Muon capture on deuteron and 3He

TL;DR

This study calculates muon capture rates on deuteron and helium-3 using realistic nuclear potentials and consistent weak currents, showing weak model dependence and providing precise theoretical predictions.

Contribution

It introduces a comprehensive framework combining realistic nuclear potentials with chiral effective field theory for weak currents to accurately predict muon capture rates.

Findings

Capture rate on deuteron: 392.0 +/- 2.3 Hz

Capture rate on helium-3: 1484 +/- 13 Hz

Weak model dependence of results

Abstract

The muon capture reactions 2H(\mu^-,\nu_\mu)nn and 3He(\mu^-,\nu_\mu)3H 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 (chiEFT) framework. There is one parameter (either the N-to-\Delta axial coupling constant in the meson-exchange model, or the strength of a contact term in the chiEFT model) which is fixed by reproducing the Gamow-Teller matrix element in tritium beta-decay. The model dependence relative to the adopted interactions and currents (and cutoff sensitivity in the chiEFT currents) is weak, resulting in total rates of 392.0 +/- 2.3 Hz for A=2, and 1484 +/- 13 Hz for A=3, where the spread accounts for this model dependence.