The photoproduction of the bottomonium-like states
and
via
scattering is studied within an effective Lagrangian approach and the vector-meson-dominance model. The Regge model is employed to calculate the photoproduction of
states via the t-channel with
exchange. The numerical results show that the values of the total cross-sections of
and
can reach 0.09 nb and 0.02 nb, respectively, near the center-of-mass energy of 22 GeV. Experimental measurements and studies of the photoproduction of
states near the energy region around
GeV are suggested. Moreover, with the help of eSTARlight and STARlight programs, we have obtained the cross-sections and numbers of events for
production in electron-ion collisions (EIC) and ultraperipheral collisions (UPCs). The results show that a considerable number of
events can be produced in the relevant experiments on EICs and UPCs. We have also calculated the rates and kinematic distributions for
in
and
collisions via EICs and UPCs. The results will provide an important reference for the RHIC, LHC, EIC-US, LHeC, and FCC experiments in searching for bottomonium-like
states.
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