We present a two-beam mode-mismatched thermal lens method for pulse excitation aimed for the
determination of one- and two-photon absorption coefficient with high sensitivity. In this scheme the
excitation beam is focused onto the sample in the presence of a collimated CW probe light of low power. The
Z-scan signature is single peaked with a width that depends on the number of photons involved in the
absorption. We show that the method is at least two orders of magnitude more sensitive than the well-known
open Z-scan transmission method commonly used for multi-photon absorption measurement. Using the proposed method we measure a two photon absorption coefficient for nitrobenzene of β=1.12 10<sup>-10</sup> cm/W for nanosecond pulses and a wavelength of 532 nm.