In this work we study the radiative capture of He-3 on He-4 within the halo effective field theory (EFT) framework. At leading order the capture amplitude comprises the initial state s-wave strong and Coulomb interactions summed to all orders. At the same order in the expansion, leading two-body currents contribute as well. We find delicate cancelations between the various contributions, and the two-body current contributions can be replaced by appropriately enhancing the asymptotic normalizations of the Be-7 ground and first excited state wave functions. The next-to-leading order corrections come from the s-wave shape parameter and the pure Coulomb d-wave initial state interactions. We fit the EFT parameters to available scattering data and most recent capture data. Our zero-energy astrophysical S-factor estimate, S-34 similar to 0.55 keV b, is consistent within error bars with the average in the literature.

In this article we review the recent progress in radiative reaction calculations in halo effective field theory. We look at radiative capture and breakup processes that involve a halo nucleus with a single valence neutron or proton. Looking at Li-7(n,gamma)Li-8, C-14(n,gamma)C-15 and related reactions, the dominant source of theoretical uncertainty in sand p-wave halo nuclei reaction calculations is quantified in a model-independent framework. The analysis for neutron halos is extended to proton halo systems. The effective field theory results quantify which observable parameters of the strong interaction at low energy need to be determined more precisely for accurate cross-section calculations.

Elhatisari, Serdar
Lee, Dean
Rupak, Gautam
Epelbaum, Evgeny
Krebs, Hermann
Laehde, Timo A.
Luu, Thomas
Meissner, Ulf-G.

Processes such as the scattering of alpha particles (He-4), the triple-alpha reaction, and alpha capture play a major role in stellar nucleosynthesis. In particular, alpha capture on carbon determines the ratio of carbon to oxygen during helium burning, and affects subsequent carbon, neon, oxygen, and silicon burning stages. It also substantially affects models of thermonuclear type Ia supernovae, owing to carbon detonation in accreting carbon-oxygen white-dwarf stars(1-3). In these reactions, the accurate calculation of the elastic scattering of alpha particles and alpha-like nuclei-nuclei with even and equal numbers of protons and neutrons-is important for understanding background and resonant scattering contributions. First-principles calculations of processes involving alpha particles and alpha-like nuclei have so far been impractical, owing to the exponential growth of the number of computational operations with the number of particles. Here we describe an ab initio calculation of alpha-alpha scattering that uses lattice Monte Carlo simulations. We use lattice effective field theory to describe the low-energy interactions of protons and neutrons, and apply a technique called the 'adiabatic projection method' to reduce the eight-body system to a two-cluster system. We take advantage of the computational efficiency and the more favourable scaling with system size of auxiliary-field Monte Carlo simulations to compute an ab initio effective Hamiltonian for the two clusters. We find promising agreement between lattice results and experimental phase shifts for s-wave and d-wave scattering. The approximately quadratic scaling of computational operations with particle number suggests that it should be possible to compute alpha scattering and capture on carbon and oxygen in the near future. The methods described here can be applied to ultracold atomic few-body systems as well as to hadronic systems using lattice quantum chromodynamics to describe the interactions of quarks and gluons.

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. (C) 2014 The Authors. Published by Elsevier B. V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

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. (C) 2014 The Authors. Published by Elsevier B. V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Laehde, Timo A.
Epelbaum, Evgeny
Krebs, Hermann
Lee, Dean
Meissner, Ulf-G
Rupak, Gautam

Extrapolations in Euclidean time form a central part of nuclear lattice effective field theory (NLEFT) calculations using the projection Monte Carlo method, as the sign problem in many cases prevents simulations at large Euclidean time. We review the next-to-next-to-leading order NLEFT results for the alpha nuclei up to Si-28, with emphasis on the Euclidean time extrapolations, their expected accuracy and potential pitfalls. We also discuss possible avenues for improving the reliability of Euclidean time extrapolations in NLEFT.

We demonstrate and test the adiabatic projection method, a general new framework for calculating scattering and reactions on the lattice. The method is based upon calculating a low-energy effective theory for clusters which becomes exact in the limit of large Euclidean projection time. As a detailed example we calculate the adiabatic two-body Hamiltonian for elastic fermion-dimer scattering in lattice effective field theory. Our calculation corresponds to neutron-deuteron scattering in the spin-quartet channel at leading order in pionless effective field theory. We show that the spectrum of the adiabatic Hamiltonian reproduces the spectrum of the original Hamiltonian below the inelastic threshold to arbitrary accuracy. We also show that the calculated s -wave phase shift reproduces the known exact result in the continuum and infinite-volume limits. When extended to more than one scattering channel, the adiabatic projection method can be used to calculate inelastic reactions on the lattice in future work.

Thermodynamic properties of a Fermi system close to the unitarity limit, where the 2-body scattering length a approaches +/-infinity, are studied in the high temperature Boltzmann regime. For dilute systems the virial expansion coefficients in the Boltzmann regime are expected, from general arguments, to be universal. A model independent finite temperature T calculation of the third virial coefficient b3(T) is presented. At the unitarity limit, b3infinity approximately 1.11 is a universal number. The energy density up to the third virial expansion is derived. These calculations are of interest in dilute neutron matter and could be tested in current atomic experiments on dilute Fermi gases near the Feshbach resonance.

We extend chiral perturbation theory to include linear dependence on the lattice spacing a for the Wilson action. The perturbation theory is written as a double expansion in the small quark mass m q and lattice spacing a. We present formulas for the mass and decay constant of a flavor-nonsinglet meson in this scheme to order a and m q2. The extension to the partially quenched theory is also described

We derive an energy density functional for non-relativistic spin one-half fermions in the limit of a divergent two-body scattering length. Using an epsilon expansion around d = 4 - epsilon spatial dimensions we compute the coefficient of the leading correction beyond the local density approximation (LDA). In the case of N fermionic atoms trapped in a harmonic potential this correction has the form E = E(LDA)(1 + c(s)(3N)(-2/3)), where E(LDA) is the total energy in LDA approximation. At next-to-leading order in the epsilon expansion we find c(s) = 1.68, which is significantly larger than the result for non-interacting fermions. c(s) = 0.5. (C) 2008 Elsevier B.V. All rights reserved.