Abstract
Background: We consider the muon capture reaction , which presents a “clean” two-neutron system in the final state. We study here its capture rate in the doublet hyperfine initial state . The total capture rate for the muon capture is also analyzed, although, in this case, the system is not so clean anymore.
Purpose: We investigate whether (and could be sensitive to the -wave scattering length , and we check on the possibility to extract from an accurate measurement of .
Method: The muon capture reactions are studied with nuclear potentials and charge-changing weak currents, derived within chiral effective field theory. The next-to-next-to-next-to-leading-order chiral potential with cutoff parameter MeV is used, but the low-energy constant (LEC) determining is varied so as to obtain , and fm. The first value is the present empirical one, while the last one is chosen such as to lead to a di-neutron bound system with a binding energy of 139 keV. The LEC's and , present in the three-nucleon potential and axial-vector current , are constrained to reproduce the binding energies and the triton Gamow-Teller matrix element.
Results: The capture rate is found to be for and fm; and for fm. However, in the case of fm, the result of is obtained, when the di-neutron system in the final state is unbound (bound). The total capture rate for muon capture on is found to be 1494(15), 1491(16), 1488(18), and 1475(16) for , and fm, respectively. All the theoretical uncertainties are due to the fitting procedure and radiative corrections.
Conclusions: Our results seem to exclude the possibility of constraining a negative with an uncertainty of less than fm through an accurate determination of the muon capture rates, but the uncertainty on the present empirical value will not complicate the interpretation of the (forthcoming) experimental results for . Finally, a comparison with the already available experimental data discourages the possibility of a bound di-neutron state (positive .
- Received 16 September 2014
DOI:https://doi.org/10.1103/PhysRevC.90.054001
©2014 American Physical Society