Modification of the superconducting order parameter $\Delta(k)$ by long-range interactions

It is demonstrated that the inclusion of long-range intersite interactions qualitatively modifies the dependence of a superconducting gap on quasimomentum for both $s$-and $d$-symmetry types. In particular, the order parameter of a superconducting phase with $d_{x^2-y^2}$ the symmetry type depends on two amplitudes and has the form $\Delta(k)= \Delta_1 (\cos{k_x}-\cos{k_y})+\Delta_2 (\cos{2k_x}-\cos{2k_y})$. In this case, the theoretical dependence of the critical temperature on the degree of doping agrees with the experimental dependence.