Proton capture cross sections on neutron-magic ${}^{144}\text{Sm}$ at astrophysically relevant energies

Background: The $p$ nuclei, which are not produced by neutron capture processes, are present with a typical isotopic abundance of 0.01%–0.3%. Abundance decreases with an increase in atomic number. However, the neutron-magic isotopes of ${}^{92}\text{Mo}$ and ${}^{144}\text{Sm}$ exhibit unusually large abundances in comparison. A combination of proton and $\alpha$-particle capture reactions and neutron emission reactions are key to understanding this issue. Currently, complex network calculations do not have access to much experimental data, and hence require theoretically predicted reaction rates in order to estimate final abundances produced in nucleosynthesis.

Purpose: Few experimental cross sections of $(p$,γ) reactions on heavy nuclides with mass numbers of 130–150 have been reported. The ${}^{144}\text{Sm}(p,\gamma ){}^{145}\text{Eu}$ reaction is the main destruction pathway for the nucleosynthesis of the ${}^{144}\text{Sm}$ nuclide. In the present paper, experimental cross sections of the ${}^{144}\text{Sm}(p,\gamma ){}^{145}\text{Eu}$ reaction at a range including astrophysically relevant energies for the $p$ process were determined to compare with theoretical predictions using the Hauser-Feshback statistical model.

Methods: The ${}^{144}\text{Sm}$ was deposited on a high-purity Al foil with the molecular plating method. Stacks consisting of Ta degrader foils, ${}^{144}\text{Sm}$ targets, and Cu foils used as flux monitors were irradiated with 14.0-MeV proton beams. The ${}^{144}\text{Sm}(p,\gamma ){}^{145}\text{Eu}$ cross sections were determined from the ${}^{145}\text{Eu}$ activities and the proton fluence estimated from the ${}^{65}\text{Zn}$ activity in the Cu monitor foil. The proton energies bombarded on each ${}^{144}\text{Sm}$ target were estimated using srim2013.

Results: We determined the ${}^{144}\text{Sm}(p,\gamma ){}^{145}\text{Eu}$ cross sections at proton energies between 2.8 and 7.6 MeV. These energies encompass nucleosynthesis temperatures between 3 and 5 GK. The cross sections at energies higher than 3.8 MeV agreed well with theoretically predicted cross sections using talys using the generalized superfluid (GS) model for level densities. However, calculations using non-smoker overestimated the cross section. When the components of the energy uncertainties in the experimental cross sections were corrected, the cross sections at energies lower than 3.8 MeV showed comparable values with talys but higher than those predicted by both non-smoker and talys.

Conclusions: talys using the GS model reproduced well the experimental cross sections without correction of the proton widths at energies between 2.8 and 7.6 MeV. Thus, the reaction rates of ${}^{144}\text{Sm}(p,\gamma ){}^{145}\text{Eu}$ in the stellar environment at 2.5–5 GK estimated with talys corresponded with those by the experimental cross section within 10%. However, the reaction rates depended on the extrapolation of the cross section at energies of 0–2.8 MeV at temperatures of 0.5–2.5 GK. The reaction rate estimated by talys employing the GS model showed an uncertainty within a factor of 2 at 1.5–3.5 GK for nucleosynthesis temperatures of the $p$ nuclei.

Figure 1

Arrangement of the monitor and target stacks. The 20-μm-thick Al foil was not installed in target stack 1 but was placed between the first and the second ${}^{144}\text{Sm}$ target in target stack 2.

Figure 2

(a) $\gamma$-ray spectra of the Cu monitor foil and ${}^{144}\text{Sm}$ target in the monitor stack. (b) $\gamma$-ray spectra of the detector background (black line), ${}^{144}\text{Sm}$ targets activated by 5.4 MeV (blue line), and 2.8 MeV (red line) in the target stack.

Figure 3

The experimental cross sections and theoretical cross sections obtained using non-smoker and talys. $E_{\mathrm{th}\left(p,n\right)}$ denotes the threshold of the ${}^{144}\text{Sm}(p,n){}^{145}\text{Eu}$ reaction. The experimental cross sections corrected based on talys using the GS model are shown with an open circle. Regions of the Gamow peak covering 2σ (95%) of the area at temperatures between 1.5 and 5.0 GK are shown with arrows.

Figure 4

Sensitivity of the ${}^{144}\text{Sm}(p,\gamma ){}^{145}\text{Eu}$ reaction when the proton width, γ width, neutron width, and $\alpha$ width are separately changed by a factor of 2. The arrows indicate energy regions of the Gamow peak covering 2σ (95%) of the area. Resonance energies of ${}^{145}\text{Eu}$, equivalent to the sum of the $Q$ value of the ${}^{144}\text{Sm}(p,\gamma ){}^{145}\text{Eu}$ reaction and center-of-mass energy of the proton beams, are related to the incident energies.

Figure 5

The astrophysical $S$ factors of the ${}^{144}\text{Sm}(p,\gamma ){}^{145}\text{Eu}$ reaction calculated from the experimental cross sections and theoretical predictions using non-smoker and talys employing CTFG, BSFG, GS, and HT as a level-density model.

Figure 6

(a) The reaction rates estimated from the different extrapolations and theoretical predictions using non-smoker, talys, and reaclib. (b) Demonstration of the different fits used to extrapolate the measurement to lower energies and the $S$ factors of the ${}^{92}\text{Mo}(p,\gamma ){}^{93m+g}\mathrm{Tc}$ reaction multiplied by 100. In Fit 1, a constant value taken from the lowest datum is used; for Fit 2 an exponential form based on the higher energy data was assumed. See the text for a further discussion.

Figure 7

Ratios of the reaction rates using theoretical predictions using non-smoker, talys, and reaclib for the data estimated using two different extrapolations. The gray broken line indicates the ratio as 1.0.