Indirect measurement of the 57.7 keV resonance strength for the astrophysical $\gamma$-ray source of the ${}^{25}\mathrm{Mg}(p,\gamma ){}^{26}\mathrm{Al}$ reaction

${}^{25}\mathrm{Mg}(p,\gamma ){}^{26}\mathrm{Al}$ is the most important reaction in the Mg-Al cycle in the hydrogen burning regions of stars. Its cross sections at stellar energies are essential to understand the issues of radioactive ${}^{26}\mathrm{Al}$ in the galaxy and meteorites. The 57.7 keV resonance dominate the ${}^{25}\mathrm{Mg}(p,\gamma ){}^{26}\mathrm{Al}$ astrophysical reaction rates at relative low temperature, but it is very difficult to measure its resonance strength directly, and the indirect measurement results deviate by a factor of about 2 by far. In this work, the angular distributions of ${}^{25}\mathrm{Mg}({}^7\mathrm{Li},{}^6\mathrm{He}){}^{26}\mathrm{Al}$ leading to 6.364 MeV and eleven low-lying states in ${}^{26}\mathrm{Al}$ have been measured by the Q3D magnetic spectrometer of the HI-13 tandem accelerator. The spectroscopic factors were derived and used to deduce the proton width and 57.7 keV resonance strength. The astrophysical ${}^{25}\mathrm{Mg}(p,\gamma ){}^{26}\mathrm{Al}$ reaction rates at stellar energies have been updated by using the present result.

Figure 1

The spectra of the (${}^7\mathrm{Li},{}^6\mathrm{He}$) reaction for ${}^{25}\mathrm{Mg}$ and ${}^{24}\mathrm{Mg}$ targets at ${\theta }_{\mathrm{lab}}={12}^{\circ }$, $0\text{–}10$ represent the ground and first ten excited states in ${}^{26}\mathrm{Al}$.

Figure 2

Angular distributions for present ${}^{25}\mathrm{Mg}({}^7\mathrm{Li},{}^7\mathrm{Li}){}^{25}\mathrm{Mg}$ at $E\left({}^7\mathrm{Li}\right)=31.5$ MeV and earlier ${}^{27}\mathrm{Al}({}^6\mathrm{Li},{}^6\mathrm{Li}){}^{27}\mathrm{Al}$ at $E\left({}^6\mathrm{Li}\right)=18$ MeV [29] are donated as solid and open circles together with the DWBA fitting results in different lines.

Figure 3

Measured angular distributions of ${}^{25}\mathrm{Mg}({}^7\mathrm{Li},{}^6\mathrm{He}){}^{26}\mathrm{Al}$ transfer reactions together with the DWBA calculations in using the corresponding sets of optical potential parameters for the entrance and exit channels, respectively.

Figure 4

Calculated angular distributions of ${}^{25}\mathrm{Mg}({}^7\mathrm{Li},{}^6\mathrm{He}){}^{26}\mathrm{Al}$ leading to $J^{\pi }=3^{+}$ states with the excitation energies range from 6.0 to 6.3 MeV in energy step of 50 keV.

Figure 5

Angular distributions of ${}^{25}\mathrm{Mg}({}^3\mathrm{He}$, $d){}^{26}\mathrm{Al}^{*}$ at three energies [7, 13, 14] together with corresponding DWBA calculations. Three types of the lines are the angular distributions calculated with one set of the optical potential parameters for the entrance channel and three sets for the exit channel included in twofnr code.

Figure 6

The present total astrophysical reaction rates and major components of ${}^{25}\mathrm{Mg}(p,\gamma ){}^{26}\mathrm{Al}$ in $\pm 1\sigma$ confidence intervals, together with the corresponding proportions of these resonances in the total.

Figure 7

Comparison between the present recommended reaction rates of ${}^{25}\mathrm{Mg}(p,\gamma ){}^{26}\mathrm{Al}$ and those reported by NACRE [44], Iliadis et al. [42] and Straniero et al. [20] in dashed and dotted lines, respectively. The grid, dotted, shaded, and slash areas represent the corresponding $\pm 1\sigma$ uncertainties of the present and the other works, respectively.