(received ; accepted ) PACS. 74.20F g -BCS theory and its development. PACS. 71.70Ej -Spin-orbit coupling, Zeeman and Stark splitting. PACS. 74.62Dh -Effects of crystal defects, doping and substitution.Abstract. -When non-magnetic impurities are introduced in a d-wave superconductor, both thermodynamic and spectral properties are strongly affected if the impurity potential is close to the strong resonance limit. In addition to the scalar impurity potential, the charge carriers are also spin-orbit coupled to the impurities. Here it is shown that (i) close to the unitarity limit for the impurity scattering, the spin-orbit contribution is of the same order of magnitude than the scalar scattering and cannot be neglected, (ii) the spin-orbit scattering is pair-breaking and (iii) induces a small idxy component to the off-diagonal part of the self-energy.In high-T c superconductors, disorder has important effects on both thermodynamic and spectral properties. The critical temperature T c and the superfluid density ρ s are lowered by non-magnetic impurity substitution [1,2,3,4] and disorder induced by irradiation [5,6]. Recent ARPES data show clearly how disorder leads to a redistribution of spectral intensity by adding new states at the Fermi level [6]. The basic elements of the current theory have been inspired by previous studies on heavy fermion superconductors and are given by the anisotropy of the order parameter and the strong resonance limit for the impurity potential [7,8]. These elements, adjusted to describe condensates with a d-wave symmetry of the order parameter, are able to account for most of the features observed by experiments on high-T c d-wave superconductors [9,10,11]. However, discrepancies still exist, like the overestimation of the T c -suppression [12]. In order to correct this situation, and to provide a more realistic picture, several improvements of the theory have been proposed [13,14,15], and, recently, the effect of spatial variation of the order parameter has been taken into account [12,16,17].In addition to the scalar impurity potential, the charge carriers are also spin-orbit coupled to the impurities. So far, this additional scattering channel has not been considered because the spin-orbit interaction is believed to provide, if any, only negligible effects (at least in the absence of a Zeeman magnetic field). This argument is based on the observation that the spin-orbit potential is of order v so ∼ ∆g v where v is the impurity potential and ∆g is the shift of the g-factor [18]. The value of ∆g depends on the specific impurity, however its order of magnitude is roughly ∆g ≃ 0.1. From this estimate, it is expected therefore that the spin-orbit scattering rate 1/τ so ≃ N 0 v 2 so , where N 0 is the charge carriers density of Typeset using EURO-L a T E X