Neutrons from Negative-Muon Capture

Average neutron-emission and neutron-multiplicity distributions from ${\mu }^{-}$ capture in Al, Si, Ca, Fe, Ag, I, Au, and Pb were measured. A high-efficiency (54.5% for fission neutrons) cadmium-loaded liquid-scintillator tank was used as the neutron detector. Simple nuclear models with Fermi-gas and Gaussian nucleon-momentum distributions were used to fit the experimental results. A reduced nucleon effective mass was employed to yield the observed average neutron multiplicity, and values were obtained as a function of the width of the assumed nucleon-momentum distributions. Use of the Gaussian momentum distribution obtained in experiments on quasi-elastic scattering gives effective masses ranging from ≅0.7 $M_p$ in the lighter nuclei to ≅0.45 $M_p$ in the heavier nuclei. An excited-Fermi-gas distribution gives larger effective masses for the lighter nuclei and smaller effective masses for the heavier nuclei than does the Gaussian model. Neither of these models gives good agreement with the neutron-multiplicity distributions, although calculations in which direct neutron emission and nucleon clustering on the nuclear surface are assumed improve the fit. For both the Fermi-gas and Gaussian models, the average nuclear excitation energy varies linearly with average neutron multiplicity and is relatively insensitive to the model parameters. When the average nuclear excitation is expressed in units of the muon mass reduced by its $K$-shell binding energy, the result (with the exception of calcium) is constant, 0.18±0.01, over the wide range of atomic numbers covered in the experiment. For ${\mathrm{Ca}}^{40}$ we also made a shell-model calculation using a simple harmonic-oscillator potential. The agreement with the observed average neutron multiplicity is good although perhaps fortuitous.