γ  =  Sqrt[k^2 - α^2 Z^2]

eDirac[n_, 
        k_]  =  1/(α^2 Sqrt[
              1 +  α^2 Z^2 /(γ + n - 
                          k)^2])

enonrel  =  
      Normal[Simplify[Series[eDirac[n, k], {Z, 0, 6}] - 1/α^2, 
          Assumptions  ->  k > 0]]

enr[n1_, k1_]  =  enonrel

de   = 
      Expand[219474.6 ( enr[2, 2] - enr[2, 1]) /.  α ->  
            1/137.036]