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Light-element reactions at low energies in the resolved resonance region are important for a range of applications in basic and applied sciences including nuclear reactors, nonproliferation, cultural heritage, forensics and environmental control, rare event investigations and nuclear astrophysics. In this paper, we report on an effort to evaluate charged-particle cross sections in the resolved resonance region and produce evaluated nuclear data files for further processing and inclusion in evaluated data libraries. We discuss the open issues in R-matrix calculations as we extend to higher energies, such as dealing with the rapidly growing number of open channels and merging with the regime of smooth cross sections described by the statistical model, and present attempts to address these issues in neutron-induced reactions relevant to nuclear reactor applications.

Unitarity, the mathematical expression of the conservation of probability in multichannel reactions, is an essential ingredient in the development of accurate nuclear reaction networks appropriate for nucleosynthesis in a variety of environments. We describe our ongoing program to develop a "unitary reaction network" for the big-bang nucleosynthesis environment and look at an example of the need and power of unitary parametrizations of nuclear scattering and reaction data. Recent attention has been focused on the possible role of the 9B compound nuclear system in the resonant destruction of 7Li during primordial nucleosynthesis. We have studied reactions in the 9B compound system with a multichannel, two-body unitary R-matrix code (EDA) using the known elastic and reaction data, in a four-channel treatment. The data include elastic 6Li(3He, 3He)6Li differential cross sections from 0.7 to 2.0 MeV, integrated reaction cross sections for energies from 0.7 to 5.0 MeV for 6Li(3He,p)8Be* and from 0.4 to 5.0 MeV for the 6Li(3He,d)7Be reaction. Capture data have been added to the previous analysis with integrated cross section measurements from 0.7 to 0.825 MeV for 6Li(3He,γ) 9B. The resulting resonance parameters are compared with tabulated values from TUNL Nuclear Data Group analyses. Previously unidentified resonances are noted and the relevance of this analysis and a unitary reaction network for big-bang nucleosynthesis are emphasized. © Owned by the authors, published by EDP Sciences, 2014.

We develop a resonance model of the transition matrix for three-body breakup reactions of the A = 6 system and present calculations for the nucleon observed spectra, which are important for inertial confinement fusion and Big Bang nucleosynthesis (BBN). The model is motivated by the Faddeev approach where the form of the T matrix is written as a sum of the distinct Jacobi coordinate systems corresponding to particle configurations (α, n-n) and (n; n-α) to describe the final state. The structure in the spectra comes from the resonances of the two-body subsystems of the three-body final state, namely the singlet (T = 1) nucleon-nucleon (NN) anti-bound resonance, and the Nα resonances designated the ground state (Jπ = 3−2${{{3^ - }} \over 2}$) and first excited state (Jπ = 1−2${{{1^ - }} \over 2}$) of the A = 5 systems 5He and 5Li. These resonances are described in terms of single-level, single-channel R-matrix parameters that are taken from analyses of NN and Nα scattering data. While the resonance parameters are approximately charge symmetric, external charge-dependent effects are included in the penetrabilities, shifts, and hard-sphere phases, and in the level energies to account for internal Coulomb differences. The shapes of the resonance contributions to the spectrum are fixed by other, two-body data and the only adjustable parameters in the model are the combinatorial amplitudes for the compound system. These are adjusted to reproduce the observed nucleon spectra from measurements at the Omega and NIF facilities. We perform a simultaneous, least-squares fit of the tt neutron spectra and the 3He3He proton spectra. Using these amplitudes we make a prediction of the α spectra for both reactions at low energies. Significant differences in the tt and 3He3He spectra are due to Coulomb effects.

We present an R-matrix-based model for three-body final states that has aspects of the Faddeev approach to three-particle scattering. The model is applied to describing the nucleon spectra for breakup reactions in the A = 6 systems. Calculations using a charge-symmetric parametrization agree fairly well with the experimental data, although they indicate larger contributions from the 5He or 5Li ground state are necessary.

Unitarity, the mathematical expression of the conservation of probability in multichannel reactions, is an essential ingredient in the development of accurate nuclear reaction networks appropriate for nucleosynthesis in a variety of environments. We describe our ongoing program to develop a “unitary reaction network” for the big-bang nucleosynthesis environment and look at an example of the need and power of unitary parametrizations of nuclear scattering and reaction data. Recent attention has been focused on the possible role of the 9B compound nuclear system in the resonant destruction of 7Li during primordial nucleosynthesis. We have studied reactions in the 9B compound system with a multichannel, two-body unitary R-matrix code (EDA) using the known elastic and reaction data, in a four-channel treatment. The data include elastic 6Li(3He,3He)6Li differential cross sections from 0.7 to 2.0 MeV, integrated reaction cross sections for energies from 0.7 to 5.0 MeV for 6Li(3He,p)8Be* and from 0.4 to 5.0 MeV for the 6Li(3He,d)7Be reaction. Capture data have been added to the previous analysis with integrated cross section measurements from 0.7 to 0.825 MeV for 6Li(3He,γ)9B. The resulting resonance parameters are compared with tabulated values from TUNL Nuclear Data Group analyses. Previously unidentified resonances are noted and the relevance of this analysis and a unitary reaction network for big-bang nucleosynthesis are emphasized.

We study the zero channel radius limit of Wigner's R-matrix theory for two cases and show that it corresponds to nonrelativistic effective quantum field theory. We begin with the simple problem of single-channel np elastic scattering in the ¹S0 channel. The dependence of the R-matrix width g² and level energy Eλ on the channel radius a for fixed scattering length a0 and effective range r0 is determined. It is shown that these quantities have a simple pole for a critical value of the channel radius, ap = ap(a0,r0). The ³H(d,n)4He reaction cross section, analyzed with a two-channel effective field theory in the previous paper [Phys. Rev. C 89, 014622 (2014)], is then examined using a two-channel, single-level R-matrix parametrization. The resulting S matrix is shown to be identical in these two representations in the limit that R-matrix channel radii are taken to zero. This equivalence is established by giving the relationship between the low-energy constants of the effective field theory (couplings gc and mass m...) and the R-matrix parameters (reduced width amplitudes γc and level energy Eλ). An excellent three-parameter fit to the observed astrophysical factor S is found for "unphysical" values of the reduced widths, γ²c < 0. [ABSTRACT FROM AUTHOR]

An effective, nonrelativistic quantum field theory for the dt → nα fusion reaction in the low-energy, resonance region is presented. The theory assumes that the reaction is dominated by an intermediate 5He* unstable spin-3/2+ resonance. It involves two parameters in the coupling of the dt and nα particles to the unstable resonant state and the resonance energy level--only three real parameters in all. All Coulomb corrections to this process are com-puted. The resultant field theory is exactly solvable and provides an excellent description of the dt fusion process. [ABSTRACT FROM AUTHOR]