Using luminosity distributions to determine luminosity in a collider with a coupled lattice

The traditional method for calculating luminosity in the Fermilab Tevatron during collider operations assumes a knowledge of the machine lattice at the locations of the flying wires and the luminous regions. In this paper we investigate an alternative method of determining the luminosity which does not require a knowledge of the lattice functions and can be applied even in the case of a transversely coupled lattice. By measuring a set of longitudinal luminosity distributions each with a different intentionally added separation between the proton and antiproton closed orbits the transverse widths of the luminous region can be determined and used to calculate the luminosity. As an example we apply this method to a set of Monte Carlo generated luminosity distributions using a Tevatron lattice that is transversely coupled due to a roll in one of the low beta quadrupole magnets