$({}^6\mathrm{Li}, d)$ and $({}^6\mathrm{Li}, t)$ reactions on ${}^{22}\mathrm{Ne}$ and implications for $s$-process nucleosynthesis

We studied $\alpha$ cluster states in ${}^{26}\mathrm{Mg}$ via the ${}^{22}\mathrm{Ne}({}^6\mathrm{Li},d\gamma ){}^{26}\mathrm{Mg}$ reaction in inverse kinematics at an energy of 7 MeV/nucleon. States between $E_x$ = 4–14 MeV in ${}^{26}\mathrm{Mg}$ were populated and relative $\alpha$ spectroscopic factors were determined. Some of these states correspond to resonances in the Gamow window of the ${}^{22}\mathrm{Ne}(\alpha ,\mathrm{n})$${}^{25}\mathrm{Mg}$ reaction, which is one of the main neutron sources in the astrophysical $s$-process. Using our new ${}^{22}\mathrm{Ne}(\alpha ,\mathrm{n})$${}^{25}\mathrm{Mg}$ and ${}^{22}\mathrm{Ne}(\alpha ,\gamma ){}^{26}\mathrm{Mg}$ reaction rates, we performed new $s$-process calculations for massive stars and asymptotic giant branch stars and compared the resulting abundances with the abundances obtained using other ${}^{22}\mathrm{Ne}+\alpha$ rates from the literature. We observe an impact on the $s$-process abundances up to a factor of three for intermediate-mass AGB stars and up to a factor of ten for massive stars. Additionally, states in ${}^{25}\mathrm{Mg}$ at $E_x <$ 7.5 MeV are identified via the ${}^{22}\mathrm{Ne}({}^6\mathrm{Li},t){}^{25}\mathrm{Mg}$ reaction for the first time. We present the $({}^6\mathrm{Li}, t)$ spectroscopic factors of these states and note similarities to the $(d,p)$ reaction in terms of reaction selectivity.

Figure 1

Total photopeak efficiency (sum of efficiency by each clover), together with data obtained using some conventional $\gamma$ sources. Note the error bars are smaller than the symbol size.

Figure 2

(a) Energy versus scattering angle plot from ${}^{22}\mathrm{Ne}+{\mathrm{CD}}_2$. Theoretical elastic $(d,d)$ and $(d,p)$ ground state kinematic lines are shown together. The elastic $(p,p)$ line is because of contaminants in the target. (b) $E-\mathrm{\Delta }E$ plot from a Barrel detector, where protons, deuterons, tritons, and He are observed.

Figure 3

(a) Angular differential cross sections of ${}^{22}\mathrm{Ne}(d,p)$ reactions for populating low-lying states of ${}^{23}\mathrm{Ne}$. (b) Excitation spectra of ${}^{23}\mathrm{Ne}$ from the Hyball at ${\theta }_{\text{c.m.}}$ = ${\mathrm{5–12}}^{\circ }$ (whole detector). Inset: Barrel at ${\theta }_{\text{c.m.}}$ = ${\mathrm{18–19}}^{\circ }$.

Figure 4

$E_x$ versus hit position on the focal plane in the Oxford detector. All excitation energies are constructed from Hyball-detected light particle momenta, assuming the ${}^{22}\mathrm{Ne}({}^6\mathrm{Li},d)$ reaction. Right panel: gated on ${}^{26}\mathrm{Mg}$ recoil. Left panel: gated on ${}^{25}\mathrm{Mg}$ recoil. Clear correlations from the binary reactions $\left({}^6\mathrm{Li},d\right)$ and $\left({}^6\mathrm{Li},t\right)$ can be observed. In the ${}^{25}\mathrm{Mg}$ recoils, $\left({}^6\mathrm{Li},d\right)$ kinematic lines are spread in x-direction due to neutron evaporation. Transition from ${}^{26}\mathrm{Mg}$ to ${}^{25}\mathrm{Mg}$ is clearly occurring at the neutron separation energy of ${}^{26}\mathrm{Mg}$ (11.09 MeV).

Figure 5

${}^{25}\mathrm{Mg}$ excitation energy spectrum measured from the ${}^6\mathrm{Li}({}^{22}\mathrm{Ne},t){}^{25}\mathrm{Mg}$ reaction at ${\theta }_{\text{c.m.}}$ = $7^{\circ }$–${14}^{\circ }$.

Figure 6

Angular differential cross sections of ${}^{22}\mathrm{Ne}({}^6\mathrm{Li},t)$ reaction for populating various states of ${}^{25}\mathrm{Mg}$, compared with DWBA calculations. The excitation energies denoted on top of each panel are ${}^{25}\mathrm{Mg}$ excitation energies deduced from the spectra in Fig. 5. $J^{\pi }$ and energies in the legends are from Ref. [66].

Figure 7

${}^{26}\mathrm{Mg}$ excitation energy spectrum measured from the ${}^6\mathrm{Li}({}^{22}\mathrm{Ne},d){}^{26}\mathrm{Mg}$ reaction at ${\theta }_{\mathrm{c}.\mathrm{m}.}$ = $7^{\circ }$–${14}^{\circ }$. All states considered in the present data analysis are labeled in the figure. These states are mostly determined with the help of the coincident $\gamma$ rays and past $\left({}^6\mathrm{Li},d\right)$ experiments. The energies shown are adopted by comparing our measured energies with Table 4.

