Re-examining the ${}^{26}\mathrm{Mg}(\alpha ,{\alpha }^{\prime }){}^{26}\mathrm{Mg}$ reaction: Probing astrophysically important states in ${}^{26}\mathrm{Mg}$

Background: The ${}^{22}\mathrm{Ne}$($\alpha ,n$)${}^{25}\mathrm{Mg}$ reaction is one of the neutron sources for the $s$ process in massive stars. The properties of levels in ${}^{26}\mathrm{Mg}$ above the $\alpha$-particle threshold control the strengths of the ${}^{22}\mathrm{Ne}$($\alpha ,n$)${}^{25}\mathrm{Mg}$ and ${}^{22}\mathrm{Ne}$($\alpha ,\gamma$)${}^{26}\mathrm{Mg}$ reactions. The strengths of these reactions as functions of temperature are one of the major uncertainties in the $s$ process.

Purpose: Information on the existence, spin, and parity of levels in ${}^{26}\mathrm{Mg}$ can assist in constraining the strengths of the ${}^{22}\mathrm{Ne}$($\alpha ,\gamma$)${}^{26}\mathrm{Mg}$ and ${}^{22}\mathrm{Ne}$($\alpha ,n$)${}^{25}\mathrm{Mg}$ reactions, and therefore in constraining $s$-process abundances.

Methods: Inelastically scattered $\alpha$ particles from a ${}^{26}\mathrm{Mg}$ target were momentum-analyzed in the K600 magnetic spectrometer at iThemba LABS, South Africa. The differential cross sections of states were deduced from the focal-plane trajectory of the scattered $\alpha$ particles. Based on the differential cross sections, spin and parity assignments to states are made.

Results: A newly assigned $0^{+}$ state was observed in addition to a number of other states, some of which can be associated with states observed in other experiments. Some of the deduced $J^{\pi }$ values of the states observed in the present study show discrepancies with those assigned in a similar experiment performed at RCNP Osaka. The reassignments and additions of the various states can strongly affect the reaction rate at low temperatures.

Conclusion: The number, location, and assignment of levels in ${}^{26}\mathrm{Mg}$ that may contribute to the ${}^{22}\mathrm{Ne}+\alpha$ reactions are not clear. Future experimental investigations of ${}^{26}\mathrm{Mg}$ must have an extremely good energy resolution to separate the contributions from different levels. Coincidence experiments of ${}^{26}\mathrm{Mg}$ provide a possible route for future investigations.

Figure 1

Excitation-energy spectra for the ${}^{26}\mathrm{Mg}$($\alpha ,{\alpha }^{\prime }$)${}^{26}\mathrm{Mg}$ reaction for the ${\theta }_{\mathrm{lab}}<2^{\circ }$ angle bite (top), $2^{\circ }<{\theta }_{\mathrm{lab}}<3^{\circ }$ (second), $3^{\circ }<{\theta }_{\mathrm{lab}}<4^{\circ }$ (middle), $4^{\circ }<{\theta }_{\mathrm{lab}}<5^{\circ }$ (fourth), and $5^{\circ }<{\theta }_{\mathrm{lab}}<6^{\circ }$ (bottom). The solid vertical lines are states with fixed energies, the dashed vertical lines are states without fixed energies, and the dotted lines show the positions of the $\alpha$-particle and neutron thresholds. The solid red line is the total fit and the dashed red lines are the contributions from individual peaks.

Figure 2

Excitation-energy spectra taken with the field setting that includes the elastic peak with the spectrometer aperture centered on $\theta =6^{\circ }$. The top spectrum is ${}^{26}\mathrm{Mg}$ data and the bottom spectrum is ${}^{24}\mathrm{Mg}$ data. The broad background up to around 9 MeV is due to $p(\alpha ,{\alpha }^{\prime })p$ reactions off water in the target.

Figure 3

Experimental differential cross sections for various states in ${}^{26}\mathrm{Mg}$. The states are labeled on the corresponding figure. The red solid lines are the angle-averaged DWBA differential cross sections for that particular state, normalized to the $0^{\circ }$ datum for $\ell =0$ transitions, and to the ${\theta }_{\text{c.m.}}=3–4^{\circ }$ degree datum for $\ell =1$ transitions. For more detailed discussions of the differential cross sections, consult the text.

Figure 4

Ratio of the new to old median rates. For details of the calculation inputs, see the text. The black curve is the ratio with a $J^{\pi }=2^{+}$ assumption for the 10.89-MeV state while the red curve is the calculation assuming a $J^{\pi }=3^{-}$ assignment.

Figure 5

Same as Fig. 4 except for the ratios of the upper limits of the rates.