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Electron capture of strongly screening nuclides $^{56}$Fe, $^{56}$Co, $^{56}$Ni , $^{56}$Mn ,$^{56}$Cr and $^{56}$V in presupernova

According to the Shell-Model Monte Carlo method, basing on the Random Phase Approximation and the linear response theory, we carried out an estimation on electron capture of strongly screening nuclides $^{56}$Fe, $^{56}$Co, $^{56}$Ni , $^{56}$Mn ,$^{56}$Cr and $^{56}$V in strong electron screening (SES)in presupernova. The EC rates are decreased greatly and even exceed $21.5\%$ in SES. We also compare our results with those of Aufderheide (AFUD), which calculated by the method of Aufderheide in SES. Our results are agreed reasonably well with AUFD at higher density-temperature surroundings (e.g. $ρ_7>60, T_9=15.40$) and the maximum error is $\sim $0.5$\%$. However, the maximum error is $\sim $13.0$\%$ at lower density surroundings (e.g. $^{56}$Cr at $ρ_7=10, T_9=15.40, Y_e=0.41$ ). On the other hand, we also compared our results in SES with those of FFN's and Nabi's, which is in the case without SES. The comparisons show that our results are lower more than one order magnitude than FFN's, but about $7.23\%$ than Nabi's.