II. RELATIVISTIC THEORY OF THE NUCLEAR RECOIL EFFECT A. Basic formulas Since the electron mass is small compared to the nucleus mass, most of the contributions to the binding energies can be evaluated within the infinite nuclear mass approximation. Taking into account a finite nuclear mass shifts the energies. This is so called nuclear recoil effect. Since this effect is different for different isotopes, it also results in an isotope shift of the energy levels. Generally, the isotope shift arises as a sum of the finite nuclear mass effect (mass shift) and a non-zero nuclear size effect (field shift). In this section we focus on calculations of the mass shift in Li-like ions. In the nonrelativistic theory the mass shift (MS) is usually represented as a sum of the normal mass shift (NMS) and the specific mass shift (SMS), H (nonrel) M = H$_{NMS}$ + H$_{SMS}$ , where [27] Here, p$_{i}$ is the electron momentum operator and M is the nuclear mass. A rigorous relativistic theory of the mass shift can be formulated only in the framework of QED. Such a theory was formulated in Refs. [28, 29] (see also Refs. [30, 31] and references therein), where the complete αZ -dependent formulas for the recoil correction to the atomic energy levels to first order in m/M were derived. Within the Breit approximation this theory leads to the following many-body relativistic MS Hamiltonian: where α is a vector incorporating the Dirac matrices. An independent derivation of Hamil- tonian (2) was presented in Ref. [32]. As follows from expression (2), the lowest-order relativistic correction to the one-electron mass shift operator is given by H$_{NMS}$ = 1 2 M ∑ i p 2 $_{i}$, H$_{SMS}$ = 1 2 M i = j p$_{i}$ · p$_{j}$ . (1) H$_{M}$ = 1 2 M ∑ i,j { p$_{i}$ · p$_{j}$ − αZ r$_{i}$ [ α i + ( α i · r$_{i}$ ) r$_{i}$ r 2 i ] · p$_{j}$ } , (2) H$_{RNMS}$ = − 1 2 M ∑ i αZ r$_{i}$ [ α i + ( α i · r$_{i}$ ) r$_{i}$ r 2 i ] · p$_{i}$ , (3) 4