The effects of ultra-strong magnetic fields on electron capture rates for iron group nuclei in the outer crust of magnetars

Based on the work of Wang et al. (Chin. Phys. Lett. 29:049701, 2012), we re-investigated electron capture on iron group nuclei in the outer crust of magnetars and studied magnetar evolution. Effects of ultra-strong magnetic field on electron capture rates for ⁵⁷Co have been analyzed in the nuclear shell model and under the Landau-level-quantization approximation, and the electron capture rates and the neutrino energy loss rates on iron group nuclei in the outer crust of magnetar have been calculated. The results show that electron capture rates on ⁵⁷Co are increase greatly in the ultra-strong magnetic field, and above 3 orders of magnitude generally; and the neutrino energy loss rates by electron capture on iron group nuclei increase above 3 orders of magnitude in the range from B=4.414×10¹³ G to B=4.414×10¹⁵ G. These conclusions play an important role in future studying the evolution of magnetar. Furthermore, we modify the expressions of the electron chemical potential (Fermi energy) and phase space factor by introducing Dirac δ-function, and select appropriate parameters of temperature T, magnetic field B and matter density ρ in the our crust, thus our results will be reliable than those of Wang et al.