Calculation of Higher-Order Foldy-Wouthuysen Transformation Hamiltonian

The Foldy–Wouthuysen Hamiltonian of a light atomic system that has an mα⁸ contribution to energy levels is calculated. The case of a Dirac–Coulomb field is discussed. The results can be used for relativistic and radiative corrections to energy levels in the low-energy part. A divergent operator δ²(r) emerges. This is probably due to the nature of the point-like charge source. The effective method of radiation calculation may be re-checked.