Quasi two-body scaling in inclusive nuclear reactions

The hypothesis of quasi two body scaling (qtbs) in inclusive inelastic scattering by nuclei is studied. By use of qtbs, a wide range of cross section data can be correlated in terms of a universal scaling function $G(k\sb{min})$ that depends on a scaling variable $k\sb{min}.$ The scaling variable is calculated from the kinematic variables of the scattering reaction. If qtbs applies, the inelastic cross section can be written as a product of the scaling function, a known kinematic factor, and a quasielastic cross section. The quasielastic cross section can be related to experimental elastic cross sections. Then the scaling function is calculated by dividing the inelastic cross section by the two known factors. Scaling for incident electrons and for incident protons is studied, and the extent to which qtbs is valid is compared for each case. A quantitative measure of goodness of scaling is introduced using analytical fits to the scaling function for different scattering cases. Also several tests of the specific assumptions that comprise the qtbs hypothesis are introduced, and applied to the various scattering cases. An integral sum rule is derived to test whether the scaling that is observed is truly a verification of qtbs. The sum rule is well satisfied, indicating that the observed scaling does verify qtbs. Our results show that scaling is relatively good for both incident electrons and protons, but the scaling is somewhat more universal for the electrons. The production of nucleon resonances is shown to be the cause of scaling violation for negative values of the scaling variable. The electron and proton scaling functions differ in their slope on a log plot. This is attributable to a larger probability of initial and final state interactions for protons, leading to an effective scaling function for the protons. The electron scaling function is related to the nucleon momentum distribution in the nucleus. This momentum distribution is found to be universal, except for a slightly smaller slope for Helium.