Spectra for the A = 6 reactions calculated from a three-body resonance model

Theoretical Division (T-2), Los Alamos National Laboratory, Los Alamos NM 87545, USA

^a e-mail: mparis@lanl.gov
^b e-mail: ghale@lanl.gov

Published online: 21 June 2016

Abstract

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 (J^π = $$\frac{3^{-}}{2}$$) and first excited state (J^π = $$\frac{1^{-}}{2}$$) 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.