Reaction processes of muon-catalyzed fusion in the muonic molecule $ddμ$ studied with the tractable T-matrix model

Muon-catalyzed fusion has recently regained significant attention due to experimental and theoretical developments being performed. The present authors [Phys. Rev. C { 109} 054625 (2024)] proposed the tractable T-matrix model based on the Lippmann-Schwinger equation to approximate the elaborate two- and three-body coupled-channel (CC) calculations [Kamimura, Kino, and Yamashita, Phys. Rev. C { 107}, 034607 (2023)] for the nuclear reaction processes in the muonic molecule $dtμ$, (dtμ)J=0 →\!⁴ He + n + μ+ 17.6 \, MeV. % or (⁴ Heμ)ₙₗ + n + 17.6 \, MeV. The T-matrix model well reproduced almost all of the results generated by the CC work. In the present paper, we apply this model to the nuclear reaction processes in the $ddμ$ molecule, (ddμ)J=1 →\!³ He + n + μ+3.27 \, MeV or $t + p + μ+ 4.03 \,$ MeV, in which the fusion takes place via the p-wave d-d relative motion. Recently, significantly different p-wave astrophysical $S(E)$ factors of the reaction d + d →\!³ He + n or $t + p$ at E \! \! 1 keV to 1 MeV have been reported experimentally and theoretically by five groups. Employing many sets of nuclear interactions that can reproduce those five cases of p-wave $S(E)$ factors, we calculate the fusion rate of the (ddμ)J=1 molecule using three kinds of methods where results are consistent with each other. We also derive the ³ He-$μ$ sticking probability and the absolute values of the energy and momentum spectra of the emitted muon. The violation of charge symmetry in the p-wave d-d reaction and the $ddμ$ fusion reaction is discussed. Information on the emitted 2.45-MeV neutrons and 1 keV-dominant muons should be useful for the application of $ddμ$ fusion.