  We have investigated the thermal conductivity \kappa_mag of high-purity
single crystals of the spin chain compound Sr2CuO3 which is considered an
excellent realization of the one-dimensional spin-1/2 antiferromagnetic
Heisenberg model. We find that the spinon heat conductivity \kappa_mag is
strongly enhanced as compared to previous results obtained on samples with
lower chemical purity. The analysis of \kappa_mag allows to compute the spinon
mean free path l_mag as a function of temperature. At low-temperature we find
l_mag\sim0.5\mum, corresponding to more than 1200 chain unit cells. Upon
increasing the temperature, the mean free path decreases strongly and
approaches an exponential decay ~1/T*exp(T*/T) which is characteristic for
umklapp processes with the energy scale k_B T*. Based on Matthiesen's rule we
decompose l_mag into a temperature-independent spinon-defect scattering length
l0 and a temperature dependent spinon-phonon scattering length l_sp(T). By
comparing l_mag(T) of Sr2CuO3 with that of SrCuO2, we show that the spin-phonon
interaction, as expressed by l_sp is practically the same in both systems. The
comparison of the empirically derived l_sp with model calculations for the
spin-phonon interaction of the one-dimensional spin-1/2 XY model yields
reasonable agreement with the experimental data.
