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) ₉=₀ \!⁴ He + n + μ+ 17. 6 \, MeV. % or (⁴ Heμ) ₍₋ + 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) ₉=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) ₉=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.