The hyperfine splittings in heavy quarkonia are studied using new
experimental data on the di-electron widths. The smearing of the spin-spin
interaction is taken into account, while the radius of smearing is fixed by the
known J/ψ−ηc(1S) and ψ(2S)−ηc′(2S) splittings and appears to
be small, rss≈0.06 fm. Nevertheless, even with such a small radius
an essential suppression of the hyperfine splittings (∼50 is observed
in bottomonium. For the nSbbˉ states (n=1,2,...6) the values we
predict (in MeV) are 28, 12, 10, 6, 6, and 3, respectively. In single-channel
approximation for the 3S and 4S charmonium states the splittings 16(2) MeV
and 12(4) MeV are obtained.Comment: 13 pages, no figure