Regular Article

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

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

^a e-mail: felipeoak91@gmail.com

Received: 3 September 2020
Accepted: 5 October 2020
Published online: 8 December 2020

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.