Hyperfine splitting in the ground states of the lithium-muonic ions and in the 2S3 states of the lithium-muonic atoms

The hyperfine splittings in the ground 1S1(L=0) electronic states of the lithium-muonic ions Li3+6μ−e− and Li3+7μ−e− and in the triplet (electronic) 2S3(L=0) states of the lithium-muonic atoms Li3+6μ−e2− and Li3+7μ−e2− are determined numerically with the use of highly accurate variational wave functions. The three-body lithium-muonic ions (Li3+6μ−e− and Li3+7μ−e−) and triplet states in the four-body lithium-muonic atoms (Li3+6μ−e2− and Li3+7μ−e2−) have been found to be very promising systems to study the hyperfine splitting in atom-muonic systems. The hyperfine splitting in the helium-muonic and beryllium-muonic atoms are also briefly discussed.