“…We insert the atom-field coupling into the above formula and retain only the leading-order chiral contributions which are due to cross-terms of electric-dipole and Röntgen couplings. Evaluating the matrix elements by means of the field expansions ( 2) and (3) and using the completeness relation (5), we find (7) with atomic transition frequencies ω nk = (E n − E k )/ , the electric dipole matrix elements d nk = n| d|k and the Cauchy principal value P. As a consistency check, we note that the above energy shift hence vanishes when (i) the dipole moments are linearly polarised (d nk = d kn ) and hence the atom does not exhibit handedness. Upon splitting the Green tensor G = G (0) + G (1) into its bulk and scattering parts G (0) and G (1) , respectively, the former does not contribute due to the symmetry G (0) (r, r ) = G (0) (r , r).…”