A new insight into neutrino energy loss by electron capture of iron group nuclei in magnetar surfaces
Based on the relativistic mean-field effective interactions theory, and the Lai dong model, we discuss the influences of superstrong magnetic fields (SMFs) on electron Fermi energy, nuclear blinding energy, and single-particle level structure in magnetar surfaces. Using the Shell-Model Monte Carlo method and the Random Phase Approximation theory, we analyze the neutrino energy loss rates (NELRs) by electron capture for iron group nuclei in SMFs. First, when B {sub 12} < 100, we find that the SMFs have a slight influence on the NELRs for most nuclides at relativistic low temperatures (e.g., T {sub 9} = 0.233); nevertheless, the NELRs increase by more than four orders of magnitude at relativistic high temperatures (e.g., T {sub 9} = 15.53). When B {sub 12} > 100, the NELRs decrease by more than three orders of magnitude (e.g., at T {sub 9} = 15.53 for {sup 52–61}Fe, {sup 55–60}Co, and {sup 56–63}Ni). Second, for a certain value of magnetic field and temperature, the NELRs increase by more than four orders of magnitude when ρ{sub 7}⩽10{sup 3}, but as the density increases (i.e., when ρ{sub 7}>10{sup 3}), there is almost no influence on the density of NELRs. For the density around ρ{sub 7}=10{sup 2}, there is an abrupt increase in NELRs when B {sub 12} ≥ 10{sup 3.5}. Such jumps are an indication that the underlying shell structure has changed due to single-particle behavior by SMFs. Finally, we compare our NELRs with those of Fuller et al. (FFN) and Nabi and Klapdor-Kleingrothaus (NKK). For the case without SMFs, one finds that our rates for certain nuclei are close to about five orders of magnitude lower than FFN and NKK at relativistic low temperatures (e.g., T {sub 9} = 1). However, at a relativistic high temperature (e.g., T {sub 9} = 3), our results are in good agreement with NKK, but about one order of magnitude lower than FFN. For the case with SMFs, our NELRs for some iron group nuclei can be about five orders of magnitude higher than those of FFN and NKK. (Note that B {sub 12}, T {sub 9}, and ρ {sub 7} are in units of 10{sup 12} G, 10{sup 9} K, and 10{sup 7} g cm{sup −3}, respectively.)