Periodic Solutions of the 4-Body Electromagnetic Problem and Application to Li Atom

The 4-body equations of motion are derived in our previously published paper. Here we prove the existence and uniqueness of a periodic solution by applying the fixed point method for a suitable introduced operator. A natural example of such a problem is the Lithium atom, which has three electrons orbiting the nucleus. The inequalities that ensure the existence of a periodic solution allow us to estimate the minimal distances between the electrons on the first and second Bohr-Sommerfeld stationary states.