Stellar $β^{\pm}$ decay rates of iron isotopes and its implications in astrophysics

$β$-decay and positron decay are believed to play a consequential role during the late phases of stellar evolution of a massive star culminating in a supernova explosion. Recently the microscopic calculation of weak-interaction mediated rates on key isotopes of iron was introduced using the proton-neutron quasiparticle random phase approximation (pn-QRPA) theory with improved model parameters. Here I discuss in detail the improved calculation of $β^{\pm}$ decay rates for iron isotopes ($^{54,55,56}$Fe) in stellar environment. The pn-QRPA theory allows a microscopic "state-by-state" calculation of stellar rates as explained later in text. Excited state Gamow-Teller distributions are much different from ground state and a microscopic calculation of decay rates from these excited states greatly increases the reliability of the total decay rate calculation specially during the late stages of stellar evolution. The reported decay rates are also compared with earlier calculations. The positron decay rates are in reasonable agreement with the large-scale shell model calculation. The main finding of this work includes that the stellar $β$-decay rates of $^{54,55,56}$Fe are around 3 -- 5 orders of magnitude smaller than previously assumed and hence irrelevant for the determination of the evolution of $Y_{e}$ during the presupernova phase of massive stars. The current work discourages the inclusion of $^{55,56}$Fe in the list of key stellar $β$-decay nuclei as suggested by former simulation results.