2014/09/30 by L. E. Marcucci, R. Machleidt · 6 citations
Chemistry · Physics and Astronomy · #Advanced NMR Techniques and Applications #Atomic physics #Deuterium #Energy (signal processing) #Muon #Muon capture #Neutron #Nuclear physics #Nuclear physics research studies #Particle physics #Physics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Scattering #nucl-th
paper · pdf · doi:10.1103/physrevc.90.054001
published in Physical Review C 90(5) (American Institute of Physics) · 5 pages, 2 figures; revisited version accepted for publication on Phys. Rev. C
openalex publication_date 2014/11/07 · arxiv created 2014/11/12 · arxiv updated 2014/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Background: We consider the muon capture reaction \ensuremathμ^\ensuremath-+2H\ensuremath→\ensuremathν_\ensuremathμ+n+n, which presents a ``clean'' two-neutron (nn) system in the final state. We study here its capture rate in the doublet hyperfine initial state (\ensuremathΓD). The total capture rate for the muon capture \ensuremathμ^\ensuremath-+3He\ensuremath→\ensuremathν_\ensuremathμ+3H (\ensuremathΓ0) is also analyzed, although, in this case, the nn system is not so clean anymore.Purpose: We investigate whether \ensuremathΓD (and \ensuremathΓ0) could be sensitive to the nn S-wave scattering length (ann), and we check on the possibility to extract ann from an accurate measurement of \ensuremathΓD.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 \ensuremathΛ=500 MeV is used, but the low-energy constant (LEC) determining ann is varied so as to obtain ann=\ensuremath-18.95,\ensuremath-16.0,\ensuremath-22.0, and +18.22 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 cD and cE, present in the three-nucleon potential and axial-vector current (cD), are constrained to reproduce the A=3 binding energies and the triton Gamow-Teller matrix element.Results: The capture rate \ensuremathΓD is found to be 399(3)\phantom\rule0.28em0exs^\ensuremath-1 for ann=\ensuremath-18.95 and \ensuremath-16.0 fm; and 400(3)\phantom\rule0.28em0exs^\ensuremath-1 for ann=\ensuremath-22.0 fm. However, in the case of ann=+18.22 fm, the result of 275(3)\phantom\rule0.28em0exs^\ensuremath-1 [135(3)\phantom\rule0.28em0exs^\ensuremath-1] is obtained, when the di-neutron system in the final state is unbound (bound). The total capture rate \ensuremathΓ0 for muon capture on 3He is found to be 1494(15), 1491(16), 1488(18), and 1475(16) s^\ensuremath-1 for ann=\ensuremath-18.95,\ensuremath-16.0,\ensuremath-22.0, and +18.22 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 ann with an uncertainty of less than \ensuremath∼\ifmmode±\else\textpm\fi3 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 \ensuremathΓD. Finally, a comparison with the already available experimental data discourages the possibility of a bound di-neutron state (positive ann).