We investigated the pulsar radio luminosity(L),emission efficiency(ratio of radio luminosity to its spin-down power E),and death line in the magnetic field(B)versus spin period(P)diagram.We found that the dependence of pulsar radio luminosity on its spin-down power(L-E)is very weak,shown as L ～ E0.06,which deduces an equivalent inverse correlation between emission efficiency and spin-down power as ξ ～ E-0.94.Furthermore,we examined the distributions of radio luminosity of millisecond and normal pulsars and found that for the similar spin-down powers,the radio luminosity of millisecond pulsars is about one order of magnitude lower than that of the normal pulsars.The analysis of pulsar radio flux suggests that these correlations are not due to a selective effect but are intrinsic to the pulsar radio emission physics.Their radio radiations may be dominated by the different radiation mechanisms.The cut-off phenomenon of currently observed radio pulsars in B-P diagram is usually referred as the “pulsar death line”,which corresponds to E ≈ 1030ergs-1 and is obtained by the cut-off voltage of electron acceleration gap in the polar cap model of pulsar proposed by Ruderman and Sutherland.Observationally,this death line can be inferred by the actual observed pulsar flux S ≥ 1 mJy and 1 kpc distance,together with the maximum radio emission efficiency of 1％.However,the observation data show that the 37 pulsars pass over the death line,including the recently observed two pulsars with long periods of 23.5 s and 12.1 s,which violate the prediction of the polar cap model.At present,the actual observed pulsar flux can reach 0.01 mJy by FAST telescope.This will arise the observational limit of spin-down power of pulsars as low as E ≈ 1028ergs-1.This means that the new death line is downward shifted two orders of magnitude,which might be favorably referred as the “observational limit-line”.Accordingly,the pulsar theoretical model for the cut-off voltage of gap should be heavily modified.