Magneto-transmission measurements in magnetic fields in the range B=20-60T have been performed to probe the H and K-point Landau level transitions in natural graphite. At the H-point, two series of transitions, whose energy evolves as $sqrt{B}$ are observed. A reduced Slonczewski, Weiss and McClure (SWM) model with only two parameters to describe the intra-layer (gamma0) and inter-layer (gamma1) coupling correctly describes all observed transitions. Polarization resolved measurements confirm that the observed apparent splitting of the H-point transitions at high magnetic field cannot be attributed to an asymmetry of the Dirac cone.
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