Muon capture on ${}^3\mathrm{H}$

The ${\mu }^{-}+{}^3\mathrm{H}\to {\nu }_{\mu }+n+n+n$ capture reaction is studied under full inclusion of final-state interactions. Predictions for the three-body breakup of ${}^3\mathrm{H}$ are calculated with the AV18 potential, augmented by the Urbana IX three-nucleon force. Our results are based on the single-nucleon weak-current operator comprising the dominant relativistic corrections. This work is a natural extension of our investigations of the ${\mu }^{-}+{}^3\mathrm{He}\to {\nu }_{\mu }+{}^3\mathrm{H},{\mu }^{-}+{}^3\mathrm{He}\to {\nu }_{\mu }+n+d$ and ${\mu }^{-}+{}^3\mathrm{He}\to {\nu }_{\mu }+n+n+p$ capture reactions presented in Golak et al. [J. Golak, R. Skibiński, H. Witała, K. Topolnicki, A. E. Elmeshneb, H. Kamada, A. Nogga, and L. E. Marcucci, Phys. Rev. C 90, 024001 (2014)].

Figure 1

The kinematically allowed region in the $E_{\nu }-E_n$ plane calculated relativistically (solid curve) and nonrelativistically (dashed curve) for the ${\mu }^{-}+{}^3\mathrm{H}\to {\nu }_{\mu }+n+n+n$ process.

Figure 2

The differential capture rates ($F=0$) ${d\mathrm{\Gamma }}^{F=0}/d{E}_{\nu }$ (a), ($F=1$) ${d\mathrm{\Gamma }}^{F=1}/d{E}_{\nu }$ (b), and (total) $d\mathrm{\Gamma }/d{E}_{\nu }$ (c) for the ${\mu }^{-}+{}^3\mathrm{H}\to {\nu }_{\mu }+n+n+n$ process calculated with the single-nucleon current operator without (dashed line) and with (solid line) relativistic corrections. The calculations are based on the AV18 nucleon-nucleon potential [21] only.

Figure 3

The differential capture rates ($F=0$) ${d\mathrm{\Gamma }}^{F=0}/d{E}_{\nu }$ (a), ($F=1$) ${d\mathrm{\Gamma }}^{F=1}/d{E}_{\nu }$ (b), and (total) $d\mathrm{\Gamma }/d{E}_{\nu }$ (c) for the ${\mu }^{-}+{}^3\mathrm{H}\to {\nu }_{\mu }+n+n+n$ process calculated with the single-nucleon current operator including relativistic corrections and different types of $3\mathrm{N}$ dynamics: (symmetrized) plane wave (dotted curve), with total omission of the $3\mathrm{N}$ force (dashed curve) and with consistent inclusion of the $2\mathrm{N}$ and $3\mathrm{N}$ forces (solid curve). The calculations are based on the AV18 nucleon-nucleon potential [21] and the Urbana IX $3\mathrm{N}$ force [22].

Figure 4

The $3\mathrm{N}$ force effects in the differential capture rates ($F=0$) ${d\mathrm{\Gamma }}^{F=0}/d{E}_{\nu }$ (a), ($F=1$) ${d\mathrm{\Gamma }}^{F=1}/d{E}_{\nu }$ (b), and (total) $d\mathrm{\Gamma }/d{E}_{\nu }$ (c) calculated without the $3\mathrm{N}$ force (dash-dotted line), including the $3\mathrm{N}$ force only in the initial state (dotted line), only in the final state (dashed line), and with the $3\mathrm{N}$ forces taken consistently in the initial and final states (solid line). The dash-dotted and dashed lines overlap. The same is true for the dotted and solid lines.

Figure 5

The differential capture rates ($F=0$) $\langle {d\mathrm{\Gamma }}^{F=0}/d{E}_n\rangle$ (top panels), ($F=1$) $\langle {d\mathrm{\Gamma }}^{F=1}/d{E}_n\rangle$ (middle panels), and (total) $\langle d\mathrm{\Gamma }/d{E}_n\rangle$ (bottom panels), for the ${\mu }^{-}+{}^3\mathrm{H}\to {\nu }_{\mu }+n+n+n$ process averaged over 5-MeV neutron energy bins. The same results are shown on a linear scale (left panels) and a logarithmic scale (right panels). The predictions are obtained using the full solution of Eq. (2.22). The three overlapping curves represent results where the energies of nucleon 1 (solid line), nucleon 2 (dashed line), and nucleon 3 (dotted line) are considered.

Figure 6

The same as in Fig. 5 but the capture rates are averaged over 2-MeV neutron energy bins.