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A bidimensional quasi-adiabatic model for muon-catalyzed fusion in muonic hydrogen molecules

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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.

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Authors and Affiliations

  1. Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud, 150, 22290-180, Urca, Rio de Janeiro, RJ, Brazil

    Francisco Caruso & Amos Troper

  2. Instituto de Físicas Armando Dias Tavares, Universidade do Estado do Rio de Janeiro, Rua São Francisco Xavier, 524, 20550-900, Maracanã, Rio de Janeiro, RJ, Brazil

    Vitor Oguri & Felipe Silveira

Authors
  1. Francisco Caruso
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  2. Amos Troper
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  3. Vitor Oguri
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  4. Felipe Silveira
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Correspondence to Felipe Silveira.

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Caruso, F., Troper, A., Oguri, V. et al. A bidimensional quasi-adiabatic model for muon-catalyzed fusion in muonic hydrogen molecules. Eur. Phys. J. D 74, 240 (2020). https://doi.org/10.1140/epjd/e2020-10479-6

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