Proton-proton elastic scattering has been measured by the TOTEM experiment at the CERN Large Hadron Collider at {surd}s = 7 TeV in dedicated runs with the Roman Pot detectors placed as close as seven times the transverse beam size (sbeam) from the outgoing beams. After careful study of the accelerator optics and the detector alignment, |t|, the square of four-momentum transferred in the elastic scattering process, has been determined with an uncertainty of d t = 0.1GeV p|t|. In this letter, first results of the differential cross section are presented covering a |t|-range from 0.36 to 2.5GeV2. The differential cross-section in the range 0.36 < |t| < 0.47 GeV2 is described by an exponential with a slope parameter B = (23.6{pm}0.5stat {pm}0.4syst)GeV-2, followed by a significant diffractive minimum at |t| = (0.53{pm}0.01stat{pm}0.01syst)GeV2. For |t|-values larger than ~ 1.5GeV2, the cross-section exhibits a power law behaviour with an exponent of -7.8_pm} 0.3stat{pm}0.1syst. When compared to predictions based on the different available models, the data show a strong discriminative power despite the small t-range covered.
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