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We have studied the break-up of accelerated hydrogen cluster ions passing through an argon gas target. The absolute dissociation cross section has been measured for a wide variety of H (odd masses only) cluster ions, with n between 5 and 23 and with projectile velocities ranging from 1.5 to 5 × 10 cm/s. We discuss the dissociation processes and the dependence of their cross-sections upon the cluster mass and velocity. [ABSTRACT FROM AUTHOR]