Bound state properties and hyperfine splitting in the [formula omitted]-states of the lithium–muonic systems

Abstract

The bound state properties of the ground S ( L = 0 ) -states in the Li 3 + 6 μ − e − and Li 3 + 7 μ − e − lithium–muonic ions are determined numerically with the use of highly accurate variational wave functions. We also obtain the analogous bound state properties for the triplet (electronic) 2 S 3 ( L = 0 ) -states in the lithium–muonic atoms Li 3 + 6 μ − e 2 − and Li 3 + 7 μ − e 2 − . The hyperfine splitting in each of these three- and four-body lithium–muonic system is evaluated numerically. It is shown that the three-body lithium–muonic ions ( Li 3 + 6 μ − e − and Li 3 + 7 μ − e − ) and triplet states in the four-body lithium–muonic atoms ( Li 3 + 6 μ − e 2 − and Li 3 + 7 μ − e 2 − ) are very promising systems to study the hyperfine splitting.