Photoproduction with a Leading Proton at HERA 
Diffractive interactions, i.e. those in which the
scattering only takes place peripherally, have been of interest to experimentalists
and theorists for a long time. They have been studied both in hadron hadron
and in lepton hadron collisions. These processes are characterized by a
small momentum transfer, resulting in small scattering angles. The scattering
partners can each either stay intact or dissociate. In a Regge motivated
picture, the interaction is thought of as a tchannel exchange of particles.
Depending on the kinematic range, the type of the exchange varies.
At HERA, both real and virtual photons, emitted by a beam electron, can collide with a beam proton. The first is referred to as photoproduction, the latter as deep inelastic scattering (DIS). The photon and the proton may undergo the hadronic interaction mentioned. We distinguish cases where the elastically scattered proton retains almost all of its momentum (z=1) from those where it loses a substantial fraction (here: 1030%, such that 0.7<z<0.9).  This paper completes a set of investigations in the following
way:


The Process gamma p > Xp'

Kinematic Dependence of the Production Rate 

The differential cross section dsigma(W,z)/dz for gamma p > X p' is
shown in the adjacent figure. z varies between 0.878 and 0.683, which implies
that the proton lost a longitudinal momentum of 100 to 260 GeV in the collision
with the photon.
The production rate is found to be independent of W and z within experimental errors. The average value is 8.05 +/ 0.06(stat) +/ 0.89(syst) microbarn. The effective composition of the exchanges hence exhibit only a soft W and z dependence over the range studied. 

Quantitatively a fit based on a Regge inspired model gives a good representation of the data. In this model, the process is thought of as the exchange of an effective trajectory alpha_{i} between the photon and the proton. The total cross section for the interaction between alpha_{i} and the photon is modelled by the exchange of a further effective trajectory alpha_{k}. The fit results are the intercepts of the trajectories, alpha_{i}(0)=0.33 +/ 0.04(stat) +/ 0.04(syst) and alpha_{k}(0)=0.99 +/ 0.01(stat) +/ 0.05(syst), as well as an indirectly determined value for the slope parameter b describing the t dependence according to e^{bt}, b=6.6 +/ 0.7(stat) +/ 1.5(syst) GeV^{2} at z=0.78. This confirms previous findings that within the z range under study, reactions involving a pomeron are suppressed relative to those with pions and Reggeons. Additionally, the result for alpha_{k} is consistent with the scattering between the photon and alpha_{i} being mediated by Pomeron exchange, which is the dominant contribution at the center of mass energies of the alpha_{i}photon system reached here (32GeV < M_{X} < 130GeV). 
From Real to Virtual Photons
The validity of this simple picture has been investigated. The result is depicted in the adjacent figure. The fraction of all events per unit z that contain a leading proton, f_{LP}, has been studied as a function of Q^{2} to investigate the transition from real to virtual photons in bins of W for four values of z. Surprisingly this fraction rises with Q^{2}. 