We report measurements of the cross sections σ_{l-mix} for angular momentum mixing of the K(n^{2}F)(n=6, 7, 8) states with the K(n,l > 3) states, induced in thermal collisions with parent ground state K(4^{2}S) atoms. The experiment was performed in a cell heated to ca. 450K. The n^{2}F states were excited in two steps: 4^{2}S → 4^{2}P → n^{2F} by using a diode laser for the first step (a dipole-transition) and a pulsed dye laser for the second step (a quadrupole-transition). The measured values σ_{l-mix} (6^{2}F)=3.6+-2.2, σ_{l-mix} (7^{2}F)=4.2+-2.6 and σ_{l-mix} (8^{2}F)=8.0+-4.6 (in units of 10^{-13}cm^{-1}) are close to the corresponding values of the geometrical cross sections.
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