The Neutrino Energy Loss by Electron Capture of Nuclides ^{52,53,54,55,56}Fe in Core-Collapse Supernova

Using the shell-model Monte Carlo method and random phase approximation theory, we carry out an estimation on neutrino energy loss (NEL) of ^{52,53,54,55,56}Fe. We find the NEL rates increase greatly at some typical stellar conditions, and even exceed eight orders of magnitude. On the other hand, in order to compare our results of λ_{SMMC^LJ (which are calculated by using the SMMC method) with those of λFFN^LJ (which are calculated by using the Fuller-Fowler-Newman (FFN) method), the error factor C, between λSMMC^LJ and λFFN^LJ, is discussed and shows that at higher density and temperature, the fit is fairly good for the two results (λSMMC^LJ and λFFN^LJ), and the maximum error is ～6.20%. However, the maximum error is ～95.50% (e.g. ⁵³Fe) at lower density and temperature.}