Figure 8

(a) $\gamma$-ray spectrum from ${}^{22}\mathrm{Ne}(d,p\gamma ){}^{23}\mathrm{Ne}$ reaction in coincidence with $E_x$ = GS to 5 MeV from the proton excitation-energy spectrum. (b) $\gamma$-ray spectrum from the ${}^{22}\mathrm{Ne}({}^6\mathrm{Li},d\gamma ){}^{26}\mathrm{Mg}$ reaction in coincidence with $E_x$ = 4–11.5 MeV. (c) $\gamma$-ray spectrum from the ${}^{22}\mathrm{Ne}({}^6\mathrm{Li},dn\gamma ){}^{25}\mathrm{Mg}$ reaction in coincidence with $E_x \left({}^{26}\mathrm{Mg}\right)$ = 11.0–14.0 MeV deuterons.

Figure 9

Angular differential cross sections of ${}^{22}\mathrm{Ne}({}^6\mathrm{Li},d)$ reactions for populating various states of ${}^{26}\mathrm{Mg}$, compared with DWBA calculations.

Figure 10

Coincident $({}^6\mathrm{Li},d) \gamma$-ray spectra, gated on specific excitation energy ranges in ${}^{26}\mathrm{Mg}$. Note the last two panels (the blue-shaded histogram) were obtained by gating on ${}^{25}\mathrm{Mg}$ recoils instead of ${}^{26}\mathrm{Mg}$. The vertical dotted lines indicate the energies of major transitions from the low-lying states in ${}^{26}\mathrm{Mg}$: (a) 1003, (b) 1129, (c) 1808, and (d) 2510/2523 keV, respectively [see Fig. 8]. The vertical lines indicate 389, 585, 974, and 1611 keV transitions [major transitions from the low-lying states in ${}^{25}\mathrm{Mg}$; see Fig. 8] in the last two panels.

Figure 11

Calculated $s$-process overproduction factors for the 3 and 5 $M_{\odot }$ stars using various available ${}^{22}\mathrm{Ne}(\alpha ,\mathrm{n})$ and ${}^{22}\mathrm{Ne}(\alpha ,\gamma )$ rates. See text for details. Isotopes of the same elements are connected by adjoining lines [some key $s$-process peak isotopes $({}^{88}\mathrm{Sr}, {}^{138}\mathrm{Ba}$, and ${}^{208}\mathrm{Pb})$ are labeled for clarification].

Figure 12

Calculated $s$-process overproduction factors for the 25 $M_{\odot }$ star using various available ${}^{22}\mathrm{Ne}(\alpha ,\mathrm{n})$ and ${}^{22}\mathrm{Ne}(\alpha ,\gamma )$ rates. See text for details. Isotopes of the same elements are connected by adjoining lines [some key $s$-process peak isotopes $({}^{88}\mathrm{Sr}, {}^{138}\mathrm{Ba}$, and ${}^{208}\mathrm{Pb})$ are labeled for clarification].

Figure 13

Calculated $s$-process overproduction factors using various available ${}^{22}\mathrm{Ne}(\alpha ,\mathrm{n})$ and ${}^{22}\mathrm{Ne}(\alpha ,\gamma )$ rates, for $s$-only nuclei. Top, middle, and bottom panels correspond to 3, 5, and 25 (in the middle of the C shell burning) $M_{\odot }$ cases, respectively. Note that the rate given by Massimi et al. [38] is their upper limit (see texts for details).

Figure 14

Ratios of calculated $s$-process abundances to TAMU abundances for the 3 and 5 $M_{\odot }$ stars (see Fig. 11) using ${}^{22}\mathrm{Ne}(\alpha ,\mathrm{n})$ and ${}^{22}\mathrm{Ne}(\alpha ,\gamma )$ rates in which strength of some resonances are changed. See text for details. Isotopes of the same elements are connected by adjoining lines [some key $s$-process peak isotopes $({}^{88}\mathrm{Sr}, {}^{138}\mathrm{Ba}$, and ${}^{208}\mathrm{Pb})$ are labeled for clarification].

Figure 15

Ratios of calculated $s$-process abundances to TAMU abundances for the 25 $M_{\odot }$ (see Fig. 12) using ${}^{22}\mathrm{Ne}(\alpha ,\mathrm{n})$ and ${}^{22}\mathrm{Ne}(\alpha ,\gamma )$ rates in which strength of some resonances are changed. See text for details. Isotopes of the same elements are connected by adjoining lines [some key $s$-process peak isotopes $({}^{88}\mathrm{Sr}, {}^{138}\mathrm{Ba}$, and ${}^{208}\mathrm{Pb})$ are labeled for clarification].

Figure 16

Calculated $s$-process abundance ratio to TAMU abundances for s-only nuclei (see Figs. 14 and 15) using ${}^{22}\mathrm{Ne}(\alpha ,\mathrm{n})$ and ${}^{22}\mathrm{Ne}(\alpha ,\gamma )$ rates in which strength of some resonances are changed. Top, middle, and bottom panels correspond to 3, 5, and 25 (in the middle of the C shell burning) $M_{\odot }$ cases, respectively.