The total cross section for radiative neutron capture on a proton, np → dγ , is evaluated at big-bang nucleosynthesis (BBN) energies. The electromagnetic transition amplitudes are calculated up to next-to-leadingorder within the framework of pionless effective field theory with dibaryon fields. We also calculate the dγ → np cross section and the photon analyzing power for the d γ → np process from the amplitudes. The values of low-energy constants that appear in the amplitudes are estimated by a Markov Chain Monte Carlo analysis using the relevant low-energy experimental data. Our result agrees well with those of other theoretical calculations except for the np → dγ cross section at some energies estimated by an R-matrix analysis. We also study the uncertainties in our estimation of the np → dγ cross section at relevant BBN energies and find that the estimated cross section is reliable to within ∼1% error.

Background: The explicit density dependence in the coupling coefficients entering the nonrelativistic nuclear energy-density functional (EDF) is understood to encode effects of three-nucleon forces and dynamical correlations. The necessity for the density-dependent coupling coefficients to assume the form of a preferrably small fractional power of the density ρ is empirical and the power is often chosen arbitrarily. Consequently, precision-oriented parameterisations risk overfitting in the regime of saturation and extrapolations in dilute or dense matter may lose predictive power. Purpose: Beginning with the observation that the Fermi momentum kF , i.e., the cubic root of the density, is a key variable in the description of Fermi systems, we first wish to examine if a power hierarchy in a kF expansion can be inferred from the properties of homogeneous matter in a domain of densities which is relevant for nuclear structure and neutron stars. For subsequent applications we want to determine a functional that is of good quality but not overtrained. Method: For the EDF, we fit systematically polynomial and other functions of ρ 1/3 to existing microscopic, variational calculations of the energy of symmetric and pure neutron matter (pseudodata) and analyze the behavior of the fits. We select a form and a set of parameters which we found robust and examine the parameters' naturalness and the quality of resulting extrapolations. Results: A statistical analysis confirms that low-order terms such as ρ 1/3 and ρ 2/3 are the most relevant ones in the nuclear EDF beyond lowest order. It also hints at a different power hierarchy for symmetric vs. pure nutron matter, supporting the need for more than one density-dependent terms in non-relativistic EDFs. The functional we propose easily accommodates known or adopted properties of nuclear matter near saturation. More importantly, upon extrapolation to dilute or asymmetric matter, it reproduces a range of existing microscopic results, to which it has not been fitted. It also predicts a neutron-star mass-radius relation consistent with observations. The coefficients display naturalness. Prospects: Having been already determined for homogeneous matter, a functional of the present form can be mapped onto extended Skyrme-type functionals in a straightforward manner, as we outline here, for applications to finite nuclei. At the same time, the statistical analysis can be extended to higher orders and for different microscopic (ab initio) calculations with sufficient pseudodata points and for polarized matter.

