A semi-classical study of muon-enhanced proton-boron-11 fusion
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866913177935020032 |
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| author | Wang, Hong-Yi Chen, Ming-Yu Ma, Hao-Le Cui, Zhu-Fang |
| author_facet | Wang, Hong-Yi Chen, Ming-Yu Ma, Hao-Le Cui, Zhu-Fang |
| contents | A recent theoretical study has suggested that muons can enhance proton-boron-11 (p-$^{11}$B) reaction cross-section by several orders of magnitude in the low-energy regime. In this work, we investigate this reaction process using a semi-classical treatment, that is, a muon and a proton first form a muonic hydrogen atom p$μ$, which subsequently collides with a $^{11}$B nucleus. During the collision, the p$μ$ atom approaches the $^{11}$B nucleus and is then repelled by the Coulomb repulsive potential. At the distance of closest approach between the proton and the $^{11}$B nuclei in this classical scattering process -- namely, the classical turning point -- quantum tunneling through the Coulomb barrier can occur, allowing the proton to penetrate into the range of the nuclear force of the $^{11}$B and trigger the fusion reaction. We determine the turning point statistically by using the classical trajectory Monte Carlo method, where the initial phase-space distributions of the proton and muon are sampled from the ground-state microcanonical distribution. Our results show that, compared with the bare-nucleus case, the reaction cross-section is enhanced by several orders of magnitude in the low-energy region. A comparison with the static charge-shielding treatment reveals certain differences; however, both approaches demonstrate that the catalytic effect of the muon can significantly enhance the low-energy p-$^{11}$B reaction cross-section. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2606_01551 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A semi-classical study of muon-enhanced proton-boron-11 fusion Wang, Hong-Yi Chen, Ming-Yu Ma, Hao-Le Cui, Zhu-Fang Nuclear Theory Nuclear Experiment Plasma Physics A recent theoretical study has suggested that muons can enhance proton-boron-11 (p-$^{11}$B) reaction cross-section by several orders of magnitude in the low-energy regime. In this work, we investigate this reaction process using a semi-classical treatment, that is, a muon and a proton first form a muonic hydrogen atom p$μ$, which subsequently collides with a $^{11}$B nucleus. During the collision, the p$μ$ atom approaches the $^{11}$B nucleus and is then repelled by the Coulomb repulsive potential. At the distance of closest approach between the proton and the $^{11}$B nuclei in this classical scattering process -- namely, the classical turning point -- quantum tunneling through the Coulomb barrier can occur, allowing the proton to penetrate into the range of the nuclear force of the $^{11}$B and trigger the fusion reaction. We determine the turning point statistically by using the classical trajectory Monte Carlo method, where the initial phase-space distributions of the proton and muon are sampled from the ground-state microcanonical distribution. Our results show that, compared with the bare-nucleus case, the reaction cross-section is enhanced by several orders of magnitude in the low-energy region. A comparison with the static charge-shielding treatment reveals certain differences; however, both approaches demonstrate that the catalytic effect of the muon can significantly enhance the low-energy p-$^{11}$B reaction cross-section. |
| title | A semi-classical study of muon-enhanced proton-boron-11 fusion |
| topic | Nuclear Theory Nuclear Experiment Plasma Physics |
| url | https://arxiv.org/abs/2606.01551 |