Experimental study of ${}^{38}\mathrm{Ar}+\alpha$ reaction cross sections relevant to the ${}^{41}\mathrm{Ca}$ abundance in the solar system

In massive stars, the ${}^{41}\mathrm{Ca}(n,\alpha ){}^{38}\mathrm{Ar}$ and ${}^{41}\mathrm{K}(p,\alpha ){}^{38}\mathrm{Ar}$ reactions have been identified as the key reactions governing the abundance of ${}^{41}\mathrm{Ca}$, which is considered as a potential chronometer for solar system formation. So far, due to experimental limitations, the ${}^{41}\mathrm{Ca}(n,\alpha ){}^{38}\mathrm{Ar}$ reaction rate is solely based on statistical model calculations. In the present study, we have measured the time-inverse ${}^{38}\mathrm{Ar}(\alpha ,n){}^{41}\mathrm{Ca}$ and ${}^{38}\mathrm{Ar}(\alpha ,p){}^{41}\mathrm{K}$ reactions using an active target detector. The reactions were studied in inverse kinematics using a 133-MeV ${}^{38}\mathrm{Ar}$ beam and ${}^4\mathrm{He}$ as the active-gas target. Both excitation functions were measured simultaneously in the energy range of $6.8\le E_{\mathrm{c}.\mathrm{m}.}\le 9.3$ MeV. Using detailed balance the ${}^{41}\mathrm{Ca}(n,\alpha ){}^{38}\mathrm{Ar}$ and ${}^{41}\mathrm{K}(p,\alpha ){}^{38}\mathrm{Ar}$ reaction rates were determined, which suggested a 20% increase in the ${}^{41}\mathrm{Ca}$ yield from massive stars.

Figure 1

Schematic of the asymmetric segmentation of the anode strips 1–16 inside the MUSIC detector. The black line shows the ${}^{38}\mathrm{Ar}$ beam going through the center of the detector and the red and blue lines (solid and dashed, respectively) show the outgoing reaction particles for a reaction occurring in strip 5.

Figure 2

The top panel (a) shows the $\mathrm{\Delta }E$ signals measured over 16 strips of the MUSIC detector from ${}^{38}\mathrm{Ar}(\alpha ,n){}^{41}\mathrm{Ca}$ (blue), ${}^{38}\mathrm{Ar}(\alpha ,p){}^{41}\mathrm{K}$ (red), and ${}^{38}\mathrm{Ar}(\alpha ,{\alpha }^{\prime }){}^{38}\mathrm{Ar}^{*}$ (green) reactions occurring in strip 5, along with the beam (black). The $\mathrm{\Delta }E$ values of all strips have been normalized to the $\mathrm{\Delta }E$ value in strip 0. The bottom panel (b) is the same as (a), but averaged over four consecutive strips (${\mathrm{Av}}_4$).

Figure 3

Two-dimensional plot of $\mathrm{\Delta }E$ values for events occurring in strip 5 averaged over ten (${\mathrm{Av}}_{10}$) and nine strips (${\mathrm{Av}}_9$), respectively, to improve the separation between events corresponding to the ${}^{38}\mathrm{Ar}(\alpha ,{\alpha }^{\prime }){}^{38}{\mathrm{Ar}}^{*}$, ${}^{38}\mathrm{Ar}(\alpha ,p){}^{41}\mathrm{K}$, and ${}^{38}\mathrm{Ar}(\alpha ,n){}^{41}\mathrm{Ca}$ reactions.

Figure 4

One-dimensional projection of $\mathrm{\Delta }E$ values for events occurring in strip 5 averaged over ten consecutive strips (${\mathrm{Av}}_{10}$) highlighting three peaks corresponding to events from ($\alpha ,{\alpha }^{\prime }$), ($\alpha ,p$), and ($\alpha ,n$) reactions on ${}^{38}\mathrm{Ar}$. The red curve represents the total fit to the spectrum and the black dashed lines represent the individual Gaussian fits to each peak.

Figure 5

Excitation functions of the ${}^{38}\mathrm{Ar}(\alpha ,n){}^{41}\mathrm{Ca}$ (blue circles) and ${}^{38}\mathrm{Ar}(\alpha ,p){}^{41}\mathrm{K}$ (red circles) reactions determined in the present study in comparison with the statistical-model calculations: talys default (dotted lines) and best-fit calculation (dashed lines, see Sec. 3).

Figure 6

Comparison of reaction rates $N_A〈\sigma v〉$ for the (a) ${}^{41}\mathrm{K}$($p,\alpha$)${}^{38}\mathrm{Ar}$ and (b) ${}^{41}\mathrm{Ca}$($n,\alpha$)${}^{38}\mathrm{Ar}$ reactions. The rates of Sevior et al. [24] from their original fit and from a later fit in REACLIB (usually referred to as “SM86”) are normalized to the new recommended rate. The gray-shaded uncertainties are discussed at the end of Sec. 4a. Note the different scale factors in the top and the bottom panels. See text for further discussion.

Figure 7

Final ${}^{41}\mathrm{Ca}$ mass fraction as a function of interior mass coordinate one year after the 1.0 B explosion of presupernova model s28a28 from Ref. [41] for the indicated reaction networks.

Figure 8

Time evolution of the ${}^{41}\mathrm{Ca}$ mass fraction in zone 284 during the 1.0 B explosion of pre-supernova model s25a28 from Ref. [41] for the indicated reaction networks.

Figure 9

Integrated currents for zone 284 after the 1.0 B explosion of pre-supernova model s25a28 from Ref. [41] for the REACLIB V2.0 reaction network updated with the rates of this work.

Figure 10

Integrated current differences between the REACLIB V2.0 reaction network and REACLIB V2.0 reaction network updated with the rates of this work for zone 284 after the 1.0 B explosion of pre-supernova model s25a28 from Ref. [41]. As discussed in the text, the strength of an arrow in this figure represents how much greater the integrated current is in the calculation with the updated reaction rates than in the calculation with the default reaction rate set (REACLIB V2.0 only). A reversed arrow relative to the integrated current graph (Fig. 9) indicates the integrated current from the default reaction rate set is greater than in the calculation with the default set updated with our new reaction rates.