LAUSR

perpendicular (E⊥int) or parallel (E k int) to r, whereas α is the atomic polarizability and k0 1⁄4 2jE2 − E1j=ħc, where E2 − E1 1⁄4 E1=4 − E1 is the energy difference between the first two levels of hydrogen [1]. Given the different scaling for the retarded and nonretarded regimes, the authors interpreted this field-induced interaction as “dispersion.” In their Comment, Abrantes et al. [2] interpreted the results of Ref. [1] as a combination of dispersion and electrostatic interactions, employing a classical picture without referring to quantum electrodynamics (QED) used by Fiscelli et al. [1], who still argued in their Reply [3] that Eq. (1) corresponds to the dispersion interaction between fluctuating dipoles upon exchanging one virtual photon. By using second-order perturbation theory in QED with properly orthogonalized atomic states, we show that the resulting interaction between two hydrogen atoms in static fields corresponds to a field-induced electrostatic energy scaling as r−3 for any r. Our derivation settles recent conflicting discussions in Refs. [1–4] and proves that the QED second-order interaction between two atoms in static electric fields has a purely electrostatic origin. Unperturbed states in QED perturbation theory must satisfy the closure relation P n jnihnj 1⁄4 1 [5]. Following the approach of Ref. [1], we obtain the eigenstates of a twolevel hydrogen in the static field E as