Thermonuclear ${}^{46}\mathbf{Cr}(p,\gamma ){}^{47}\mathbf{Mn}$ rate in type-I x-ray bursts

The thermonuclear rate of the ${}^{46}\mathrm{Cr}(p,\gamma ){}^{47}\mathrm{Mn}$ reaction has been determined using a newly evaluated proton separation energy of $S_p\left({}^{47}\mathrm{Mn}\right)=380\pm 30\mathrm{keV}$ and nuclear structure information from the mirror nucleus ${}^{47}\mathrm{Ti}$. The astrophysical impact of this new rate and previously available rates has been investigated through one-zone postprocessing type-I x-ray burst calculations. The present ${}^{46}\mathrm{Cr}(p,\gamma ){}^{47}\mathrm{Mn}$ rate leads to a mass fraction at $A=46$ that is 60 times larger than that obtained using a statistical model rate. The new results constrain the calculated maximum and minimum mass fractions at $A=46$ and $A=48$ to be within factors of 12 and 4, respectively. Experimental studies of the level structure of ${}^{47}\mathrm{Mn}$ near the proton threshold are required to improve these model predictions.

Figure 1

Percentage contributions of dominant resonances contributing more than 5% to the ${}^{46}\mathrm{Cr}(p,\gamma ){}^{47}\mathrm{Mn}$ resonant rate up to $T=2\mathrm{GK}$. See text for details.

Figure 2

Energy differences between (a) $T_z=1/2$ and (b) $T_z=1$ levels of mirror pairs over $A=41\text{–}74$ [45]. $E_x^{Z<}$ and $E_x^{Z>}$ denote the excitation energies for the members of the pair with lower and higher $Z$. Here, the rms energy differences are 103 and 87 keV (shown as the solid lines) for $T_z=1/2$ and 1 pairs, respectively.

Figure 3

The presently calculated ${}^{46}\mathrm{Cr}(p,\gamma ){}^{47}\mathrm{Mn}$ reaction rates (in units of ${\mathrm{cm}}^3{\mathrm{mol}}^{-1}{\mathrm{s}}^{-1}$). Here, the grey band indicates the upper and lower limits of the present total rate.

Figure 4

Ratios between the total ${}^{46}\mathrm{Cr}(p,\gamma ){}^{47}\mathrm{Mn}$ reaction rate from the present work and other rates available in JINA REACLIB [28]. The grey band indicates the upper and lower limits of the present rate.

Figure 5

Selected abundances (as mass fractions summed over mass number) following one-zone XRB calculations with the present and laur [26], nfis [30], rath [27], and ths8 [30] rates of ${}^{46}\mathrm{Cr}(p,\gamma ){}^{47}\mathrm{Mn}$. Abundances using lower and upper limits to the present rate (see Table 2) are indicated as error bars on the abundances using the present rate. Here, the present ($S_p=380\mathrm{keV}$) and laur ($S_p=470\mathrm{keV}$) rates are based on information from the mirror nucleus, the rath ($S_p=324\mathrm{keV}$) and ths8 ($S_p=477\mathrm{keV}$) rates are based on the statistical model, and the nfis ($S_p=477\mathrm{keV}$) rate is based on the shell model.