The proton-proton fusion reaction, pp → de + ν, is studied in pionless effective field theory (EFT) with di-baryon fields up to next-to leading order. With the aid of the di-baryon fields, the effective range corrections are naturally resummed up to the infinite order and thus the calculation is greatly simplified. Furthermore, the low-energy constant which appears in the axial-current-di-baryon-di-baryon contact vertex is fixed through the ratio of two-and one-body matrix elements which reproduces the tritium lifetime very precisely. As a result we can perform a parameter free calculation for the process. We compare our numerical result with those from the accurate potential model and previous pionless EFT calculations, and find a good agreement within the accuracy better than 1%. PACS IntroductionThe proton-proton fusion process, pp → de + ν e , is a fundamental reaction for the nuclear astrophysics, especially important for the understanding of the star evolutions [1] and solar neutrinos [2,3,4]. However, the process has never been studied experimentally because the event is extremely unlikely to take place in the laboratory at the proton energies in the sun. The calculation of the transition rate and its uncertainty has naturally become a challenge to nuclear theory. The first calculation of the process was carried out by Bethe and Critchfield [5] in 1938. This estimation was improved by Salpeter [6] 2 in 1952. Later, small corrections, such as the electromagnetic radiative corrections, were considered by Bahcall and his collaborators [8,9] in the framework of effective range theory. Recently, accurate phenomenological potential models were employed to study the process [10,11]. Furthermore, in Ref.[12] the two-nucleon current operators were calculated from heavybaryon chiral perturbation theory (HBχPT) up to next-to-next-to-next-to leading order (N 3 LO), and Park et al. obtained quite an accurate estimation (∼ 0.3% uncertaity) for the process by fixing an unknown parameter, so-called low energy constant (LEC), which appears in the two-nucleon-axial-current contact interaction in terms of the tritium lifetime [13,14].The kinetic energy relevant to the pp fusion process at the core of the sun is quite low, kT c ≃ 1.18 keV, where T c is the core temperature of the sun, T c ≃ 13.7 × 10 6 K, and k is the Boltzmann constant. The proton momentum at the core, p c ≃ 2m p kT c ≃ 1.5 MeV, where m p is the proton mass, is still significantly small compared to the pion mass, m π ≃ 140 MeV. Therefore, we may regard the pion as a heavy degree of freedom for the pp fusion process. It may be convenient and suitable to employ a pionless effective field theory (EFT) [15], in which the pions are integrated out of the effective Lagrangian for the process in question. The pp fusion process in the pionless theory has been studied by Kong and Ravndal [16] up to next-to leading order (NLO) and by Butler and Chen [17] up to fifth order (N 4 LO). Thanks to the perturbative scheme in EFT, the accuracy of the N 4 LO calculation w...

Pionless effective field theory with dibaryon fields is reexamined for observables involving the deuteron. The electromagnetic form factors of the deuteron and the total cross section of radiative neutron capture on the proton, n p → d γ, are calculated. The low energy constants of vector(photon)-dibaryon-dibaryon vertices in the effective lagrangian are fixed primarily by the one-body vector(photon)-nucleon-nucleon interactions. This scheme for fixing the values of the low energy constants satisfactorily reproduces the results of the effective range theory. We also show that, by including higher order corrections, one can obtain results that are close to those of Argonne v18 potential model. PACS: 25.10.+s, 25.30.Bf, 25.40 IntroductionEffective field theory (EFT) has proven to provide a useful tool for describing a wide class of meson-meson, meson-nucleon, and nucleon-nucleon (NN) processes with and without external probes in the low energy regime [1]. However, special care for the NN processes is required to deal with the 1 S 0 channel for its long scattering length (or existence of a quasi bound state) and the 3 S 1 − 3 D 1 channel for existence of the deuteron. In general, EFT is based on the perturbative expansion of physical observables in terms of small external momenta, but a non-perturbative treatment would be required for positions of the singularity at the small energy scales, which associated with the long scattering length and the small binding energy, compared to the chiral symmetry breaking scale, pion mass m π .3 To deal with the problem, Weinberg has suggested counting rules that allow one to handle this non-perturbative problem and derive the NN potential systematically [3]. With the potential calculated to a given order, the S-matrix is calculated from a wave function obtained by solving the Schrödinger equation. This scheme has shown good accuracy and convergence with only a few leading terms [4,5,6,7]. Kaplan, Savage, and Wise (KSW) suggested new counting rules, in which pions are treated perturbatively and do not appear in leading order (LO). They also employed the power divergence subtraction scheme for regularization [8]. Only a LO contact two-nucleon interaction is treated nonperturbatively and thus physical observables can be directly calculated from Feynman diagrams expanded order by order. Over the last decade both the Weinberg and KSW schemes have been used extensively in studying few-nucleon systems.4 For reviews, see, e.g., Refs.[10] and [11].Convergence of deuteron observables becomes slow near the deuteron pole due to a large expansion parameter γ ρ d ≃ 0.4, where γ ≃ 45.7 MeV and ρ d ≃ 1.764 fm in the KSW scheme. This would be a typical expansion parameter of the deuteron channel both in pionless effective field theory (pionless EFT) [12,13], where the pions are regarded as heavy degrees of freedom in study of very low energy reactions and integrated out from effective lagrangian, and in theories that treat pions perturbatively. It was suggested, however, that adjusting the de...