A $6.8 \ {\rm nb^{-1}}$ sample of $pp$ collision data collected under low-luminosity conditions at $\sqrt{s} = 7$ TeV by the ATLAS detector at the Large Hadron Collider is used to study diffractive dijet production. Events containing at least two jets with $p_\mathrm{T} > 20$ GeV are selected and analysed in terms of variables which discriminate between diffractive and non-diffractive processes. Cross sections are measured differentially in $\Delta\eta^F$, the size of the observable forward region of pseudorapidity which is devoid of hadronic activity, and in an estimator, $\tilde{\xi}$, of the fractional momentum loss of the proton assuming single diffractive dissociation ($pp \rightarrow pX$). Model comparisons indicate a dominant non-diffractive contribution up to moderately large $\Delta\eta^F$ and small $\tilde{\xi}$, with a diffractive contribution which is significant at the highest $\Delta\eta^F$ and the lowest $\tilde{\xi}$. The rapidity-gap survival probability is estimated from comparisons of the data in this latter region with predictions based on diffractive parton distribution functions.
The cross section differential in the forward rapidity gap size, DELTA(C=RAPGAP), for events with at least two jets of pt > 20 GeV found by the anti-kt jet algorithm with R=0.6.
The cross section differential in the forward rapidity gap size, DELTA(C=RAPGAP), for events with at least two jets of pt > 20 GeV found by the anti-kt jet algorithm with R=0.4.
The cross section differential in the fraction of the proton four-momentum carried by the Pomeron, LOG10(C=XI), for events with at least two jets of pt > 20 GeV found by the anti-kt jet algorithm with R=0.6.
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