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

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 Schrodinger 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.