\neq 4 c^2$. For purely electrostatic interactions the self-adjointness of $A_{\eta, 0}$ for critical $\eta = \pm 2 c$ was studied in [@BH17; @OV17] and some surprising spectral effects like possible appearance of additional essential spectrum were shown. Eventually, in [@HOP17] a detailed study of the spectral properties of $A_{0, \tau}$ for purely scalar potentials was provided; in particular, it was shown that the discrete eigenvalues in the large mass limit are characterized by an effective operator on the surface $\Sigma$. Furthermore, there is a great interest recently in the study of self-adjoint Dirac operators on domains with boundary conditions, see, e.g., [@ALTR17; @ALTMR18; @BFSB17_1; @BFSB17_2; @FS14; @LTO18; @LO18; @MOP18; @S95].

Our goal in this note is to extend many of the above mentioned results, which were shown for purely electrostatic or purely scalar interactions, to the more general case of combinations of electrostatic and scalar interactions. For that we use a uniform approach which is based on the considerations in [@BEHL17; @BH17]. After presenting some preliminary material on integral operators which are associated to the Green function of the resolvent of the free Dirac operator, we introduce in Section \[section\_self\_adjoint\] the operator $A_{\eta, \tau}$ in a mathematically rigorous way 