  We investigate the isoscalar and isovector E1 response of neutron-rich
nuclei, within a semi-classical transport model employing effective
interactions for the nuclear mean-field. In particular, we adopt the recently
introduced SAMi-J Skyrme interactions, whose parameters are specifically tuned
to improve the description of spin-isospin properties of nuclei. Our analysis
evidences a relevant degree of isoscalar/isovector mixing of the collective
excitations developing in neutron-rich systems. Focusing on the low-lying
strength emerging in the isovector response, we show that this energy region
essentially corresponds to the excitation of isoscalar-like modes, which also
contribute to the isovector response owing to their mixed character.
Considering effective interactions which mostly differ in the isovector
channels, we observe that these mixing effects increase with the slope L of the
symmetry energy at saturation density, leading to a larger strength in the
low-energy region of the isovector response. This result appears connected to
the increase, with L, of the neutron/proton asymmetry at the surface of the
considered nuclei, i.e., to the extension of the neutron skin.
