Proton spin structure in the rest frame

It is shown that the quark-parton model in the standard infinite momentum approach overestimate the proton spin structure function $g_1(x)$ in comparison with the approach taking consistently into account the internal motion of quarks described by a spherical phase space in the proton rest frame. Particularly, it is shown the first moment of the spin structure function in the latter approach, assuming only the valence quarks contribution to the proton spin, does not contradict to the experimental data.