High-precision $(p,t)$ reaction measurement to determine ${}^{18}\mathrm{Ne}(\alpha ,p){}^{21}\mathrm{Na}$ reaction rates

x-ray bursts are identified as thermonuclear explosions in the outer atmosphere of accreting neutron stars. The thermonuclear runaway is fueled by the $\alpha p$ process that describes a sequence of $(\alpha ,p)$ reactions triggered by the ${}^{18}\mathrm{Ne}(\alpha ,p){}^{21}\mathrm{Na}$ breakout reaction from the hot CNO cycles. We studied the level structure of the compound nucleus ${}^{22}\mathrm{Mg}$ by measuring the ${}^{24}\mathrm{Mg}(p,t){}^{22}\mathrm{Mg}$ reaction at the Grand Raiden spectrometer at Research Center for Nuclear Physics, Osaka. A large number of $\alpha$-unbound states was identified and precise excitation energies were determined. Based on shell model and $\alpha$-cluster model calculations we predict the level parameters for determining the stellar reaction rate of ${}^{18}\mathrm{Ne}(\alpha ,p){}^{21}\mathrm{Na}$ for a wide temperature range. x-ray burst simulations have been performed to study the impact of the reaction on the x-ray burst luminosity.

Figure 1

The measured ${}^{24}\mathrm{Mg}(p,t){}^{22}$Mg spectra at $8^{°}$ and 98.7 MeV incident proton energy are shown at three magnetic-field settings, B1, B2, and B3.

Figure 2

The spectrum of the ${}^{24}\mathrm{Mg}$($p,t){}^{22}$Mg reaction measured at 98.7 MeV incident energy and the magnetic-field setting B1 is shown. Excited states used in the calibration are marked by their excitation energies in MeV.

Figure 3

These ${}^{24}\mathrm{Mg}(p,t){}^{22}$Mg spectra show the low-lying states. They were taken at 98.7 MeV incident energy and at spectrometer angles −${0.3}^{ˆ},8^{°}$, and ${17}^{°}$. The calibration lines are marked by an asterisk.

Figure 4

The ${}^{22}\mathrm{Mg}$ spectra measured above the proton-emission threshold. All ${}^{12}\mathrm{C}(p,t){}^{10}$C and ${}^{16}\mathrm{O}(p,t){}^{14}$O contaminant peaks have been subtracted. The determined excitation energies for ${}^{22}\mathrm{Mg}$ are listed in the third column of Table . For an expanded view of the multipet of the four states between 7.027 and 7.079 MeV, see Fig. 11.

Figure 5

The ${}^{22}\mathrm{Mg}$ spectra above the $\alpha$-emission threshold. The energy for each peak is marked in the specific spectrum, where it was determined at $-0.3^{°},8^{°}$, or ${17}^{°}$. All ${}^{12}\mathrm{C}(p,t){}^{10}$C and ${}^{16}\mathrm{O}(p,t){}^{14}$O contaminant peaks were subtracted. The excitation energies determined for ${}^{22}\mathrm{Mg}$ are listed in the second column of Table .

Figure 6

The ${}^{24}\mathrm{Mg}(p,t){}^{22}$Mg spectrum above 10.5 MeV, measured at the scattering angle of ${17}^{°}$. The excitation energies determined for ${}^{22}\mathrm{Mg}$ are listed in the second column of Table .

Figure 7

The ${}^{22}\mathrm{Mg}$ mirror assignments for states below the proton-emission threshold are shown. The ${}^{22}\mathrm{Mg}$ spin-parity assignments are taken from previous experiments [30, 35] as shown in detail in Table . The spin-parity values of the mirror nucleus ${}^{22}\mathrm{Ne}$ are taken from Ref. [35].

Figure 8

The ${}^{22}\mathrm{Mg}$ mirror assignments for states between 5 MeV and the $\alpha$-emission threshold at 8.140 MeV. For details, see text.

Figure 9

Mirror spin-parity assignments for the ${}^{22}\mathrm{Mg}$ levels above the $\alpha$-emission threshold. The excitation-energy and spin-parity values marked by the superscript T are from shell-model calculations, Ref. [36]. Level energies for ${}^{22}\mathrm{Ne}$ were taken from Ref. [35]. The spin-parity value labeled a is from Ref. [13]. The excitation energies labeled b are from Ref. [32].

Figure 10

Spin-parity assignments for the ${}^{22}\mathrm{Mg}$ levels above 10.5 MeV. Assignments marked by a $\#$ were taken from Ref. [37]. For further details, see text.

Figure 11

Expanded view of the multiplet of four states between 7.027 and 7.079 MeV in the ${}^{22}\mathrm{Mg}$ spectra shown in Fig. 4. The fitted curve (solid line) consists of the the sum of four Gaussian peaks and a constant background (dashed lines).

Figure 12

Shown are cross-section angular distributions of six states in ${}^{22}\mathrm{Mg}$ labeled by their excitation energies in units of MeV. The measured data points at three angles are connected by solid lines to guide the eye. Statistical errors are smaller than the data points. The dotted curves represent DWBA calculations. The spin parities of the three states in the upper panels are well known. For a discussion of the spin parities of the group of three states around 6 MeV; see text.

Figure 13

Spectrum of the ${}^{24}\mathrm{Mg}(p,t){}^{22}$Mg reaction taken at an angle of $-0.3^{°}$ with fits to the five resolved levels between 8.5 and 8.8 MeV. The dashed line is the sum of the individual peaks shown as solid lines and a constant background of two counts. The excitation energies determined for ${}^{22}\mathrm{Mg}$ are listed in the second column of Table .

Figure 14

The ${}^{18}\mathrm{Ne}(\alpha ,p){}^{21}$Na reaction rates calculated as a function of temperature. The different curves indicate reaction rates calculated by Chen et al. [18], Bradfield et al. [21], Groombridge et al. [22], Görres et al. [13], as well as the one calculated in the present work with ${\mathrm{S}}_{\alpha }$ values from those references.

Figure 15

The two luminosity curves have been calculated on the basis of the previously published reaction rate (GW95) [13] and the present rate (GU07). The difference between the two curves demonstrates the impact of the modified ${}^{18}\mathrm{Ne}$($\alpha ,p){}^{21}$Na reaction rate on the light curve of a type I x-ray burst calculated in the framework of a spherically symmetric model [9, 11].