$\beta$-decay rate of ${}^{59}\mathrm{Fe}$ in shell burning environment and its influence on the production of ${}^{60}\mathrm{Fe}$ in a massive star

We deduced the stellar $\beta$-decay rate of ${}^{59}\mathrm{Fe}$ at typical carbon-shell burning temperature by taking the experimental Gamow-Teller transition strengths of the ${}^{59}\mathrm{Fe}$ excited states. The result is also compared with those derived from large-scale shell model calculations. The new rate is up to a factor of 2.5 lower than the theoretical rate of Fuller, Fowler, and Newman (FFN) and up to a factor of 5 higher than decay rate of Langanke and Martínez-Pinedo (LMP) in the temperature region $0.5\le T\le 2$ GK. We estimated the impact of the newly determined rate on the synthesis of cosmic $\gamma$ emitter ${}^{60}\mathrm{Fe}$ in C-shell burning and explosive C/Ne burning using a one-zone model calculation. Our results show that ${}^{59}\mathrm{Fe}$ stellar $\beta$ decay plays an important role in ${}^{60}\mathrm{Fe}$ nucleosynthesis, even though the uncertainty of the decay rate is rather large due to the error of $B$(GT) strengths.

Figure 1

The stellar $\beta$ decay of ${}^{59}\mathrm{Fe}$. The red lines represent the allowed transitions to the ground state of ${}^{59}\mathrm{Co}$ while the black lines indicate the allowed transition to the excited states of ${}^{59}\mathrm{Co}$.

Figure 2

The experimental and shell model energy levels up to 1 MeV of ${}^{59}\mathrm{Fe}$. The two dubious states (613 and 642 keV) excluded in the present work are shown with shaded marks.

Figure 3

(a) The stellar $\beta$-decay rate of ${}^{59}\mathrm{Fe}$ as a function of temperature. The shaded area represents the uncertainty incurred by the experimental $B$(GT) values. FFN and LMP rates are plotted with dotted and dashed lines, respectively. Shell model calculations based on GXPF1a and GXPF1j interactions are also plotted with solid and dash-dotted lines. (b) The $\beta$-decay rates contributed by various transitions of ${}^{59}\mathrm{Fe}\to {}^{59}\mathrm{Co}$ as a function of temperature. The red line represents the dominant transition ${}^{59}\mathrm{Fe}$ ($472\mathrm{keV})\to {}^{59}\mathrm{Co}$ (g.s.), while the shaded area represents the uncertainty due to the experimental $B$(GT) error. The ground state decay and other allowed transitions are presented with dashed and solid lines, respectively.

Figure 4

The impact on ${}^{59}\mathrm{Fe}$ stellar $\beta$-decay rate from various uncertainties. Dotted lines represent the uncertainty due to the experiment data error of $B$(GT). The rates with empirical $\log ft=4.9$ and $\log ft$ = infinity are presented with dashed and solid lines, respectively. Shell model calculations with GXPF1a and GXPF1j interactions for other transitions are plotted with short-dashed and dash-dotted lines, respectively.

Figure 5

(a) The alternative mapping of the shell model calculation with 571 keV assigned to $5/2^{-}$. The mappings with two dubious sates (613 and 643 keV) are shown with dotted lines. (b) The relative decay rates with alternative assignment of shell model energy levels of ${}^{59}\mathrm{Fe}$. Shell model calculations with 571 keV assigned to $5/2^{-}$ for GXPF1a and GXPF1j interactions, and with two additional dubious states for GXPF1a and GXPF1j interactions, are plotted with dotted, solid, dash-dotted and dashed lines, respectively.

Figure 6

Net current chart of ${}^{60}\mathrm{Fe}$ nucleosynthesis in C-shell burning. The red lines present $\beta$ decay, while the black lines present the nuclear reactions such as $(n,\gamma )$ and $(p,n)$. Line width indicates the flow current in logarithmic scale.

Figure 7

Relative ${}^{60}\mathrm{Fe}$ abundances in the C-shell burning scenario calculated respectively with terrestrial rate, FFN rate, LMP rate, GXPF1a rate, GXPF1j rate, and our rate for ${}^{59}\mathrm{Fe}\beta$ decay. The results have been normalized by the ${}^{60}\mathrm{Fe}$ abundances obtained with the terrestrial ${}^{59}\mathrm{Fe}$ rate. The ${}^{60}\mathrm{Fe}$ abundance obtained with our rate based on charge exchange data is shown as a red diamond. The ${}^{60}\mathrm{Fe}$ abundance uncertainty incurred by ${}^{59}\mathrm{Fe}\left(n,\gamma \right)$ is shown for comparison.

Figure 8

Net current chart of ${}^{60}\mathrm{Fe}$ nucleosynthesis in explosive burning.