Use the procedure of Example 8-3 to estimate the spin-orbit interaction energy in the n=2, l=1 state of a muonic atom, defined in Example 4-9.
Example 8-3. Estimate the magnitude of the orientational potential energy ΔE for the n=2, l=1 state of the hydrogen atom, to check whether it is of the same order of magnitude as the observed fine-structure splitting of the corresponding energy level. (There is no spin-orbit energy in the n=1 state, since for n=1 the only possible value for l is l=0, which means L=0.)
Example 4-9. A muonic atom contains a nucleus of charge Ze and a negative muon, μ^(-), moving about it. The μ^(-) is an elementary particle with charge -e and a mass that is 207 times as large as an electron mass.
(a) Calculate the muon-nucleus separation, D, of the first Bohr orbit of a muonic atom with Z=1.