The inclusive production cross sections of the strange vector mesons K*0, K*0bar, and phi have been measured in interactions of 920 GeV protons with C, Ti, and W targets with the HERA-B detector at the HERA storage ring. Differential cross sections as a function of rapidity and transverse momentum have been measured in the central rapidity region and for transverse momenta up to pT=3.5 GeV/c. The atomic number dependence is parametrised as sigma(pA) = sigma(pN)*A**alpha, where sigma(pN) is the proton-nucleon cross section. Within the phase space accessible, alpha(K*0) = 0.86+/-0.03, alpha(K*0bar) = 0.87+/-0.03, and alpha(phi) = 0.96+/-0.02. The total proton-nucleon cross sections, determined by extrapolating the differential measurements to full phase space, are sigma(pN->K*0) = 5.06+/-0.54 mb, sigma(pN->K*0bar) = 4.02+/-0.45 mb, and sigma(pN->phi) = 1.17+/-0.11 mb. The Cronin effect is observed for the first time for vector mesons containing strange quarks; compared to the measurements of Cronin et al. for K+- mesons, the measured values of alpha for phi mesons coincide with those of K- mesons for all transverse momenta, while the enhancement for K*0 / K*0bar mesons is smaller.
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