Open AccessExploiting Dirac equations solution for exact integral calculations in processes of muonic atoms
Author(s) -
P. G. Giannaka,
Odysseas Kosmas,
Ioannis G. Tsoulos,
T. S. Kosmas
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1730/1/012140
Subject(s) - muon , wave function , physics , dirac (video compression format) , dirac equation , exotic atom , quantum , gauss , quantum mechanics , neutrino
Precise muon wave functions are calculated by solving the Dirac equations within a method based on modern neural networks and stochastic optimization techniques. The reduced radial wave functions (up and bottom) of a bound muon in muonic atoms are then given as linear combinations of the well behaved sigmoid functions. As concrete applications, the known muonnucleus overlap integrals, which determine the structure and evolution of muonic atoms (twobody quantum systems bound together due to the fundamental electromagnetic interactions), may accurately be calculated. In this work, the muon-nucleus integrals for a set of nuclei including the 28 Si and 64 Zn entering the ordinary muon capture rates are exactly obtained through numerical integrations using Gauss integration algorithms.