Abstract

A two-dimensional model for muonic molecules with nuclei composed of proton-proton, deuterium-deuterium, and tritium-tritium is proposed and solved. The effective molecular potential is analytically calculated within a quasi-adiabatic approximation. The molecular wave-functions and energies involved in the elementary process of muon-catalyzed nuclear fusion described by a Schrödinger equation were numerically calculated. Predictions are compared with three-dimensional results, showing that the dimensionality of space and the choice of potential energy have a great influence on some parameters used to calculate the probability of nuclear fusion. In particular, a 10⁹ times greater probability was found for the ttμ molecule compared to the prediction in three-dimensions. Finally, we conclude that, from the theoretical point of view, these results highlight the distinguished role of the ``centrifugal potential’’ in the 2D effective potential, showing that the geometrical nature of planar space plays a quite relevant role in s-state muonic molecules in two spatial dimensions.

Graphical abstract

中文翻译：

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介子氢分子中介子催化融合的二维拟绝热模型

摘要

提出并求解了具有质子-质子，氘-氘和tri- composed组成的核子的分子离子的二维模型。在准绝热近似中通过分析计算有效分子势。数值计算了薛定ding方程描述的介子催化核聚变基本过程中涉及的分子波函数和能量。将预测结果与三维结果进行了比较，表明空间的维数和势能的选择对用于计算核聚变概率的某些参数有很大的影响。特别是，发现ttμ的概率大10 ⁹倍分子与三维预测相比。最后，我们得出结论，从理论角度来看，这些结果突出了``离心势''在二维有效势中的杰出作用，表明平面空间的几何性质在s状态中起着非常重要的作用在两个空间维度上的分子分子。

图形概要