Using new VLT/XShooter spectral observations we analyse the physical properties of five z~0.3-0.4 confirmed LyC leakers. Strong resonant MgII 2796,2803 emission lines (I(2796,2803)/I(Hbeta)=10-38 per cent) and non-resonant FeII* 2612,2626 emission lines are observed in spectra of five and three galaxies, respectively. We find high electron densities Ne~400cm-3, significantly higher than in typical low-z, but comparable to those measured in z~2-3 star-forming galaxies. The galaxies have a mean value of logN/O=-1.16, close to the maximum values found for star-forming (SF) galaxies in the metallicity range of 12+logO/H=7.7-8.1. All 11 low-z LyC emitting galaxies found by Izotov et al. (2016, 2018), including the ones considered in the present study, are characterised by high EW(Hbeta)~200-400A, high ionisation parameter (log(U)=-2.5 to -1.7), high average ionising photon production efficiency xi= 10^{25.54} Hz erg-1 and hard ionising radiation. On the BPT diagram we find the same offset of our leakers from low-$z$ main-sequence SFGs as that for local analogues of LBGs and extreme SF galaxies at z~2-3. We confirm the effectiveness of the HeI emission lines diagnostics proposed by Izotov et al. (2017) in searching for LyC leaker candidates and find that their intensity ratios correspond to those in a median with low neutral hydrogen column density N(HI)=10^{17}-5x10^{17} cm-2 that permit leakage of LyC radiation, likely due to their density-bounded HII regions.
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