It was found before that experimental $(\gamma, 1n)$, $(\gamma, 2n)$ and $(\gamma, 3n)$ reactions cross sections obtained for many nuclei using the beams of quasimonoenergetic annihilation photons and the method for photoneutron multiplicity sorting do not satisfy to objective physical criteria of data reliability. Using the experimental-theoretical method of evaluation the new data on partial and total photoneutron reaction cross sections satisfying the mentioned criteria were obtained. It was shown that in the majority of cases significant disagreements between evaluated and experimental cross sections are because presence of noticeable systematical uncertainties of the processes of identification of multiplicities of detected neutrons. The new kind uncertainties from the loss of many neutrons from $(\gamma, 1n)$ reaction were found out for several nuclei ($^{75}$As, $^{127}$I, $^{181}$Ta). The evaluation of reliable cross sections $\sigma(\gamma, 1n)$, $\sigma(\gamma, 2n)$, $\sigma(\gamma, 3n)$, $\sigma(\gamma, sn) = \sigma(\gamma, 1n) + \sigma (\gamma, 2n) + \sigma (\gamma, 3n)$ and $\sigma(\gamma, xn) = \sigma(\gamma, 1n) + 2\sigma (\gamma, 2n) + 3\sigma (\gamma, 3n)$ was done for $^{206,207}$Pb. It was shown that for both isotopes $^{206,207}$Pb as well as for $^{208}$Pb investigated before similar to $^{75}$As, $^{127}$I, $^{181}$Ta the competitions between various reactions cross sections testify to unreliability of experimental data.
$^1$Physics Department, M.V. Lomonosov Moscow State University, chair of General Nuclear Physics.\
$^2$Lomonosov Moscow State University, Skobeltsyn Institute of Nuclear Physics, Moskow 119991, Russia.