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Low-energy dipole excitations are analyzed for the stable isotopes $^{40}$Caand $^{48}$Ca in the framework of the Skyrme-second random-phase approximation.The corresponding random-phase approximation calculations provide a negligiblestrength distribution for both nuclei in the energy region from 5 to 10 MeV.The inclusion and the coupling of 2 particle-2 hole configurations in thesecond random-phase approximation lead to an appreciable dipole response at lowenergies for the neutron-rich nucleus $^{48}$Ca. The presence of a neutron skinin the nucleus $^{48}$Ca would suggest the interpretation of the low-lyingresponse in terms of a pygmy excitation. The composition of the excitationmodes (content of 1 particle-1 hole and 2 particle-2 hole configurations),their transition densities and their collectivity (number and coherence of thedifferent contributions) are analyzed. This analysis indicates that, ingeneral, these excitations cannot be clearly interpreted in terms ofoscillations of the neutron skin against the core with the exception of thepeak with the largest $B(E1)$ value, which is located at 9.09 MeV. For thispeak the neutron transition density dominates and the neutron and protontransition densities oscillate out of phase in the internal part of the nucleusleading to a strong mixing of isoscalar and isovector components. Therefore,this state shows some features usually associated to pygmy resonances.

Low-lying dipole response in the stable $^{40,48}$Ca nuclei with the second random-phase approximation