Muon capture on deuteron andHe3

Abstract

The muon capture reactions 2 H(µ − , νµ)nn and 3 He(µ − , νµ) 3 H are studied with conventional or chiral realistic potentials and consistent weak currents. The initial and final A = 2 and 3 nuclear wave functions are obtained from the Argonne v18 or chiral N3LO two-nucleon potential, in combination with, respectively, the Urbana IX or chiral N2LO three-nucleon potential in the case of A = 3. The weak current consists of polar-and axial-vector components. The former are related to the isovector piece of the electromagnetic current via the conserved-vector-current hypothesis. These and the axial currents are derived either in a meson-exchange or in a chiral effective field theory (χEFT) framework. There is one parameter (either the N -to-∆ axial coupling constant in the meson-exchange model, or the strength of a contact term in the χEFT model) which is fixed by reproducing the Gamow-Teller matrix element in tritium β-decay. The model dependence relative to the adopted interactions and currents (and cutoff sensitivity in the χEFT currents) is weak, resulting in total rates of 392.0 ± 2.3 s −1 for A = 2, and 1484 ± 13 s −1 for A = 3, where the spread accounts for this model dependence.

Break-up channels in muon capture onHe3

“…In the hybrid χEFT approach, the weak operators were derived in χEFT, but their matrix elements were evaluated between wave functions obtained from conventional potentials. Typically, the potential model and hybrid χEFT predictions are in good agreement with each other [4]. Only very recently, the two reactions have been studied in a "non-hybrid" χEFT approach [8], where both potentials and currents are derived consistently in χEFT and the low-energy constants present in the 3N potential and two-body axial-vector current are constrained to reproduce the A = 3 binding energies and the Gamow-Teller matrix element in tritium β-decay.…”

“…More recent theoretical work, focused on the µ − + 2 H → ν µ + n + n and µ − + 3 He → ν µ + 3 H reactions, has been summarized in Refs. [4,5]. Here we mention only that the calculation of Ref.…”

“…[4]. We neglect as a first step meson-exchange currents and perform a systematic study of all the A = 2 and A = 3 muon capture reactions, extending the calculations of Ref.…”

“…Here we mention only that the calculation of Ref. [4], following the early steps of Ref. [6], was performed both in the phenomenological and the "hybrid" chiral effective field theory (χEFT) approach.…”

Muon capture on the deuteron and3He

“…The additional factor R accounts for the finite volume of the 3 He charge and we assume that R = 0.98 [7]. …”