that necessarily involve the Coulomb repulsion. The lattice method for calculating nuclear reactions from an effective two-cluster Hamiltonian with an external electro-weak current in radiative neutron capture p(n, γ)d and proton-proton fusion p(p, e + ν e )d were also considered [14,15].…”