We have discovered with XMM-Newton an X-ray source in the core of the globular cluster M13, whose X-ray spectral properties suggest that it is a quiescent neutron star X-ray binary. The spectrum can be well fitted with a pure hydrogen atmosphere model, with T=76 +/- 3 eV, R=12.8 +/- 0.4 km and an X-ray luminosity of 7.3 +/- 0.6 x 10^{32} erg/s. In the light of this result, we have discovered a strong correlation between the stellar encounter rate and the number of quiescent neutron stars found in the ten globular clusters observed so far by either XMM-Newton or Chandra. This result lends strong support to the idea that these systems are primarily produced by stellar encounters in the core of globular clusters.
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