Head-on and long-range beam-beam tune shift spread in the SSC

The head-on and long-range incoherent tune shifts for the Superconducting Super Collider (SSC) are estimated using the numerical integration of the analytical expression coming from the first order in the perturbation strength. The variation of the tune shift as a function of the displacements of the charged particle in the vertical and horizontal planes is studied with the nominal parameters for the SSC. A scaling expression is obtained for the parameters involved in the beam-beam tune shifts, which allows us to predict the effect in the incoherent tune shift spread under changes in these parameters