Photon diffractive dissociation, #gamma#p#->#Xp, has been studied at HERA with the ZEUS detector using ep interactions where the virtuality Q"2 of the exchanged photon is smaller than 0.02 GeV"2. The squared four-momentum t exchanged at the proton vertex was determined in the range 0.073 < vertical stroke t vertical stroke < 0.40 GeV"2 by measuring the scattered proton in the ZEUS leading proton spectrometer. In the photon-proton centre-of-mass energy interval 176<W<225 GeV and for masses of the dissociated photon system 4<M_X<32 GeV, the t distribution has an exponential shape, dN/d vertical stroke t vertical stroke #propor to#exp(-b vertical stroke t vertical stroke), with a slope parameter b=6.8#+-#0.9(stat.)_-_1_._1"+"1"."2(syst.) GeV"-"2. (orig.)Available from TIB Hannover: RA 2999(97-238) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman