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Recently it has been shown that the gross structure of the bottomoniumspectrum is reproduced reasonably well within the non-relativistic boundstatetheory based on perturbative QCD. In that calculation, however, the finesplittings and the S-P level splittings are predicted to be considerablynarrower than the corresponding experimental values. We investigate thebottomonium spectrum within a specific framework based on perturbative QCD,which incorporates all the corrections up to O(alpha_S^5 m_b) and O(alpha_S^4m_b), respectively, in the computations of the fine splittings and the S-Psplittings. We find that the agreement with the experimental data for the finesplittings improves drastically due to an enhancement of the wave functionsclose to the origin as compared to the Coulomb wave functions. The agreement ofthe S-P splittings with the experimental data also becomes better. We find thatnatural scales of the fine splittings and the S-P splittings are larger thanthose of the boundstates themselves. On the other hand, the predictions of thelevel spacings between consecutive principal quantum numbers depend ratherstrongly on the scale mu of the operator \propto C_A/(m_b r^2). The agreementof the whole spectrum with the experimental data is much better than theprevious predictions when mu \simeq 3-4 GeV for alpha_S(M_Z)=0.1181. Thereseems to be a phenomenological preference for some suppression mechanism forthe above operator.Comment: 26 pages, 16 figures. Minor changes, to be published in PR

Improved perturbative QCD approach to the bottomonium spectrum