Reaction processes of muon-catalyzed fusion in the muonic molecule $ddμ$ studied with the tractable $T$-matrix model
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2025
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| author | Wu, Qian Cui, Zhu-Fang Kamimura, Masayasu |
| author_facet | Wu, Qian Cui, Zhu-Fang Kamimura, Masayasu |
| contents | Muon-catalyzed fusion has recently regained significant attention due to experimental and theoretical developments being performed. The present authors [Phys. Rev. C {\bf 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 {\bf 107}, 034607 (2023)] for the nuclear reaction processes in the muonic molecule $dtμ$, $(dtμ)_{J=0} \to\!^4{\rm He} + n + μ+ 17.6 \, {\rm MeV}$. % or $(^4{\rm He}μ)_{nl} + n + 17.6 \,{\rm MeV}$. 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, $(ddμ)_{J=1} \to\!^3{\rm He} + n + μ+3.27 \,$ 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 $d + d \to\!^3{\rm He} + n$ or $t + p$ at $E \! \simeq \! 1$ 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 $^3{\rm He}$-$μ$ 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 \mbox{1 keV-dominant} muons should be useful for the application of $ddμ$ fusion. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_12783 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reaction processes of muon-catalyzed fusion in the muonic molecule $ddμ$ studied with the tractable $T$-matrix model Wu, Qian Cui, Zhu-Fang Kamimura, Masayasu Nuclear Theory Nuclear Experiment Atomic Physics Muon-catalyzed fusion has recently regained significant attention due to experimental and theoretical developments being performed. The present authors [Phys. Rev. C {\bf 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 {\bf 107}, 034607 (2023)] for the nuclear reaction processes in the muonic molecule $dtμ$, $(dtμ)_{J=0} \to\!^4{\rm He} + n + μ+ 17.6 \, {\rm MeV}$. % or $(^4{\rm He}μ)_{nl} + n + 17.6 \,{\rm MeV}$. 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, $(ddμ)_{J=1} \to\!^3{\rm He} + n + μ+3.27 \,$ 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 $d + d \to\!^3{\rm He} + n$ or $t + p$ at $E \! \simeq \! 1$ 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 $^3{\rm He}$-$μ$ 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 \mbox{1 keV-dominant} muons should be useful for the application of $ddμ$ fusion. |
| title | Reaction processes of muon-catalyzed fusion in the muonic molecule $ddμ$ studied with the tractable $T$-matrix model |
| topic | Nuclear Theory Nuclear Experiment Atomic Physics |
| url | https://arxiv.org/abs/2508.12783 |