Tractable $T$-matix model for reaction processes in muon catalyzed fusion $(dtμ)_{J=v=0} \to \; α+ n + μ+ 17.6\, {\rm MeV} \; \mbox{or} \; (αμ)_{nl} + n +17.6 \,{\rm MeV}$
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929417262989312 |
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| author | Wu, Qian Kamimura, Masayasu |
| author_facet | Wu, Qian Kamimura, Masayasu |
| contents | Reaction processes in muon catalyzed fusion ($μ$CF), $(dtμ)_{J=v=0} \to α+ n + μ+ 17.6\,{\rm MeV}\:$ or $ \;(αμ)_{nl} + n + 17.6\,{\rm MeV}$ in the D-T mixture was comprehensively studied by Kamimura, Kino and Yamashita [Phys. Rev. C 107, 034607 (2023)] by solving the $dtμ$-$αnμ$ coupled channel (CC) Schrödinger equation under a boundary condition where the muonic molecule $(dtμ)_{J=v=0}$ was set as the initial state and the outgoing wave was in the $αnμ$ channel. We approximate this CC framework and propose a considerably more tractable model using the $T$-matrix method based on the Lippmann-Schwinger equation. Nuclear interactions adopted in the $T$-matrix model are determined by reproducing the cross section of the reaction $d + t \to α+ n + 17.6\,{\rm MeV}$ at low energies. The cross section of the strong-coupling rearrangement reaction is presented in a simple closed form based on our new model. This $T$-matrix model have reproduced most of the calculated results on the above $μ$CF reaction reported by Kamimura et al. (2023) and is applicable to other $μ$CF systems such as $(ddμ)$, $(ttμ)$, $(dtμ)^*$, $(ddμ)^*$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_17358 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tractable $T$-matix model for reaction processes in muon catalyzed fusion $(dtμ)_{J=v=0} \to \; α+ n + μ+ 17.6\, {\rm MeV} \; \mbox{or} \; (αμ)_{nl} + n +17.6 \,{\rm MeV}$ Wu, Qian Kamimura, Masayasu Nuclear Theory Nuclear Experiment Atomic and Molecular Clusters Reaction processes in muon catalyzed fusion ($μ$CF), $(dtμ)_{J=v=0} \to α+ n + μ+ 17.6\,{\rm MeV}\:$ or $ \;(αμ)_{nl} + n + 17.6\,{\rm MeV}$ in the D-T mixture was comprehensively studied by Kamimura, Kino and Yamashita [Phys. Rev. C 107, 034607 (2023)] by solving the $dtμ$-$αnμ$ coupled channel (CC) Schrödinger equation under a boundary condition where the muonic molecule $(dtμ)_{J=v=0}$ was set as the initial state and the outgoing wave was in the $αnμ$ channel. We approximate this CC framework and propose a considerably more tractable model using the $T$-matrix method based on the Lippmann-Schwinger equation. Nuclear interactions adopted in the $T$-matrix model are determined by reproducing the cross section of the reaction $d + t \to α+ n + 17.6\,{\rm MeV}$ at low energies. The cross section of the strong-coupling rearrangement reaction is presented in a simple closed form based on our new model. This $T$-matrix model have reproduced most of the calculated results on the above $μ$CF reaction reported by Kamimura et al. (2023) and is applicable to other $μ$CF systems such as $(ddμ)$, $(ttμ)$, $(dtμ)^*$, $(ddμ)^*$. |
| title | Tractable $T$-matix model for reaction processes in muon catalyzed fusion $(dtμ)_{J=v=0} \to \; α+ n + μ+ 17.6\, {\rm MeV} \; \mbox{or} \; (αμ)_{nl} + n +17.6 \,{\rm MeV}$ |
| topic | Nuclear Theory Nuclear Experiment Atomic and Molecular Clusters |
| url | https://arxiv.org/abs/2401.17358 |