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Electron capture on $^{20}$Ne is critically important for the final stage ofevolution of stars with the initial masses of 8 - 10 $M_{\odot}$. In thepresent paper, we evaluate electron capture rates for a forbidden transition$^{20}$Ne (0$_{g.s.}^{+}$) $\rightarrow$ $^{20}$F (2$_{g.s.}^{+}$) in stellarenvironments by the multipole expansion method with the use of shell-modelHamiltonians. These rates have not been accurately determined in theory as wellas in experiments. Our newly evaluated rates are compared with those obtainedby a prescription that treats the transition as an allowed Gamow-Teller (GT)transition with the strength determined from a recent $\beta$-decay experimentfor $^{20}$F (2$_{g.s.}^{+}$) $\rightarrow$ $^{20}$Ne (0$_{g.s.}^{+}$)\citep{Kirsebom}. We find that different electron energy dependence of thetransition strengths between the two methods leads to sizable differences inthe weak rates of the two methods. We also find that the Coulomb effects, thatis, the effects of screening on ions and electrons are non-negligible. We applyour e-capture rates on $^{20}$Ne to the calculation of the evolution ofhigh-density O-Ne-Mg cores of 8 - 10 $M_{\odot}$ stars. We find that our newrates affect the abundance distribution and the central density at the finalstage of evolution.

astrophysical journal/the astrophysical journal

Electron-capture Rates in $^{20}$Ne for a Forbidden Transition to the  Ground State of $^{20}$F Relevant to Final Evolution of High-density O-Ne-Mg  Cores