  The two-magnon (2M) excitation at 3000 cm-1 in Sr_14Cu_24O_41 two-leg ladder
is studied by Raman scattering. A slight anisotropy of the superexchange
coupling J_{\perp}/J_{||} \approx 0.8 with J_{||} = 110 \pm 20 meV is proposed
from the analysis of the magnetic scattering. The resonant coupling across the
charge transfer gap increases the 2M intensity by orders of magnitude. The
anisotropy of Raman scattering is dependent upon the excitation energy. The 2M
relaxation is found to be correlated with the temperature dependent electronic
Raman continuum at low frequencies.
