Recently by dielectric spectroscopy a new secondary relaxation process in polyisobutylene (PIB) was detected showing all the signatures of a Johari-Goldstein relaxation [Richter, D; Arbe, A.; Colmenero, J.; Monkenbusch, M.; Farago, B.; Faust, R. Macromolecules 1998, 31, 1133]. Using high resolution neutron backscattering, we investigated the quasielastic neutron spectra from protonated PIB which are related to this process as a function of momentum transfer and temperature. In addition we studied the elastically scattered intensity over a wide temperature range. After multiple scattering corrections all results can be described consistently in terms of a local jump process with the distribution parameters from the dielectric beta-relaxation. The spatial extent of the associated protonic motion was determined to be d = 2.7 Å. A comparison with the existing body of data for PIB leads to the conclusion that the dielectric beta-process and the earlier found delta-process must be identical, thereby revising the assignment of the delta-process as due to methyl group rotation. Finally, we remark on aspects of the relation between quasielastic coherent and incoherent scattering and address the seemingly contradictory result of different length scales revealed for the same process with the two techniques.